Naval Surface Warfare Center Carderock Division

Transcription

1 a a r. r. C 3 0 Naval Srface Warfare Center Carderock Division & West Bethesda, Maryland X NSWCCD-50-TR-2011/012 Febrary 2011 g Hydromechanics Department Report r3 OJ a < i _J Characterization of Reglar Wave, Irreglar Wave, and Large-Amplitde Wave Grop Kinematics in an Experimental Basin d U > r3 By Lisa M. Minnick Christopher C. Bassler Scott Percival g Laren W. Hanyok J > sd J3 ~B so <+o a o ed 'C * i J XJ U IN e 35 H o O "^BL^HftS+J^1 U Approved for pblic release; distribtion is nlimited. Z CQ

2 I REPORT DOCUMENTATION PAGE Form Approved OMB No Iiblic reporting brden (or this collection of information is estimated to average 1 hor per response, inclding the time for reviewing instrctions, searching existing data sorces gathering and maintaining the data leded, and completing and reviewing this collection of information Send comments regarding this brden estimate or any other aspect of this collection of information, inclding sggestions for redcing this brden to Department of Defense. Washington Headqarters Services. Directorate for Information Operations and Reports ( ) Jefferson Davis Highway, Site Arlington, VA Respondents shold be aware thai notwithstanding any other provision of law. no person shall be sbject to any penalty for failing to comply with a collection of information if it does not display a crrently valid OMB control nmbei EASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS REPORT DATE (DD/MM/YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To) f Fi nal l-ag dec TITLE AND SUBTITLE 5a. CONTRACT NUMBER Iharacterization of Reglar Wave, Irreglar Wave, and Largemplitde Wave Grop Kinematics in an Experimental Basin 6. AUTHOR(S) Lisa M. Minnick, Christopher C. Bassler, Scott Percival, Laren W. Hanyok 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) AND ADDRESS(ES) I aval Srface Warfare Center arderock Division 9500 Macarthr Bolevard I est Bethesda, MD SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) James S. Webster I aval Sea Systems Command EA 05D1 Washington Navy Yard ashington, DC t DISTRIBUTION / AVAILABILITY STATEMENT pproved for pblic release; distribtion is nlimited. 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER N 5d. PROJECT NUMBER and 5c. TASK NUMBER 5f. WORK UNIT NUMBER i 8. PERFORMING ORGANIZATION REPORT NUMBER NSWCCTJ-50-1 I : ' SPONSOR/MONITOR'S ACRONYM(S) NAVSEA 05D1 11. SPONSOR/MONITOR'S REPORT NUMBER(S) 13. SUPPLEMENTARY NOTES ABSTRACT An experiment was performed to measre and characterize wave kinematics in the Manevering and Seakeeping fvlask.) basin at the Naval Srface Warfare Center Carderock Division (NSWCCD). The experiment is part of an ngoing effort to improve predictions and measrements of ship motions in waves, inclding more accrate characterization of the near-field wave environment and its inflence on ship motions. The primary objective of this Ixperiment was to measre and characterize the wave kinematics of reglar waves of varying steepness and scaled reglar seaways, inclding irreglar waves with embedded wave grops. Measrements, inclding free-srface elevations and velocity field measrements nder the free srface, are presented and discssed. I I SUBJECT TERMS eglar Waves, Irreglar Waves, Wave Grops, Particle Image Velocimetry, ministic Mode] esting, Extreme Waves, Roge Waves, Dynamic Stability, Slamming 16. SECURITY CLASSIFICATION OF: REPORT UNCLASSIFIED I I b. ABSTRACT UNCLASSIFIED c. THIS PAGE UNCLASSIFIED 17. LIMITATION OF ABSTRACT UL 18. NUMBER OF PAGES 86 19a. NAME OF RESPONSIBLE PERSON Christopher C. Bassler 19b. TELEPHONE NUMBER (inclde area code) { 30 \)

3 CONTENTS ABSTRACT 1 ADMINISTRATIVE INFORMATION 1 ACKNOWLEDGEMENTS 1 BACKGROUND 3 EXPERIMENTAL APPROACH 6 Facility Description 6 Test Description 8 Wave Generation Method 9 Experimental Set-Up 10 Wave-Maker Operation 12 Reglar Waves 12 Irreglar Waves 13 Irreglar Waves with Embedded Grops 13 INSTRUMENTATION 13 Velocity Field Measrements 13 Camera 14 Lasers 14 PIV Data Acqisition 15 Flow Tracer Particles 15 Wave Srface Elevation Measrements 15 Video 15 INSTRUMENT CALIBRATION AND UNCERTAINTY 15 Senix Ultrasonic Wave Probes 15 Calibration and Uncertainty 16 Particle Image Velocimetry 19 Calibration 19 Uncertainty 19 VELOCITY FIELD MEASUREMENTS AND DATA PROCESSING 25 RESULTS 27 Wave Srface Elevation Measrements 27 Reglar Waves 29 Irreglar Waves with Embedded Wave Grops 39 i

4 Hrricane Camille 39 Bretschneider Sea State 8 47 CONCLUSIONS AND RECOMMENDATIONS 51 REFERENCES 53 APPENDIX A: REGULAR WAVE TIME HISTORIES APPENDIX B: WAVE THEORY Linear Wave Theory Stokes 2 nd Order Wave Theory APPENDIX C: IRREGULAR WAVE TIME HISTORIES Hrricane Camille Bretschneider Sea State 8 (BS -SS8) 4

5 FIGURES Figre 1. Schematic of the MASK basin with bridge monted wave probes 7 Figre 2. Illstration of the experimental set-p in the MASK basin, inclding PIV instrmentation and seeding mechanism 12 Figre 3. Schematic of interrogation windows and PIV evalation method 14 Figre 4. Calibration of Senix wave gage #1 17 Figre 5. Relative calibration ncertainty of Senix wave gage #1 18 Figre 6. Calibration image (A) and dewarped image with mapping fnction (B) shown in red 19 Figre 7. Plot of the relative error in velocity magnitde for reglar waves with I 50 wave steepness 22 Figre 8. Plot of the relative error in velocity magnitde for reglar waves with 1/30 wave steepness 23 Figre 9. Plot of the relative error in velocity magnitde for reglar waves with 115 wave steepness 23 Figre 10. Plot of the relative error in velocity vector angle for reglar waves with I 50 wave steepness 24 Figre 11. Plot of the relative error in velocity vector angle for reglar waves with 1/30 wave steepness 24 Figre 12. Plot of the relative error in velocity vector angle for reglar waves with 115 wave steepness 25 Figre 13. Raw (A) and masked (B) PIV images with particle seeding in the wave-field below the free srface 26 Figre 14. Example of a processed PIV image showing calclated velocity vectors (in yellow) for reglar waves, H/>.= l/30; for clarity, only every 4th vector is shown. 26 Figre 15. Reglar wave, 1/15 steepness, free srface elevation time-history from MASK basin wave probe 3 (black dots), PIV free srface interpolation (green line) 28 Figre 16. Irreglar wave with embedded wave grop, BS-SS8, free srface elevation time-history from MASK basin wave probe 3 (black dots) and free srface data from PIV images (green line) 29 Figre 17. Reglar wave, 1/50 steepness, free srface elevation time-history from MASK basin wave probe 3 (black dots), PIV free srface interpolation (black lines), with comparisons to linear (red sqares) and 2nd-order Stokes (green triangles) wave theory predictions 30 Figre 18. Reglar wave, 1/30 steepness, free srface elevation time-history from MASK basin wave probe 3 (black dots), PIV free srface interpolation (black lines), with comparisons to linear (red sqares) and 2nd-order Stokes (green triangles) wave theory predictions 31 in

6 Figre 19. Reglar wave, 1/15 steepness, free srface elevation time-history from MASK basin wave probe 3 (black dots), PIV free srface interpolation (black lines), with comparisons to linear (red sqares) and 2nd-order Stokes (green triangles) wave theory predictions 31 Figre 20. Free srface data of the reglar waves, 1/15. MASK basin wave probe 3 (black dots) and free srface data from PIV images (black and colored lines) 33 Figre 21. Theoretical and measred (for wave locations A-I) velocity profiles for reglar waves, 1/50 34 Figre 22. Theoretical and measred (for wave locations A-I) velocity profiles for reglar waves, 1/30 34 Figre 23. Theoretical and measred (for wave locations A-I) velocity profiles for reglar waves, 1/15 35 Figre 24. Total velocity contors for reglar waves, 1/50 wave steepness 35 Figre 25. Total velocity contors for reglar waves, 1/30 wave steepness 36 Figre 26. Total velocity contors for reglar waves, 1/15 wave steepness 36 Figre 27. Undistorted plot of three wave crests of reglar wave condition, 1/15 wave steepness 37 Figre 28. Undistorted plot of close-p of one wave crest for reglar wave condition, 1/15 wave steepness 37 Figre 29. Hrricane Camille realizations with embedded wave grops. The red tracing indicates a wave grop 40 Figre 30. Velocity contor plot with total velocity vectors for wave grop 42 embedded in a 30 lh scale Hrricane Camille spectrm, distorted 43 Figre 31. Velocity contor plot with total velocity vectors for wave grop 43 embedded in a 30 lh scale Hrricane Camille spectrm, distorted 43 Figre 32. Velocity contor plots with total velocity vectors for wave grop 42 and wave grop Figre 33. Velocity contor plot with total velocity vectors for wave grop 42 embedded in a 30 th scale Hrricane Camille spectrm, ndistorted 45 Figre 34. Velocity contor plot with total velocity vectors for wave grop 43 embedded in a 30 th scale Hrricane Camille spectrm ndistorted 45 Figre 35. Time history from wave height probe 3 of 30* scale Hrricane Camille realization with no embedded grops 46 Figre 36. Velocity contor plot with total velocity vectors for a 30 lh scale Hrricane Camille spectrm withot an embedded grop, distorted 46 Figre 37. Velocity contor plots with total velocity vectors for wave grop 42 and wave grop IV

7 Figre 38. BS-SS8 realizations with embedded wave grops. The red tracing indicates a wave grop 48 Figre 39. Velocity contor plot with total velocity vectors for wave grop 37 embedded in a BS-SS8 spectrm 49 Figre 40. Velocity contor plot with total velocity vectors for wave grop 38 embedded in a BS-SS8 spectrm 4 C > Appendix A Figre Al. Time histories for 1/50 wave steepness A-1 Figre A2. Time histories for 1/30 wave steepness \-2 Figre A3. Time histories for 1/15 wave steepness A-3 Appendix C Figre Cl. Hrricane Camille, 30 Scale, wave grop 42 C-l Figre C2. Hrricane Camille, 30" Scale, wave grop 43 C-2 Figre C3. Hrricane Camille, 30 lh Scale, wave grop 44 C-3 Figre C4. BS-SS8. wave grop 37 C-4 Figre C5. BS-SS8, wave grop 38 C-5

8 TABLES Table 1. Location of waveheight probes, measred from sothwest corner of the basin... 8 Table 2. Smmary of irreglar wave with embedded grop conditions 9 Table 3. Wave-maker parameters for reglar waves 12 Table 4. Smmary of Senix Wave Gage Calibrations 18 Table 5. Smmary of relative error, standard deviation, and RMS vales 22 Table 6. Reglar wave rns 29 Table 7. Smmary of irreglar wave conditions 39 VI

9 NOMENCLATURE A wavelength.v horizontal axis; positive in the direction of wave propagation z depth, calm water free srface at z=(), positive above the free srface V re f erence reference velocity, based on nominal specified wavelength V\ x velocity component V z z velocity component Vtotai total velocity (x and z components) H wave height H/X wave steepness rj free srface elevation tjn wave amplitde A- wave nmber; k=2n/x g gravity c wave celerity 0 wave phase angle h water depth Hs significant wave height Tm modal period co wave freqency At PIV time step between sccessive P1V images in an image pair <p relative error in velocity vector direction VII

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11 ABSTRACT An experiment was performed to measre and characterize wave kinematics in the Manevering and Seakeeping (MASK) basin at the Naval Srface Warfare Center Carderock Division (NSWCCD). The experiment is part of an ongoing effort to improve predictions and measrements of ship motions in waves, inclding more accrate characterization of the near-field wave environment and its inflence on ship motions. The primary objective of this experiment was to measre and characterize the wave kinematics of reglar waves of varying steepness and scaled irreglar seaways, inclding irreglar waves with embedded wave grops. Measrements, inclding free-srface elevations and velocity field measrements nder the free srface, are presented and discssed. ADMINISTRATIVE INFORMATION The work described in this report was performed by the Seakeeping Division (Code 5500) and the Manevering and Control Division (5600) of the Hydromechanics Department at the Naval Srface Warfare Center, Carderock Division (NSWCCD). The work was fnded by NAVSEA 05D1, as part of the SETA Environmental Modeling for Motions and Loads Task (Program Element N) in FY09 (Work Unit ). Additional spport for the data analysis and reporting was provided by the Naval Innovative Science and Engineering Program at NSWCCD (Program Element N) in FY10 (Work Unit ). nder the direction of Dr. John Barkyomb. ACKNOWLEDGEMENTS The athors wold like to thank Dr. Paisan Atsavapranee and Dr. David Drazen for their discssions and gidance on particle image velocimetry techniqes; Ryan Dean (NAVSEA 05D) for his assistance with the seeding mechanism design and assembly, and with the experimental set-p and testing; and Dan Hayden for his gidance with the Senix calibrations. The athors also appreciate Donnie Walker's assistance with integration of the MASK carriage data acqisition system. The athors wold like to thank Anthony Lopez and Tim Hertzfeld for their assistance with wave generation in the MASK basin, and Kiho Chm, Dennis Ralston, and Bob Sarbacker for their valable assistance dring the experimental set-p. The athors also greatly appreciate the helpfl discssions and comments on the content of this report from Martin J. Dipper and Dr. Arthr Reed.

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13 BACKGROUND The largest waves and wave grops in a seaway represent the most challenging environmental conditions for a srface ship. These severe wave conditions mst be considered for the assessment of ship performance, inclding seakeeping, dynamic stability, slamming and secondary loads, and ltimate strctral strength. Severe stability events, or even capsizing, may reslt from several initial rare events, inclding single nsally high, steep, and possibly breaking waves, as well as seqences, or grops, of large waves which expose a ship to dangeros conditions. Althogh not as well docmented as single large wave events, eye-witness acconts have been made of ships experiencing wave grops, typically consisting of three large waves (Schman, 1980; Bckley, 1983, 2005; Smith, 2006). These large-amplitde wave grops are often formed in developing seaways or by intersecting storms (Bckley. 1 *->S3; Toffoli, et al., 2004; Onorato, et al., 2006). The maritime accident investigation of the Norwegian Dawn indicated that the vessel had encontered three large waves in sccession (NTSB, 2005; Broad, 2006). A statistical comparison between reglar wave grops and large-amplitde wave grops showed the largest wave is typically accompanied by two or three large waves and the probability of the largest wave occrring in a grop is higher than for reglar large waves (Goda, 1976). Additional characteristics of large-amplitde wave grops inclde the grop period being longer than for reglar wave grops. The narrowing of the spectral bandwidth for a seaway reslts in an increase in wave gropiness (S, ei al. 1982; S, 1986; Y and Li, 1990). This spectral narrowing often occrs in a fetchlimited growing sea (Longet-Higgins, 1976), where large-amplitde wave grops wold most likely occr. S (1986) sggested a wave grop with one or more extremely large waves wold provide a better environmental design scenario than a single extreme wave or a reglar wave grop. Philips (1994) also expressed the need to develop a spatially-temporally defined extreme wave grop for ship design. To predict rare response events, wave grops can present a scenario of higher probability for extreme response than a single large-amplitde wave. The "problem of rarity" is encontered when the time between events is long compared to the wave period (Belenky, et al., 2008; 2010). For both experiments and simlations, deterministic grops of large-amplitde waves can be applied to overcome the problem of rarity by indcing realistic severe conditions for large roll motions, stability failre, or strctral failre at a known time and location (Bassler, et al., 2008; 2009; 2010; 2010a). Tools have been developed for ship design where wave grops are sed to indce a specific ship motion response. This approach was discssed by Blocki (1980) and Tikka and Palling (1990) to stdy parametric roll, sing wave grops to indce parametric excitation. Additional stdies of the applications of wave grops to parametric roll response have been made by Bokhanovsky and Degtyarev (1996) and Spyro (2004). Alford has sed a design wave train method to prodce a desired motion response (Alford, et al., 2006, 2007; Alford, 2008). Themelis and Spyro ( ) deterministically predicted the reqired critical wave grops to indce instability for a ship. Then the probability of encontering one of these critical wave grops was

14 compted for a given rote and dration. Using this critical wave grop method, instabilities were assessed inclding synchronos and parametric resonance, as well as pre loss of stability. A techniqe to identify "worst sea" and "best sea" conditions for an offshore floating strctre was applied by Fernandes, et al. (2008). This techniqe sed both envelope and atocorrelation fnction approaches to determine the highest and smallest wave grops from a spectrm. However, theoretical and nmerical models to assess srface ship dynamic stability and secondary loads performance, specifically in severe seas, are not yet flly matre. For the near ftre, model experiments may contine to be the primary method to evalate srface ship dynamic stability and secondary loads in severe waves. However, once simlation tools are flly developed, model experiments will remain a necessary method to Verify and Validate (V&V) nmerical predictions (AIAA, 1998). An important consideration for validation is the accracy of comparison between the nmerical and experimental realizations of these rare events. Model experiments to assess dynamic stability and secondary loads (slamming) performance are crrently performed sing two methods, testing in reglar waves or irreglar waves. Reglar waves, often with wave length close to ship length, are commonly sed to provide an initial assessment of ship response in critical wave conditions, for a range of wave steepness. Reglar waves are easier to prodce experimentally and can also be sed to compare directly to simlation reslts. However, reglar waves are not a realistic representation of the operating environment for a ship, and may also reslt in an overly conservative assessment of stability and strctral performance. Irreglar wave testing can be difficlt becase very long rn times are needed to ensre extreme events with low probability of occrrence are realized, inclding large waves or wave grops. Becase of the temporal and spatial limitations of the basin, it is impractical to ensre the extreme events are realized. In addition, de to their random natre, ship response in irreglar wave conditions is difficlt to compare between experiment and simlation, or even between realizations. The first approach to redce the nmber of reqired tests for reglar wave seakeeping was the transient wave techniqe, developed analytically by Davis and Zarnick (1964). At the David Taylor Model Basin, Davis and Zarnick, and Gersten and Johnson (1969) applied the transient wave techniqe to reglar wave model experiments for heave and pitch, at zero forward speed. These tests demonstrated a potential redction by an order of magnitde of the total necessary testing time. The transient wave techniqe was also applied to model testing in Japan in the mid-1970s (Takezawa and Takekawa, 1976; Takezawa and Hirayama, 1976). Class and Bergmann (1986), Class and Kehnlein (1994, 1995), and Matos, et al. (2005) sed a transient wave techniqe with Gassian wave-packets to excite model ships and offshore strctres in an experimental basin. Frther revisions to this techniqe inclded sing nonlinear transient wave trains and modified wave celerity to generate extreme waves (Class, 1999). Transient waves have even been proposed for se as part of a wave-maker calibration procedre (Masterton and Swan, 2008). Model tests have been performed with large transient waves, embedded in both reglar and random wave trains. These waves were calclated both linearly and nonlinearly, with empirically-based terms for the particle orbital motion and shallow-water effects (Class and Hennig,

15 2002). Experimentally, single extreme waves have been shown to have larger asymmetry than fll-scale storm waves, bt with a profile more similar to real extreme waves than second-order nmerical simlations (Antao and Gedes Soares, 2008). To generate desired deterministic wave seqences in the experimental basin, techniqes where singlar extreme waves were embedded in irreglar seas with a linear wave theory "first approach," and then optimized sing a flly nonlinear approach have been investigated (Class, 2000; Class, 2002a; Class and Schmittner. 2005). Experiments sing a modified "New Year Wave" have been condcted to assess both motions and strctral response for floating offshore strctres (Class, et al.. 200S). Model tests, to indce extreme roll and capsize for a ship, mst consider wave characteristics sch as wave height and steepness, wave gropiness, and the velocity and direction of wave propagation (Class and Hennig, 2004). "Nmerical wave tanks" have also been developed for the deterministic analysis of ocean strctre behavior in simlated single extreme waves (Class, et al., 2005; Ning. et al., 2008). Schmittner, et al. (2010) sed a nmerical wave tank to predict wave time traces measred in a wave basin. One nmerical tank applies potential flow codes for fast comptations and RANS codes to model breaking waves and flid-strctre interaction (Class, et al., 2005). Some agreement exists between comptations and experiments, with potential flow and RANS sed either separately, or copled. However, wave heights are shown to be generally over-predicted in a nmerical wave tank. Extreme waves simlated in nmerical tanks have also been applied to predict strctral loading on ships (Gedes Soares, et al., 2008) and offshore strctres (Class, 2002b). However, loads predictions have been shown to vary widely, depending on the wave kinematics model employed for the evalation (Sclavonos, 2005; Stansberg, et al ). models considered inclded second-order (Bitner-Gregersen and Hagen. 2004), Gre's method (Gre, et al., 2003), or the well-known Wheeler stretching method (Wheeler. 1969). Some comparisons between nmerical predictions and extreme wave model experiments were also performed by Hennig, et al. (2006). Improved nderstanding of the wave kinematics of large steep waves is also essential to the ship stability problem. Comparisons between the wave environment in nmerical predictions and experimental and fll-scale measrements are often made sing only wave elevations. Becase of the sensitivity of the ship response to the wave kinematics model sed in nmerical simlations it is important to determine the accracy of the varios wave models commonly employed. Particlarly for panel-based methods, an accrate representation of the velocity field, and sbseqent pressre field, below the free srface, is essential to characterizing the ship motion response correctly. Several approaches have been ndertaken to improve the nmerical modeling of wave kinematics (Fenton, 1985). The velocity field for a deep-water Stokes wave was obtained nmerically by Longet-Higgins (2008). A flly-nonlinear three-dimensional method differentiating the srface displacement was sed to calclate the horizontal orbital velocities of the measred moderate amplitde waves (Gre, et al., 2008). Some comparisons between wave kinematics nmerical predictions and experimental measrements were also made by Graw (1994), Stansberg, et al. (1996), Gre and Jensen (2006), Hennig, et al. (2006), and Class (2008). Skjelbreia et al., ( ) performed an extensive series of laboratory experiments to measre reglar and irreglar

16 wave kinematics sing Laser Doppler Velocimetry (LDV). Particle Image Velocity (PIV) techniqes have also been sed to measre wave-field kinematics. Gre, et al. (2003), measred the velocity profiles of 62 steep wave events and Choi (2005) sed both LDV and PIV to measre the wave velocities of reglar, irreglar, and extreme waves. PIV has also been sed to measre both the velocities and accelerations of wave events (Gre and Jensen, 2006; Jensen, et al., 2001; Jensen and Pedersen, 2004). Kristiansen et al (2005) explored the ability to se PIV as a tool for validation and verification of nmerical wave kinematics. Swan, et al. (2002) determined that empirical corrections for the flid particle kinematics in a linear random wave model did not accrately predict experimentally measred nonlinear wave loads on cylindrical strctres piercing the free srface. This reslt demonstrated the inflence and sensitivity of the flid particle kinematics model for predicting nonlinear wave loads. Given these considerations, this technical report details an experiment and sbseqent analysis performed in FY09 and FY10, as part of a contined effort at NSWCCD to improve predictions and measrement of ship motions in waves and assess the dynamic stability and seakeeping performance of naval ships. Model experiments, sch as the one described in this report are necessary to increase nderstanding of the principal physics governing dynamic stability events, and to provide validation data for the development of simlation tools. This experiment employed particle image velocimetry (PIV) techniqes to obtain a data set of the vector field below the free srface for reglar waves of varying steepness and realizations of irreglar seaways both with and withot embedded wave grops of large amplitde. This data will be sed to provide additional physical insight and validation data for wave kinematics models of moderate and steep reglar waves, and irreglar waves, inclding realizations of irreglar seaways with large-amplitde wave grops. Facility Description EXPERIMENTAL APPROACH This experiment was condcted in the Manevering and Seakeeping (MASK) basin at NSWCCD (Figre 1). Eight pnematic wave-maker nits are located along the 73m (240 ft) west side of the basin and thirteen nits along the 110m (360 ft) north side of the basin. The basin is 6m (20 ft) deep. A 115m (376 ft) bridge traverses the basin and can be moved p to a 45-degree offset from the longitdinal center of the basin. The two perpendiclar banks of wave-makers can be operated individally to prodce longcrested waves, or simltaneosly to generate a bi-directional wave-field. Sloping, perforated, concrete beaches are located on each side of the basin opposite the wavemakers to minimize wave reflections. Two methods are sed to control the flow of energy into the wave-field: varying blower motor speeds spplying air to the pnematic domes and varying the motion amplitde of the flapper valve that controls the air pmped in and ot of the domes. Hydralic cylinders with a ± 10V control signal are employed to actate the flapper valves. The control signal is generated sing a compter system and the digitized voltage signal is filtered with a low-pass smoothing filter and a high-pass ctoff freqency prior

17 to inpt to the wave-maker. The wave-maker also has a series of lips on each of the pnematic domes, which can be set in a position of either p or down, to modify high freqency distrbances in the generated wave-field. For these experiments, the MASK bridge was located in the middle of the basin, parallel to the north bank of wave-makers. In this configration, the locations of the sonic probes are given in Table 1, measred from the soth-west corner of the basin. T»WH«Tre* EliVAlON StCTWK viiw A A Of MANEUVm>W> lasfl W1IIK TKrNCM rioith H»<n c«?«tn- 6 T:.naiinm ' "" """ ' ' Bnd.*»*t 8 f.i-.l Figre 1. Schematic of the MASK basin with bridge monted wave probes.

18 Table 1. Location of waveheight probes, measred from sothwest corner of the basin. Test Description Gage Name Location x (m) Location y (m) Bridge Wave Ht # Bridge Wave Ht # Bridge Wave Ht # Bridge Wave Ht # Bridge Wave Ht # Bridge Wave Ht # The primary objectives of this experiment were to: (1) characterize the kinematics of reglar waves by examining the inflence of wave steepness on the velocity profile and (2) characterize the kinematics of irreglar waves with embedded wave grops by examining the effect of the wave grop composition, location, and scaling. Secondary objectives were to: (1) identify the inflence of the embedded wave grops on the generated spectral shape, (2) provide comparisons of wave height measrements obtained from the ltrasonic wave height probes and PIV images, and (3) provide a validation data set for wave theory and nmerical simlation tool development. Reglar waves with steepness of 1/50, 1/30, and 1/15 and a constant wavelength of 4.81m were examined. Wave steepness 1/30 was tested previosly with the ONR Topside Series hll form (DTMB Model 5613, 32nd-scale), as reported in Bishop, et al. (2005). The 1/50 wave steepness tested in this experiment was near the 1/60 tested in Bishop, et al. (2005). The third reglar wave steepness (1/15) corresponds to the steepest reglar wave that typically can be consistently generated sing the MASK basin pnematic wave-makers and also can be measred by the Senix probes withot freqent measrement drop-ots. Reglar waves were sed to examine the inflence of wave steepness on the velocity field below the free srface, and to provide comparisons between moderate to steep reglar waves and a large-amplitde wave grop in an irreglar seaway. Irreglar wave conditions inclded 30th and 46th scale realizations of Hrricane Camille and a 30th scale Bretschneider Sea State 8 (BS-SS8) spectra, and inclded realizations both with and withot embedded wave grops. These irreglar seas conditions were previosly sed (Bassler, et al., 2008) to examine the feasibility of prodcing deterministic large-amplitde wave grops in the MASK basin. The two scales considered in this stdy represent nominal scale ratios for ship model testing at NSWCCD to assess ship performance for seakeeping and dynamic stability, as well as strctral loads. A smmary of the irreglar wave conditions inclding significant wave height and modal period is provided in Table 2. Three different wave grops were embedded in the Hrricane Camille spectrm and are denoted as grops 42, 43, and 44. All three grops occr at the same location in the

19 wave train. The composition of wave grops 42 and 44 are the same, while 43 varies slightly. Wave grop 44 is a scaled version of 43. Similarly, two different wave grops were embedded in the BS-SS8 spectrm and are denoted as 37 and 38. The composition of the wave grops is identical; however, wave grop 37 occrs near the end of the wave train while wave grop 38 occrs close to the middle. Table 2. Smmary of irreglar wave with embedded grop conditions. Condition Hs inches Hs mm Tm sec Wave Generation Method Camille 30th Scale Camille 30th Camille 30th Camille 46th Scale Camille 46th BS-SS8 BS BS The conditions smmarized in Table 2 consist of deterministic irreglar waves with large amplitde wave grops embedded in seaway realizations. These conditions were generated following the previos method of Bassler, et al. (2008; 2009). In this method serial sperposition is tilized to combine wave trains of variable periods, amplitdes, and cycles into larger or smaller amplitde waves, by either constrctive or destrctive interference. The nderlying principles of this method are the deep-water dispersion relation and phase velocity, which dictate that longer waves propagate faster than shorter ones. At the pstream position, a series of waves with varied amplitde and periods are generated by a wave-maker. As wave components propagate downstream, lower freqency components coalesce with the higher freqency components and increasingly larger waves are formed. The waves coalesce at a desired, repeatable location in the basin to prodce a large grop dring a given wave realization. In general, larger waves can be prodced with increased distance between the wave-maker and concentration position. The wave grops for this experiment were generated sing for finite-wave seqences reslting in a three-wave grop occrring at a single location in the MASK basin. The composition of the grop can be changed by varying the individal finite-wave amplitdes and periods. Linear wave theory is applied to calclate the grop velocity and reglar wave grops were calclated to coalesce at a determined concentration position. The wavemaker controller seqence files for wave generation were determined sing eqations I- 6. T Start time for nth reglar wave train: t fl =? + - T n {Cyc B - l) (I) Hydralic cylinder voltage for /7th wave train at time /:

20 V{t)=H H cos '~'»- T '/4 (2) x T Time for the nth reglar wave to reach test point: t r = + - (3) cv. -Cn 4 Deep-water grop velocity of nth reglar wave: c G = = - (4) dk An 2 Wavelength, X = T n In H Wave steepness, s = (6) where T is the period of the nth reglar wave in seconds, H n is the voltage of the nth reglar wave (amplitde of flap motion), Cyc is the nmber of cycles of the nth reglar wave, x a is the distance to the concentration location (in meters), and to is the zero time before waves start in seconds. Local g is m/s 2 ± Experimental Set-Up The MASK bridge was positioned in the middle of the basin, parallel to the long bank, and the carriage was positioned at the midpoint of the bridge. The waves were generated from the short bank, on the west side of the basin (Figre 1). Wave data was collected from the six ltrasonic wave probes monted from the bridge (Figre 1) and the measrement plane was positioned near ltrasonic probe 3. At the probe 3 location, with the bridge in the center position, the wave-field is expected to be nidirectional. Effects from the basin wall were shown in nmerical prediction sing WAMIT (O'Dea and Newman, 2007) to reslt in slight crvatre on the north and soth ends of the wave front (Figre 1). However, in the center of the basin, the effects from the basin walls and crvatre of the wave-field shold be minimal (Smith, et al., 2007) and ths able to be neglected, and the wave-field appropriately considered nidirectional. Althogh not directly measred, the experimental observations appear to confirm that the waves in the region of the basin may be assmed nidirectional and practically niform. A schematic of the experimental set-p is shown in Figre 2. The PIV camera system was monted to the carriage in the MASK basin. Waves were generated from the short-bank wave-makers and propagated from west to east (Figre 1). A 0.9m by 0.9m (3 ft by 3 ft) field-of-view for PIV measrements, oriented east-west and vertical, enabled a two-dimensional ct of the waves in the direction of wave propagation. The PIV camera was monted 2.86m (9.4 ft) soth of the measrement plane, with a look-p angle of 10 degrees. The camera field-of-view was split with 0.409m (16 inches) above and 0.486m (19 inches) below the calm water free srface. The camera was sbmerged in the basin, sing a waterproof hosing and attached to a strt system monted on the MASK carriage. The center of the PIV measrement field of view was (5)!()

21 located m (1 inch) east and 0.64m (25.25 inches) soth of ltrasonic wave probe 3 (Figre 1. Table I). To illminate the PIV measrement plane, two waterproof laser probes were attached to a sbmerged tripod and oriented to prodce a 19mm (0.75 inch) thick vertical light sheet parallel to the direction of wave propagation. The lasers were located on the carriage and the laser beams were channeled into fiber optic cables connected to the sbmerged laser probes. Each laser probe is comprised of a 0.3m (12 inch) long cylindrical hosing which contains a series of optical lens designed to expand and spread the beam into a light sheet. The PIV measrement field was seeded with small silver coated particles, nominally netrally boyant and 100pm in diameter sing a mechanism attached to the MASK carriage. The mechanism consisted of a 50.8mm (2 inch) diameter PVC pipe, closed at one end, with the other end connected by a hose to a pmp in a particle mixing tank on the MASK basin carriage. A series of perforations were drilled along the vertical length of PVC pipe east to west, in the direction of wave propagation. For each measrement condition, particles were mixed with water in a mixing tank and pmped throgh the hose to the seeding mechanism. The mix was a compromise between low density (for niform particle dispersion) and high density (to minimize the flow rate and sbseqently the indced velocities into the measrement region of the flow). The PVC pipe was lowered into the water and manally traversed along a beam adjacent to the carriage, dispersing particles into a region parallel to the direction of wave propagation. After the desired particle concentration was achieved, the PVC pipe was raised ot of the water to remove it from the flow field. For each experimental condition, the following procedre was carried ot. After seeding, the pnematic wave-maker was increased to the reqired blower rpm and the specified wave voltage signal was inpt to the wave-maker control. The wave-maker then began to prodce waves and data collection began.

22 Wave Direction Particle Seeder Mechanism Free Srface Water Line Measrement f Plane A Laser Probes Figre 2. Illstration of the experimental set-p in the MASK basin, inclding PIV instrmentation and seeding mechanism. Wave-Maker Operation To generate nidirectional long crested waves, individal wave-maker nits in each bank were operated in-phase and prodced wave segments of the same nominal amplitde. Wave periods for each individal wave-maker nit can be either reglar or random. For this test, waves were generated from the short bank wave-makers on the left side and travel from west to east across the basin, as shown in Figre 1. Reglar Waves To generate reglar waves in the MASK basin, the wave-maker control ses a combination of parameters to achieve the desired amplitde and wave period. These parameters are the pnematic blower (rpm) and a wave freqency (Hz). The parameters sed for this experiment are given in Table 3. The blower (rpm) vales correspond to 1/50, 1/30, and 1/15 wave steepness, respectively. The wave freqency corresponds to a wave length of 4.81m. This wave length was chosen based on the ship length for DTMB Model # (Bishop, et al. 2005), a notional naval combatant hll form, which has been sed for nmeros sbseqent research model experiments. Table 3. Wave-maker parameters for reglar waves. Parameter Blower (rpm) Freqency (Hz) Vale 600,900,

23 To generate reglar waves the wave-maker eontrol program employed a seqence file of voltages programmed at 40 cycles per second. The compter generated digital control voltage seqences are created with a digital-to-analog (D/A) converter. The digitized voltage signal is filtered with a low-pass smoothing filter and a high-pass ctoff freqency prior to inpt to the wave-maker. In this stdy, a seqence file is a sinsoidal wave converted to a voltage signal for the hydralic wave-maker piston. The reglar waves were controlled by blower rpm, maximm voltage (the amplitde of flapper motion), freqency, and the nmber of wave cycles. Irreglar Waves A compter program was sed to generate irreglar waves. The program prodced digital control signal seqences and spplied them to the wave-maker controller throgh a digital-to-analog (D/A) converter. The digital control seqence software ses a filtered white noise techniqe, with 30 random seeds and is prodced sing a 40 Hz sampling rate for the wave-maker control signal. To prodce a desired wave spectrm, a compter generated white noise signal was sed to actate the flapper valves, reslting in wavemaker dome pressre flctations. The wave energy distribtion, as a fnction of the freqency, was adjsted with the driving freqencies for the valve controls. The blower speed was adjsted to control the wave amplitde. To represent nominal conditions for extreme waves, two long-crested irreglar wave spectra were considered for this stdy, a 30th scale Bretschneider wave spectrm for Sea State 8 and both 30th and 46.6th scale Hrricane Camille wave spectra. Irreglar Waves with Embedded Grops Wave seqences generated for particlar pnematic wave-maker blower rpm, signal amplitdes, and freqencies (Table 3) were applied to generate wave trains designed for the desired grop strctre, with repeatable wave properties, at a fixed location within the MASK. The finalized seqence file was a smmation of the voltages for the for wave trains. In some seqences, a flat spot existed, de to the signal freqency interaction, and was removed manally to smooth the motion of the hydralic pistons. Each deterministic embedded wave grop consisted of three large-amplitde waves. INSTRUMENTATION Measrements of the spatial velocity field at a specified location in the basin, the free srface at mltiple locations in the basin, and video were collected dring this experiment. Velocity Field Measrements Particle Image Velocimetry (PIV) was sed to obtain velocity field measrements beneath the free srface of the waves. PIV is an optical, non-intrsive, flow-field measrement that provides in-plane velocity measrements of a planar cross-section of a flow. Netrally boyant particles are sed as flow tracers to provide an indirect velocity measrement. The tracer particles are illminated twice in a small time period by two consective laser plses. The light scattered by the particles is recorded by a high speed 13

24 charge-copled device (CCD) camera. The distance traveled by the tracer particles in the measrement region, as observed by the recorded images between laser plses, is sed to obtain the displacement and velocities throghot the measrement region. For evalation, each image is divided into small interrogation regions and analyzed as image pairs (Figre 3). An image pair is defined as two images recorded within a small time step between laser plses. Corresponding interrogation regions between images in a pair are compared and the displacement of the tracer particles in these regions between images is determined sing a cross-correlation fnction. The signal peak of the correlation fnction identifies the particle displacement for a given interrogation region. The velocity vector field is then calclated over the entire measrement field sing the determined particle displacement and time between images, reslting in one velocity vector for each interrogation region. Interrogation Windows / 1 X». 1 Image A t «1 «Image B t + At jjr- displacement Figre 3. Schematic of interrogation windows and PIV evalation method. Camera A MegaPls ES 4.0/E camera was sed to captre the PIV images. The camera has a spatial resoltion of 2048 pixels x 2048 pixels and was operated in dal exposre mode at a frame rate of 10 fps. An image pair was taken every 200ms reslting in 5 image pairs per second. The camera was fitted with a 35 mm lens and stopped down to an f-nmber of 4.0 to provide the necessary depth of field. The time between images in a pair (At) was varied based on the flow characteristics for the condition being measred. The highest accracy is obtained by maximizing the particle displacement within the interrogation region. For this experiment, the At between sccessive plses varied from 1-30 ms, depending on the wave condition. Lasers Two cstom bilt Cynosre flash lamp-pmped dye lasers operating at 585 and 595 nm were sed to create a laser sheet, nominally 19mm (3/4 inch) thick, to illminate the 14

25 flow field. The lasers were operated at a maximm optical energy otpt of 1 J plse and the laser beam was copled into 600 micron optical fibers, 30m in length. The ability to lanch the beam into the fibers allowed for more flexibility in the experimental setp. When operating at fll power, roghly 700mJ/plse is recorded at the otpt end of the fiber. PIV Data Acqisition The PIV data acqisition system was bilt by Bolder Imaging, Inc. VisionNow software captred and stored the images at the fll camera rate onto a real time disk array with the capacity of 480 GB. The collection of the PIV images was synchronized with the ltrasonic wave probe 3 and each image pair was time-stamped to ensre correlation with the wave srface elevation data. Flow Tracer Particles Silver-coated hollow glass spheres (Potters Indstries prodct AGSL150-SI6) with a mean size of 110 microns and a specific gravity of 0.9 ±0.3 were sed as flow tracer particles in this experiment. Scattered light from the particles in the illminated measrement region was recorded by the camera. Wave Srface Elevation Measrements Single point wave height measrements were collected from an array of six bridgemonted wave probes (Figre 1) sampled at 40 Hz. Wave data collected from sonic probes on the bridge were recorded at 40 Hz. The Senix model ULTRA-SR-BP sonicsensor transmits a conical sonic beam with a nominal 12-degree total angle and measres the time of reflection from the target to calclate the distance. Measrements for steep waves may have drop-ots becase the water srface tends to scatter the sonic beam away from the sensor. The probes were connected to a compter on the bridge that transmits the wave data to a shore compter, where the data are collected and stored. Zeroes were taken at the beginning of each testing session, typically twice a day. to obtain more accrate test data and to accont for small changes in the water level of the basin. Video A digital video recorder was sed to docment individal rns dring the experiment. Video was sed to record the wave-field and visally docment largeamplitde wave events. However, de to the lack of an explicit visal reference for the wave-field (ie. no ship model), the visal data is not inclded in the analysis and discssion of the experiment presented in this report. INSTRUMENT CALIBRATION AND UNCERTAINTY Senix Ultrasonic Wave Probes The Senix wave gages were calibrated in-sit, by varying the distance above a measred calm water level in the MASK. The transdcers were located via precision machined pin locations with an estimated ncertainty of ±0.127 mm (±0.005 inch). The calibration range was ±381 mm (±15 inches), in 127-mm (5-inch) increments. The 15

26 calibration locations were-381, -254, -127, 0, +127, +254, +381 mm (-15,-10, -5, 0, +5, + 10,+15 inches). The analog otpt for the Senix is 0 to 10 V DC. Data from the Senix were collected and processed on a PC. The data were digitized with a National Instrments 16- bit data acqisition card, NI 6036, at a sample rate of 24 Hz. The anti-aliasing filters are Freqency Devices D78L8L, set at a ctoff freqency of 8 Hz. Typical data collection time was at least 100 s. Calibration and Uncertainty The normal nominal gain setting for the Senix is 76.2 mm/v (3 inches/v). The noise level of the Senix for measrements over calm water is typically between 1 and 10 mv. The maximm Type A expanded ncertainty from the ISO GUM (1995) is ±0.048 mm (± inch) for 1,000 samples, or 41.7 s averaging time. The Type A standard ncertainty is defined as A = 4L (7) where s h is the standard deviation of the height and n is the nmber of samples. The expanded ncertainty is defined as U = k f (8) where k f is the coverage factor. Normally at the 95% confidence level, k/ = «2. The maximm combined and expanded ncertainty from these two elements is mm ( inch). The contribtion of the Senix noise is negligible, compared to the machining accracy of ±0.127 mm (±0.005 inch) for the positioning device. An example calibration plot is presented in Figre 4, as a residal plot, for Senix wave gage #1. A residal plot is the difference between the data and a linear regression fit. The dashed line in Figre 4 is the prediction limit at the 95% confidence level, from the calibration theory of Scheffe (1973) and Carroll, et al. (1988). The ncertainty in the measrement from the instrment noise and position is smaller than the symbols in the figre. The red symbol in the figre is an otlier and was exclded from the linear regression analysis. The otlier is cased by the over-ranging of the Senix, in this case at 10 V. De to the location of the Senix sensor relative to the water at 0 (zero) mm, the transdcer may over-range at either 0 or 10 V, bt not both. In a few cases, the sensor was located relative to the water so that over-ranging did not occr. Most of the calibration ncertainty is de to the data scatter in the calibration. The contribtions from instrment noise and position are qite small by comparison. The relative ncertainty in the calibration is presented in Figre 5. As Figre 5 indicates, the maximm relative ncertainty is abot ±2%. The relative ncertainty is compted from the fll-range (fr) vale, which is nominally 381 mm (15 inches). Table 4 is a smmary of the calibration data acqired before the test. In this case, the calibration data were reported for the position of the probe above the water. In the experiment, the gage remained fixed, and the water moved relative to the gage. In the 16

27 data processing rotine, the signs of the gain and slope were opposite those in the table. The slope is negative and the intercept positive for the wave measrements. In Table 4, the colmn SEE is the standard error estimate from the linear regression analysis, while the r in the next colmn is the correlation coefficient. The SEE is essentially the standard deviation of the crve fit and is a measre of the randomness of the data. The precise definition may be fond in most texts on statistical analysis, sch as Ross (2004). For a highly linear crve fit, r is near one as indicated in the table, and SEE will be near zero. The colmn t-test, is the reslt of a hypothesis test for a comparison of the measred slope to the nominal slope of 76.2 mm/v (3 inches/v) from Ross (2004). The colmn ti)s is the vale of the inverse Stdent-/ from the hypothesis test. Any vale from the t-test that is less than *«is statistically the same as the nominal slope. From the table, the only wave gage that is different from the nominal slope is #6. The last two colmns are the expanded ncertainty of the gages at the 95% confidence level, at 10 Vdc. The last colmn is percent fll-range (% fr) from the measred slope, where the nominal fll-scale vale is 381 mm (15 inches). As the table indicates, the largest ncertainty was abot ±8 mm (±0.31 inches), or ±2% fr, at the 95% confidence level. Becase the calibrations are performed on a flat-plane srface, the accracy associated with signal drop-ots when attempting to measre steep waves shold be considered. However, the inflence of wave steepness on signal drop-ots for the Senix probes is not crrently known. E E, J/5 CO '</) CD F ^1 1! I I +/-95 % Confidence Limit o Wave Height Gage Data Otlier Data 8 o <D X CD > CO SinexS/N 5878 Intercept: mm Slope: mm/v -15 SEE: 1.41 mm 04/10/07 T. C. Smith -20, I _L Reference Length (mm) Figre 4. Calibration of Senix wave gage #l 17

28 03 Q Q I i i i i I i I I I I I i i I I i i ''I' I i I I I 1 i i_j i i i i I i_ Reference Height (mm) Figre 5. Relative calibration ncertainty of Senix wave gage #1 Table 4. Smmary of Senix Wave Gage Calibrations Probe # Slope Intercept SEE r t-test ta 95 U M (mm/v) (mm) (mm) (mm) (%fr)

29 Particle Image Velocimetry Calibration A spatial calibration of the P1V images was performed sing La Vision DaVis software v7.2. A calibration target, cm x cm (36x36 inches) in size and machined to ± cm (0.001 inch) accracy, is shown in Figre 6A. The target contains 121 evenly spaced '+' marks, 50.8mm (2 inches) in height and width. The target was monted in the MASK basin prior to the experiment coincident with the location of the measrement plane. For the experiment, 406 mm (16 inches) of the measrement plane was above the calm water free srface. To calibrate the images the target needed to be flly sbmerged therefore it was monted cm (16 inches) lower than then actal measrement plane so its top was even with the water srface. The camera was adjsted accordingly for calibration. The position of the laser probes were adjsted ntil the laser light sheet was visally aligned with the face of the calibration target. A calibration image was taken (Figre 6A) and imported into the DaVis software. The software creates a mapping fnction as well as applies a dewarping fnction to correct distortions de to the 10 degree look p angle of the camera. Figre 6B shows the dewarped image and the reslts of the mapping fnction, shown in red. The RMS of the fit was 0.12 pixels Figre 6. Calibration image (A) and dewarped image with mapping fnction (B) shown in red. Uncertainty Uncertainty analysis incldes both an analysis of the accracy and the repeatability of a measrement. The accracy of the measrement, often referred to as the systematic or bias error, is typically a fixed or constant vale. The repeatability of a measrement refers to the random variation in the measrement and typically incldes factors the experimentalist has little to no control over. Specially, in terms of PIV ncertainty for this experiment, the calibration and experimental setp are classified as part of the bias error and an assessment of the repeatability incldes variability in the wave-maker, the 19

30 precision in the determination of the PIV time steps, and the consistency of the PIV seeding. This section presents a method to qantify the repeatability of PIV measrements. PIV images pairs were taken every 200ms. For the reglar wave conditions one wave period traveled throgh the PIV measrement plane in approximately 1.76 sec and each processed image pair captred approximately 18.6% of the wavelength, with approximately 39% overlap between sccessive images. A comparison of the velocity measrements of the overlapping region between sccessive PIV images was sed to provide information abot the repeatability of the PIV measrements. Inherent in this repeatability is a measre of the repeatability of the generated waves. For each reglar wave condition, the overlap region between sccessive images was identified and the total velocity vectors were compared. The relative error in both the magnitde and direction (cp) of corresponding velocity vectors was calclated as shown below. relative errror _ mag V \-\V \V. (9) relative errror direction = <j) = a cos / X/v. +F'z/z., ' IK. IK, I (10) where: (ID K,.<= V x,,.,' + V 7 _ k and \V., = Jv x J + V z J (12) V 'ii v V n-\ =V Y x V.v,, ^ +V y z r V z,. or V V =\V KJcos^) Figre 7-Figre 12 provides plots of the relative error in velocity magnitde and velocity direction for reglar wave cases 1/50, 1/30, and 1/15 respectively. Each colored strip in the plots represents a portion of the wave for which an overlap region exists. A total of 28 consective cycles were measred for each condition, however for visalization prposes only a portion of the overall rn is shown in the plots. In addition, for visalization prposes the x-axis has been compressed. Frther details regarding this presentation of the data may be fond in the Reslts section. A comparison of the relative error in velocity magnitde among conditions shows the relative error is smallest in the 1/30 waves. The 1/50 waves show the error is consistently greater for the wave troghs than the wave crests. This is likely de to the method sed to choose the PIV time step. The time step was chosen so, at the maximm expected velocity, the tracer particles wold be displaced 8-12 pixels from image A to image B within a given image pair. The maximm velocity was expected to occr jst below the water srface therefore, the time step was optimized for those velocities. As a reslt, the precision of the measrement for velocities larger or smaller than this is redced. This trend is most apparent in the 1/50 wave, bt applies to the 1/30 and 1/15 (13) 20

31 waves as well. It is likely the smaller difference in error from crest to trogh in the I 30 waves sggests the chosen time step is less biased toward the crest velocities than for the 1/30 time step. In general, the repeatability in wave form for the 1/15 waves is poor, leading to a more random distribtion of error. It is also important to note the qality and consistency of the seed distribtion within each P1V frame is also likely to have an effect on the relative error. In general, the qality of the seed distribtion decreased with increasing depth in the measrement plane. It is likely the large vales of relative error present closer to the bottom of the measrement plane are de to this. Some error is also introdced becase the wave changes with time. The wave is progressing therefore the overlap regions represent the same portion of the wavelength, bt the wave itself is not exactly the same from one instant to the next. A comparison of the relative error in direction shows the largest range in error is observed in the steepest waves (1/15), bt overall there is less variability among conditions than observed for the velocity magnitde. For each overlap region shown in Figre 7-Figre 12 an average relative error was calclated and then an overall average for the entire rn was compted. These averages, as well as standard deviations and RMS vales, are shown in Table 5. As seen in the plots, the smallest vales are observed in the 1/30 waves. The difference between the RMS vales and average error vales provides an indication of the amont of scatter in the relative error throghot the rn. The larger the difference between the average and RMS vales, the greater the amont of scatter. This is also confirmed by the vales of standard deviation. The large standard deviation for the 1/15 wave steepness is likely a reslt of the variability in the wave-maker rather than the P1V measrements. As discssed in the Reslts section, 1/15 wave steepness for the specified wavelength is near the limits of the MASK wave-maker and the repeatability from one wave to the next is not as consistent as for less steep conditions. The information presented in Table 5 provides an insight into the repeatability of the PIV measrements. The ability of the wave-maker to prodce a repeatable condition has not been removed from these vales and acconts for some of the variation in error. As presented and discssed in the reslts section, the 1/30 wave steepness is shown consistently to be the most repeatable condition. This analysis is consistent with this conclsion. It is still important to note these vales are presented to provide some insight to the overall ncertainty in the PIV measrements, bt a formal analysis has not been completed. Specifically, an analysis of the accracy component of PIV ncertainty has not been completed. Typically, a control rn is performed to help qantify the ncertainty in the experimental setp. For this experiment collecting data in calm water wold have been an appropriate control rn. For this case zero velocity shold be seen across the measrement plane and the presence of any velocities wold indicate the amont of ncertainty introdced by the experimental setp and seeding process. Unfortnately, data of this natre was not collected. However, it is not nreasonable to assme the accracy component of the ncertainty is the same order of magnitde as the repeatability. Therefore a conservative estimate of the combined accracy and repeatability of the measrements wold doble the vales presented in this assessment. 21

32 Table 5. Smmary of relative error, standard deviation, and RMS vales. Wave Steepness Average Relative Error Standard Deviation RMS A/h Direction Velocity Direction Velocity Direction Velocity deg % deg % deg % 1/ / / H Magnitde Relative Error N * I Figre 7. Plot of the relative error in velocity magnitde for reglar waves with 1/50 wave steepness. 22

33 0 08 h 0 06 Magnitde Relative Error r 5 6 X/A Figre 8. Plot of the relative error in velocity magnitde tor reglar waves with I/30 wave steepness Magnitde Relative Error N XI). 10 Figre 9. Plot of the relative error in velocity magnitde for reglar waves with l/15 wave steepness. 23

34 HHH ^H Direction Relative Error ,.. i 1 1. L.... J i i J., X/A Figre 10. Plot of the relative error in velocity vector angle for reglar waves with 1/50 wave steepness LHHHHH BUM Direction Relative Error i N j J.L...J1.. I. j.k 1.L LJ J.I x/x Figre 11. Plot of the relative error in velocity vector angle for reglar waves with 1/30 wave steepness. 24

35 008 - ^^^^ ^^^^ Direction Relative Error o - N I, ) J.L...J. li..l.l 1. J Figre 12. Plot of the relative error in velocity vector angle for reglar waves with 1I15 wave steepness. VELOCITY FIELD MEASUREMENTS AND DATA PROCESSING Figre 13 shows an example of a raw PIV image (A) and a masked image (B). The bright white line spanning the image from left to right is the free srface. Above this line in the image, is a reflection of the particles, which are illminated beneath the free srface of the wave. Raw images were processed in MATLAB to create masked images that were imported and processed sing La Vision DaVis software v7.2. A mlti-pass processing techniqe was sed and the vectors were median filtered, zeroing vectors whose magnitdes were greater than 2.5 times the rms vale of neighboring vectors. Interpolation or tilling of blank spaces in each processed image was not performed. Figre 14 shows the reslting velocity field calclated by DaVis for a given image pair. The origin is defined at the center of the PIV measrement plane (x=0, z=0). Each image is 2048 x 2048 pixels in size and the images are processed in pairs. In the first processing pass the image is divided into interrogation windows 64 x 64 pixels in size. A cross-correlation scheme is then applied reslting in a velocity vector for each interrogation window. Two additional passes, each sing 32 x 32 pixel interrogation windows, are then completed bilding on the information gained from the previos pass. Each velocity vector represents the soltion for a given interrogation window and shows the magnitde of the velocity and direction at a given point in the flow field reslting in a velocity vector field of 64 x 64 vectors. 25

36 Figre 13. Raw (A) and masked (B) PIV images with particle seeding in the wave-field below the free srface. Figre 14. Example of a processed PIV image showing calclated velocity vectors (in yellow) for reglar waves, H/X=\/30; for clarity, only every 4th vector is shown. 26

37 RESULTS A comparison of wave height data from the ltrasonic wave probes and PIV images as well as wave field kinematics reslts for reglar and irreglar wave measrements is presented. For comparison, the data is normalized by the reference velocity, VREF, and wavelength, A. The deep-water wave celerity, for the reference wavelength of 4.81 m, was sed as the reference velocity, VREI-^2.14 m/s, for all cases. Reglar wave analysis incldes a comparison of experimental velocity profiles to theory (for one wave period), and velocity contor plots for each wave steepness over three wave periods. For the irreglar wave conditions, an analysis of the embedded grops is presented with a focs on the effect of grop location, grop composition, and scaling on the kinematics of the grop. PIV images pairs were taken every 200ms. For the reglar waves conditions one wave period traveled throgh the PIV measrement plane in approximately 1.76 sec and each processed image pair captred approximately 18.6% of the wavelength, with approximately 39% overlap between sccessive images. A preliminary assessment of the reslts from the experiment was reported in Minnick. et al. (2010). Wave Srface Elevation Measrements As seen in Figre 13 information abot the free srface can be gained from the PIV images. A comparison between the ltrasonic wave probe data and the free srface elevations determined from the PIV images is shown for reglar waves with a steepness of 1/15 (Figre 15) and irreglar waves (Figre 16). For each PIV image, the free srface was defined sing a 2nd-ordcr polynomial interpolation scheme. The ltrasonic wave probes provide a point measrement, while the PIV images provide free srface information for a 0.895m (2.9 ft) segment of the wave, at a given moment in time Figre 15 provides a comparison of the two measrements of the free srface for the H/A.= 1/15 reglar waves condition. The "steps" in the ltrasonic wave probe data observed at \/X=4, 4.5, and 4.9 show a limitation of the ltrasonic wave probes for the measrement of steep waves. If a wave becomes too steep, the signal retrn angle becomes too large for the ltrasonic wave probe to receive and record a measrement. When this occrs, the ltrasonic wave probe contines to otpt data from the last received retrn signal ntil receiving a new measrement (for additional discssion, see Smith, et al., 2007). The free srface information gained from the PIV images is a sefl spplement for these measrement dropots. Figre 16 shows an embedded wave grop in a BS-SS8 seaway. The steps seen in the ltrasonic wave probe data arond x/?i=24.5 (t=83) and x/x=25 (t=84 sec) again show the limitation of the ltrasonic wave probes for measrement of steep waves. The free srface information from the PIV images does not form a continos line becase, for each 0.895m (2.9 ft) segment, the free srface is continally changing. For a strict comparison, only the point in the segment that corresponds to the location of the ltrasonic probe wold be plotted. The effect is sally small, however, and the overlapping segments are sefl for visalization. Overall, the free srface data from the PIV images agree well with the ltrasonic wave probe data. It is shown that combining the two measrements can provide a more 27

38 complete pictre than either measrement alone. The free srface data collected by the PIV images is helpfl in providing free srface measrements in the data gaps experienced by the ltrasonic wave probes dring steep waves PIV (Measred) Sonic (Measred) 0.01 N o J. 4.5 X/>. Figre 15. Reglar wave, 1/15 steepness, free srface elevation time-history from MASK basin wave probe 3 (black dots), PIV free srface interpolation (green line). 28

39 PIV (Measred) Sonic (Measred) N o Figre 16. Irreglar wave with embedded wave grop, BS-SS8, free srface elevation time-history from MASK basin wave probe 3 (black dots) and free srface data from PIV images (green line). Reglar Waves Table 6 smmarizes the rns collected in reglar waves. Each spot captred 28 wave cycles. The time histories for wave probe 3 for the spots listed in Table 6 are shown in Appendix A. The time histories show the repeatability between spots as well as the repeatability of the sine wave within a spot. It is important to note the qality of the 1/15 waves. For the specified wavelength of 4.81 m, these waves are near the limits of the wave-maker and the limits of the wave probes sed to measre the free srface. Therefore, the repeatability from 1 cycle to the next is not as good as for waves of smaller steepness. Table 6. Reglar wave rns. Spot# H/A Height, inches Height, mm 10 1/ / / / / / *A=4.81 meters 29

40 Figre 17 - Figre 19 show a comparison of the measred free srface profile modeled with linear theory and 2nd-order Stokes wave predictions. Details of linear theory and 2nd-order Stokes can be fond in Appendix B. While the generation of reglar waves in an experimental basin is based on the inpt of sine fnctions to a wave-maker, as the generated waves progress, non-linear effects are introdced and the shape deviates from a perfect sine wave. Specifically, the waves develop sharper crests and flatter troghs. This deviation from a sine wave becomes more significant as a wave approaches breaking, which occrs at approximately 1/7 steepness. The onset of this effect may be observed in the 1/15 steepness waves (Figre 19), the amplitde of the wave crest and trogh are different; the trogh is shallower than the wave crest. Linear theory over-predicts the trogh, bt corresponds well with the ltrasonic data at the crest while 2nd-order theory agrees with both P1V free srface and ltrasonic data at the trogh and corresponds more with the PIV free srface data at the crest. The best correlation with linear theory is seen in the 1/30 steepness waves (Figre 18). The trogh of the 1/50 waves corresponds with theory bt the actal wave crest is higher than both linear and 2nd-order theory. This may be de to the limitations of the pnematic wave-maker. Waves of 1/50 steepness, at the given wavelength, approach the smallest waves that can be consistently prodced in the MASK facility. It is possible the waves are so small that any non-linear effects are more prevalent, casing a sharper peak than predicted. However, more investigation mst be done to flly nderstand the isse S Spot 10: 1(50 riv (measreoi Sonic (Measred) n Ltiear Theory» Stokes 2nd Theory / f >\ *T A / A / *JQ X//. Figre 17. Reglar wave, 1/50 steepness, free srface elevation time-history from MASK basin wave probe 3 (black dots), PIV free srface interpolation (black lines), with comparisons to linear (red sqares) and 2nd-order Stokes (green triangles) wave theory predictions. 30

41 0 02 Spot 4: 1/ PIV (Measred) Some (Measred) Linear Theory Stoke* 2nd Theory X/>. Figre 18. Reglar wave, 1/30 steepness, free srface elevation time-history from MASK basin wave probe 3 (black dots), PIV free srface interpolation (black lines), with comparisons to linear (red sqares) and 2nd-order Stokes (green triangles) wave theory predictions Figre 19. Reglar wave, 1/15 steepness, free srface elevation time-history from MASK basin wave probe 3 (black dots), PIV free srface interpolation (black lines), with comparisons to linear (red sqares) and 2nd-order Stokes (green triangles) wave theory predictions. 31

42 Figre 21-Figre 23 show the theoretical and experimental velocity profiles for each reglar wave case. The lettering corresponds to sccessive PIV image pairs spanning one wave period, from crest to crest, as shown in Figre 20. Profiles A and I represent velocity profiles taken at the sccessive wave crests and profile F, the wave trogh. The theoretical velocity profile is calclated sing eqation B-5 (Appendix B) sing the average wave amplitde for a given time history. Each lettered velocity profile in the figre represents the experimental velocity profile at x=0 in the PIV measrement plane for a given PIV image pair. Overall, as predicted by theory, the velocity is highest jst below the free srface and decreases with increasing depth. In addition, the velocity magnitdes and velocity gradients in the wave-field increase with increasing wave steepness. The velocity profiles across the wave-field measrement plane, for a given time, also show greater variation with increased steepness and all exhibit an exponential trend. This exponential trend becomes more prominent as wave steepness increases. Small amplitde wave theory (Appendix B) predicts a constant velocity magnitde for a given depth below the calm water free srface across all phases of the wave. Becase the experimental waves are not an idealized periodic sine fnction, the experimental velocity profiles exhibit some variation. The greatest variation can be seen in the 1/15 wave steepness case. Figre 23 shows two distinct clsters among the velocity profiles: profiles A, B, H, and I, or those near the wave crest, and profiles C, D, E, F, and G, those near the wave trogh. As wave steepness increases, the innate characteristics of experimentally generated waves (sharper peaks and flatter troghs) become more evident. The variation in amplitde between the wave crests and troghs increases reslting in two distinct trends as shown. This can also be seen in Figre 24 - Figre 26, which show the velocity contors for 1/50, 1/30, and 1/15 wave steepness conditions, respectively. These plots were generated by taking a slice at x=0 of each sccessive PIV image. The total velocity vectors for each image at the x=0 slice are sperimposed onto the contor plot. To enable better visalization, the presented contor plots have been distorted. Specifically, the x-axis has been compressed relative to the y-axis. De to this compression, the steepness shown in the plots does not correspond to the actal steepness of the generated waves. Figre 27 and Figre 28 are presented to provide an example of an ndistorted plot. In these figres the wave height is not non-dimensionalized and the x-axis represents the distance (in meters) the wave travelled since the beginning of the data collection. Within a given figre, a longer velocity vector indicates a larger velocity magnitde. The scaling of vectors varies among Figre 24 - Figre 26 (for visalization prposes), bt the color contors are consistent and can be sed to make comparisons. While the velocity profiles presented show some variation in velocity for a given depth, the relatively horizontal contors for 1/30 and 1/50 wave steepness show the variation is small. However, the steepest reglar wave condition, 1/15, shows a greater range of velocities throghot the same measrement plane and the contors begin to show more variation across the wavelength, specifically the contors begin to deviate from the relatively horizontal contors of the 1/50 and 1/30 wave steepness conditions. }2

43 N o Wave Lengths Figre 20. Free srface data of the reglar waves, 1/15. MASK basin wave probe 3 (black dots) and free srface data from PIV images (black and colored lines). 33

44 V / V Total Reference Figre 21. Theoretical and measred (for wave locations A-I) velocity profiles for reglar waves, 1/50. A' s J** / 1 * * M /^2*/1 * Is* Jr* A N - B //Sc^ */s C D - \ /»/f s^ / *// E if iff (rrfj -0.1 *-f P>.,, V / V Total Reference F G H Figre 22. Theoretical and measred (for wave locations A-I) velocity profiles for reglar waves, 1/30. 34

45 V / V Total Reference Figre 23. Theoretical and measred (for wave locations A-I) velocity profiles tor reglar waves, I/ Time, seconds 26 Figre 24. Total velocity contors for reglar waves, 1/50 wave steepness. 35

46 0.08 r I 'Tottl ' * I Umtmrnr*, \-k,--/!v =^7IV Time, seconds Figre 25. Total velocity contors for reglar waves, 1/30 wave steepness r I 0.02 h oh h -0 08H Time, seconds Figre 26. Total velocity contors for reglar waves, 1/15 wave steepness. 36

47 r- -a 2 I 1 c 2 > I I Si r, r, U S c 5 1 a Efl 2 1 ed c o -5 = 0 > - e 3 DO s ^ Q- e c en C D g bo r. r. U C C~ > c o -5 D c o > a EM > c c 3 U s. _C o _c c -a C a ~^ A a X en i_ 3 OB SJ9)8UJ 1l 6l3neAPM sjajaj JUBIOHOABM

48

49 Irreglar Waves with Embedded Wave Grops Irreglar wave conditions for the experiment inclded 30th and 46th scale realizations of Hrricane Camille and 30th scale Bretschneider Sea State 8 (BS-SS8) spectra, all with and withot embedded wave grops. These conditions were first generated and examined in Bassler, et al (2008) as part of a feasibility stdy for examining the generation of deterministic wave grops in the MASK basin. This stdy contines that examination to also inclde wave kinematics measrements. Two 30 lh scale Hrricane Camille realizations with an embedded grop were examined; wave grop 42 and wave grop 43 (see Bassler, et al., 2008 for specifics on the generated wave grops). The location of the grop within each realization is the same; however the composition of the grop varies slightly. Wave grop 44 was embedded in a 46 lh scale Hrricane Camille realization. Wave grop 44 is similar in composition and location to wave grop 42. In addition, two BS-SS8 realizations with an embedded wave grop were examined; wave grop 37 and wave grop 38. Each realization is identical except the location of the wave grop varies. Each rn was repeated once. Table 7 smmarizes the irreglar wave test conditions. Time histories for wave probe 3 for each rn are shown in Appendix C. The time histories exhibit the repeatability of the rns and of the method to embed a distinct deterministic grop within an irreglar seaway. It was assmed the addition of the deterministic wave grop wold not affect, in a measrable way, the spectrm in which it was embedded. The spectral shape of each realization was monitored to confirm this assmption and no significant changes to the spectrm were observed. Table 7. Smmary of irreglar wave conditions. Condition Hs inches Hs mm Tm sec Total Time sec Wave Grop Start, sec Camille 30th Scale Camille 30th Camille 30th Camille 46th Scale Camille 46th BS-SS8 BS BS Hrricane Camille Figre 29 contains plots of the 46th and 30th scale Hrricane Camille realizations. The time histories are from wave probe 3. The wave grops are traced in red. The first plot in the figre is a realization with wave grop 42, the second plot is a realization with wave grop 43. and the third plot with wave grop 44. All three wave grops occrred near the middle of the realization. 3 -

50 i i Hrricane Camille Spot40:Camille 30th-42 Grop T3 -Q E 0 \Af\l\Aw Time, seconds to -O E IS VV^/VAAA/^ Spot46:Camille 30th-43 Grop i P nr l/\a/\/w^^ c Time, seconds ( o CO Spot49:Camille 46th-44 Grop UA/\JV^ Time, seconds Figre 29. Hrricane Camille realizations with embedded wave grops. The red tracing indicates a wave grop. Wave grop 42 and wave grop 43 vary in wave grop composition. Both wave grops consist of three waves. The first wave is the smallest, followed by two crests significantly larger in amplitde than the other waves in the time series. For wave grop 42, the second wave is the largest and is followed by a third wave slightly larger than the first, bt smaller than the second. This is in contrast to wave grop 43 where both the second and third waves are of approximately eqal amplitde Figre 30 and Figre 31 show a long snapshot of wave grops 42 and 43, respectively, while Figre 32 shows a side by side comparison of the velocity contors of wave grops 42 and 43. These plots were generated by taking the x=0 slice of each sccessive PIV image. The total velocity vectors for each image at the x=0 slice are sperimposed onto the contor plots. The wave height is not non-dimensionalized and the x-axis represents time, with zero seconds eqal to the beginning of the data collection. The presented plots are in the reference frame of the PIV camera, where the waves are 40

51 moving right to left. The x-axis has been compressed for visalization prposes and therefore, the relative steepness among waves has been distorted. Figre 33 and Figre 34 show ndistorted plots of the second and third crest of wave grop 42 and 43 respectively. In these plots, the wave height is not normalized and the x-axis represents the distance (in meters) the wave has travelled since the beginning of the data collection. Overall, instead of relatively even-layered and symmetric velocity contors, as observed in the reglar wave measrements, the velocity contors for the grop are more chaotic and asymmetric. The velocity contor plots also demonstrate that nlike the reglar wave conditions, the velocity field for the wave grop varies with phase. The reglar wave conditions showed a strong dependence of the velocity on depth, bt little dependence on position within a wave. Almost the opposite is seen for the irreglar cases. The velocity contors for the second and third waves have distinctly different characteristics than the reglar waves, even the steepest case of 1/15. A "U-shaped" region of highest velocity is observed between the peaks of the second and third waves. The high velocity region on the backside of the second wave crest contines to the front of the third wave. This is an example of the deep water dispersion relation and the effect of the wave generation method sed in this experiment. As a reslt of dispersion, lower freqency waves travel faster than higher freqency waves. The "U-shaped" region illstrates the "over-taking" of a slower wave by a faster one, as the grop is temporarily formed and then dispersed. If this velocity field is similar in strctre to fll-scale ocean wave grops then this, along with the initial conditions at the time the ship enconters the wave grop, may significantly contribte to the severity of the response for a ship encontering the wave-field. Figre 35 shows the time history from wave probe 3 o\' a 30 lh scale Hrricane Camille realization withot an embedded grop. At approximately 30 seconds, sccessive waves in the time history resemble a grop strctre similar to the generated wave grops. Figre 36 shows the velocity contor plot of a portion of the time history presented in Figre 35. Overall, the kinematics of the indigenos grop from the irreglar seaway realization are similar to those of the generated grop shown in previos figres. This provides some indication that the wave grop generation method sed does not significantly inflence the measred kinematics. The difference in grop composition can be seen in Figre 32. The first wave in each grop is similar; however the second wave is larger in grop 42 than in grop 43. The larger wave in grop 42 leads to a smaller third wave and the highest velocities are concentrated in the face of the crest of the second wave. This is in contrast to wave grop 43 where the second and third waves are similar in height and the highest velocities are seen both coming down the crest of the second wave, throgh the trogh, and p into the crest of the third wave with a higher concentration of maximm velocities in the third wave rather than the second.

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57 Figre 37 offers a comparison of wave grop 42 and wave grop 44. The composition of each grop is the same. However, the scaling of the seaway in which the grop is embedded is different. Figre 37 demonstrates there is little effect of scaling the seaway on the kinematics of the wave grop. v,^v, 60 Time, seconds W e«time, seconds Figre 37. Velocity contor plots with total velocity vectors for wave grop 42 and wave grop 44. Bretschneider Sea State 8 Figre 38 contains two plots of BS-SS8 realizations as recorded by wave probe 3, each with a different embedded wave grop. The first plot in the figre contains wave grop 37 and the second plot, wave grop 38. The wave grops are traced in red and occr at different locations within the realization. Regardless of location, the compositions of the wave grops are similar, consisting of three waves, the second of which has the largest crest and trogh. Figre 38 shows the time history of the realization at wave probe 3. Figre 39 and Figre 40 show the velocity contor plots of each wave grop, providing a bit of the wave train before and after the wave grop. As discssed previosly, the x-axis is compressed relative to the y-axis for visalization prposes and therefore, the relative steepness among waves has been distorted. A visal comparison shows that althogh the grops occr at different locations within the realization there is little difference between the reslting kinematics of the wave grops. Jst as scaling of the seaway in which the grop is embedded had little effect on the wave grop, neither does location. It can be conclded that for the wave grop generation method sed in the MASK basin, the location within a realization does not affect the kinematics of the grop. 47

58 BS-SS8 c n E 03 "a Time, seconds Time, seconds Figre 38. BS-SS8 realizations with embedded wave grops. The red tracing indicates a wave grop. 48

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60

61 CONCLUSIONS AND RECOMMENDATIONS Overall, it was the intent of this experiment to collect and present a data set of the velocity field beneath the free srface of experimentally generated waves. The reslts from this investigation are intended to aid in the nderstanding of wave kinematics for experimental reglar and irreglar waves, specifically the kinematics of embedded wave grops within irreglar waves. In addition, the reslts of this experiment are intended to offer a fondation to a deterministic, and hopeflly more effective, approach to ship performance evalation methods for severe conditions, which are traditionally accomplished by the se of statistical methods (for additional discssion see Bassler. et al., 2010; 2010a; Belenky, et al., 2010). Overall, as predicted by theory, the reglar wave velocity profiles followed an exponential trend, and the magnitde of the velocity increased with increasing wave steepness. While the experimental measrements exhibited the same exponential decay as theory predicted; as wave steepness increased, the velocity profiles began to deviate from theory. This deviation was most apparent in the 1/15 wave steepness condition, which is likely de to the manifestation of nonlinearities in the experimentally generated wave- Beld. Both the velocity profiles and contor plots showed that the velocity field beneath reglar waves is dependent on depth, bt has little dependence on the position or phase o\' the wave. For the irreglar waves and the embedded wave grops, as expected, the kinematics of the irreglar waves was shown to be dependent on wave phase. In addition, the velocity contors for all of the embedded wave grops were asymmetric and chaotic, compared to relatively evenly distribted contors of the reglar waves. The kinematics of the embedded wave grops, in an irreglar seaway, showed a "Ushaped" region of highest velocity between the peaks of the second and third waves of the grop. This shape is most likely the reslt of the wave generation method sed in the experiment, which ses finite length sine wave sperposition, where slower waves are overtaken by faster ones as the grop is formed and then dispersed. A comparison of an indigenos wave grop occrring in an irreglar seaway with the generated wave grops indicates the wave generation method does not significantly inflence the reslting wave kinematics. If this velocity field is similar in strctre to fll-scale ocean wave grops, this may contribte to the severity of the response for a ship encontering the wave-field. An improved nderstanding of the kinematics for these large-amplitde wave grops is important to the modeling of these wave conditions in nmerical codes, particlarly for the assessment of ship performance. The effects of wave grop location, composition, and scaling on the wave grop kinematics were also examined. It was shown, sing the specified wave grop generation method, the location of the wave grop within the irreglar seaway and the scaling of the seaway did not have a significant effect on the overall kinematics of the grop. However, wave grop composition was shown to have a significant effect on the kinematics. This sggests the waves which exist prior to the grop do not significantly affect the kinematic properties of the grop enabling additional flexibility for the evalation of ship performance in severe wave conditions. The generated deterministic wave grops can be embedded in a variety of seaways withot significantly affecting the embedded grop 51

62 kinematics. The seaway before a wave grop will have an inflence on the initial conditions of the ship, affecting its attitde and orientation for when it enconters a wave grop. However, the velocities, and therefore reslting pressres and forces acting on the ship for the most severe conditions in a seaway, will be a fnction of the wave grop, and not the seaway in which the grop is embedded, or occrred. Conversely, from the experimental observations, the composition of the wave grop does inflence the grop kinematics, illstrating the importance of choosing appropriate grop compositions to meet the ship performance evalation objectives, whether experimentally or nmerically. It is the recommendation of the athors that a statistical approach to modeling a seaway still be completed first, to gain an initial nderstanding of the composition and probability of occrrence for specific rare and extreme wave events. With this knowledge, appropriate wave grops can be generated, either nmerically or in the basin, to offer a deterministic soltion to assessing and analyzing the dynamic stability and strctral loads performance for a ship encontering sch wave events. The athors hope this data set will aid in the development and improvement of nmerical tools which rely on accrate modeling of wave-field kinematics to assess ship performance. Frther development to the work presented in this report, incldes the se of new, enhanced wave-maker capabilities in the MASK basin (Hayden, et al., 2010), which will enable deterministic realizations of irreglar seaways, inclding large-amplitde wave grops to be generated more easily. Additionally, for short-crested, mlti-directional, irreglar wave conditions, which have been a sbject of interest at NS WCCD for most of the past decade, it may be possible to sed advanced PIV techniqes to obtain 3-D spatial wave-field kinematics measrements at selected locations in the basin. This type of investigation will frther provide improved nderstanding of the effects of spreading and directionality on the wave-kinematics, identifying necessary considerations for modeling, and provide additional validation data for the development of advanced nmerical simlation tools. 52

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66 Hennig, J., H. Billerbeck, G. F. Class, D. Testa, K. E. Brink, and W. L. Khnlein (2006), "Qantitative and Qalitative Validation of a Nmerical Code for the Realistic Simlation of Varios Ship Motion Scenarios," Proc. 25 lh Intl. Conf on Offshore Mechanics and Arctic Engineering, Hambrg, Germany, 4-9 Jne. Jensen, A., J. Sveen, J. Gre, J.-B. Richon, C.Gray, (2001) "Accelerations in water waves by extended particle image velocimetry," Experiments in Flids, 30, pp Jensen, A. and G. Pedersen, (2004) "Optimization of acceleration measrements sing PIV," Measrement Science and Technology, 15, pp Kristiansen, T., R. Baarholm, G. Rortiveit, E. Hansen, and C. Stansberg (2005), "Kinematics in a Diffracted Wave Field: Particle Image Velocimetry (PIV) And Nmerical Models," Proc. 24 th Intl. Conf. on Ocean, Offshore, and Arctic Engineering, Halkidiki, Greece, Jne. Longet-Higgins, M. S. (1976), "On the Nonlin-ear Transfer of Energy in the Peak of a Gravity-Wave Spectrm: A Simplified Model," Proc. Roval Society of London A, 347, pp Longet-Higgins, M. S. (2008), "On an Approximation to the Limiting Stokes Wave in Deep Water," Wave Motion, 45(6), pp Masterton, S. R. and C. Swan (2008), "On the Accrate and Efficient Calibration of a 3D Wave Basin," Ocean Engineering, 35(8-9), Jne. Matos, V., J. S. Sales Jr., and S. H. Sphaier (2005), "Seakeeping Tests with Gassian Wave Packets," 24" International Conference on Offshore Mechanics and Artie Engineering, Halkidiki, Greece, Jne. Minnick, L., C. Bassler, S. Percival, and L. Hanyok (2010), "Large-Scale Wave Kinematics Measrements of Reglar Waves and Large-Amplitde Wave Grops," Proc. 29 th Intl. Conf on Ocean, Offshore, and Arctic Engineering, Shanghai, China, Jne. National Transportation Safety Board (2005), NTSB Marine Accident Brief: Heavy- Weather Damage to Bahamas-Flag Passenger Vessel Norwegian Dawn, NTSB/MAB- 05/03, 16 April. Ning, D. Z., B. Teng, R. E. Eatock Taylor, and J. Zang (2008), "Nmerical Simlation of Non-Linear Reglar and Focsed Waves in an Infinite Water-Depth," Ocean Engineering, 35(8-9), Jne. OTJea, J.F. and J. N. Newman (2007), "Nmerical Stdies of Directional Wavemaker Performance," Proc. 28,h American Towing Tank Conf, Ann Arbor, MI, 9-10 Agst. Onorato, M., A. R. Osborne, and M. Serio (2006), "Modlational Instability in the Crossing Sea States: A Possible Mechanism for the Formation of Freak Waves," Physical Review Letters, 96. Philips, O. (1994), "The Strctre of Extreme Ocean Waves," Proc. 20th Symp. on Naval Hydrodynamics, Santa Barbara, California, Agst. Ross, S. M. (2004), Introdction to Probability and Statistics for Engineers and Scientists, Third Edition, Amsterdam: Elsevier, Academic Press. 56

67 Scheffe, H. (1973), "A Statistical Theory of Calibration:' The Annals of Statistics, 1(1). pp Schmann, E. H. (19X0). "Giant Wave," Oceans, Jly, pp Sclavonos, P. D. (2005), "Nonlinear Particle Kinematics of Ocean Waves,"./, of Flid Mechanics, 540, pp Schmittner, C, S. Kosleck, and.1. Hennig, (2010), "Predication of Wave Crest and Height Distribtions and Wave Grops Using a Nmerical Wave Tank," Proc. 2& Intl. Conf. on Ocean. Offshore, and Arctic Engineering. Shanghai, China, 6-11 Jne. Skjelbreia, J., A. Torm, E. Berek, O.T. Gdmestad, J. Heidman, N. Spidsoe. (19X9) "Laboratory Measrements of Reglar and Irreglar Wave Kinematics," E&P Form Workshop on Wave and Crrent Kinematics and Loading. Reil Malmaison. France October. Skjelbreia, J., G. Berek, Z. Bolen, O.T. Gdmestad, J. Heidman, R. Ohmark, N. Spidsoe A. Torm,. (1991) "Wave Kinematics in Irreglar Waves," Proc. IOth Intl. Conf on Ocean. Offshore, and Arctic Engineering. Stavanger, Norway, 23-2X Jne. Smith, C. B. (2006). Extreme Waves, Washington, DC: Joseph Henry Press. Smith, T.C., L. K. Hanyok, and M..I. Hghes (2007), "MASK Waves Benchmark," NSWCCD-50-TR-2007/052, October. Spyro, K. J. (2004), "Criteria for Parametric Rolling?," Proc. 7th Intl. Ship Stability Workshop, Shanghai, China, 1-3 November. Stansberg, C. T. and O. T. Gdmestad (1996), "Nonlinear Random Wave Kinematics Models Verified Against Measrements in Steep Waves," Proc. 15* Intl. Conf. Offshore Mechanics and Arctic Engineering, Florence, Italy, Jne. Stansberg, C. T., O. T. Gdmestad, and S. K. Haver (2008), "Kinematics Under Extreme Waves,",/, of Offshore Mechanics and Arctic Engineering, 130, May. Stokes, G. G. (1847), "On the Theory of Oscillatory Waves." Trans. Cambridge Philosophic Society, 8, pp S, M.-Y., M. Bergin, and S. Bales (1982), "Characteristics of Wave Grops in Storm Seas," Proc. Ocean Strctral Dynamics Symp. '82, Corvallis, Oregon, pp S, M.-Y. (1986), "Large, Steep Waves, Wave Groping and Breaking," Proc. 16th Symp. on Naval Hydrodynamics, Berkeley, California, Jly. Swan, C, T. Bashir, and O. T. Gdmestad (2002), "Nonlinear Inertia! Loading. Part I: Accelerations in Steep 2-D Water Waves, J. Flids and Strctres, 16, pp Takezawa, S. and M. Takekawa (1976), "Advanced Experiment Techniqe for Testing Ship Models in Transient Water Waves, Part I: The Transient Test Techniqe on Ship Motions in Waves," Proc. 11" Symp. on Naval Hydrodynamics, University College, London. Takezawa, S. and T. Hirayama (1976), "Advanced Experiment Techniqe for Testing Ship Models in Transient Water Waves, Part II: The Controlled Transient Water Waves 57

68 for Using in Ship Motion Tests," Proc 11 Symp. on Naval Hydrodynamics, University College, London. Themelis, N. and K. J. Spyro (2007), "Probabilistic Assessment of Ship Stability." SNA ME Maritime Technology Conf & Expo and Ship Prodction Symposim, Fort Laderdale, FL, November Themelis, N. and K. J. Spyro (2008), "Probabilistic Assessment of Ship Stability Based on the Concept of Critical Wave Grops," Proc. 10th Intl. Ship Stability Workshop, Daejeon, Korea, March. Tikka, K. K. and J. R. Palling (1990), "Predictions of Critical Wave Conditions for Extreme Vessel Response in Random Seas," 4 lh Intl. Conf. on the Stability of Ships and Ocean Vehicles (STAB '90), Naples, Italy. Toffoli, A., J. M. Lefevre, J. Monbali, and E. Bitner-Gregersen (2004), "Dangeros Sea- States for Marine Operations," Proc. 14th Intl. Offshore and Polar Engineering Conf, Tolon, France, May. Wheeler, J.D. (1969), "Method of Calclating Forces Indced by Irreglar Waves," Proc. of the First Offshore Technology Conf (OTC), Hoston, TX, 1: Y, Y.-X. and S.-X. Li (1990), "The Grop Characteristics of Sea Waves," Proc. 22nd Intl. Conf on Coastal Engineering, Delft, The Netherlands, 2-6 Jly. 58

69 APPENDIX A: REGULAR WAVE TIME HISTORIES Reglar Waves: 1/50 ca Time, seconds Spot 11 o/wvvwwwwwwwwvwwwv <D -C CD Time, seconds Figre A I. Time histories for 1/50 wave steepness A-

70 03 -o E TO Reglar Waves: 1/30 Spot 4 CD sz CD > CO Time, seconds CD "D -O E TO T CD. = 0) co Time, seconds Spot Figre A2. Time histories for 1/30 wave steepness. A-2

71 Reglar Waves: 1/ Time, seconds 50 Spot Time, seconds Figre A3. Time histories for l/l5 wave steepness. A-3

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73 Linear Wave Theory APPENDIX B: WAVE THEORY Linear wave theory assmes a 2-D inviscid, irrotational, constant density flow. To satisfy linear approximations of the bondary conditions it also assmes periodic waves of relatively small amplitde. Using linear wave theory, the velocity components for a particle at a given depth relative to the calm water free srface, r=0, in a wave can be determined sing (B-l) and (B-2). g cosh[a-(z + /?)] Q lu.. v, =// -cos# (B-l) c cosh(a7?) g sinh[a'(- + /7)l. _ v.=n - sin6? c cosh(a/7) (B-2) The derivation can be fond in standard textbooks (sch as Dean and Dalrymple. 1984). Applying the deep water approximation (depth > A/2), which assmes kh oo, (B-l) and (B-2) can be redced to: v a q o k \ e kt cos 0 (B-3) V k Is t v, ~ 7 A' e " sin 0 (B-4) V k As shown in (B-3) and (B-4), the velocity of a particle is dependent on its depth relative to the calm water references, and the phase of the wave, 6. The magnitde of the total velocity, V ToU,i, at a given depth can be determined from the individal velocity components. For a given depth below the free srface, taking, ; A lm^k as a constant, ('/, the total velocity is: V T 0,at = VV + v. 2 = ^C\ 2 {sm l 9 + cos l 0) = C, (B-5) Eqation B-5 shows that linear wave theory predicts the magnitde of the velocity of a particle at a given depth below the free srface of a reglar wave to be constant regardless of the phase of the wave. Stokes 2 nd Order Wave Theory Stokes 2nd-order approximation does not assme the waves arc infinitcsimally small, bt instead of finite height, eliminating some approximations made for linear theory. The free srface profile for a deep-water 2nd-order Stokes wave (Stokes, 1847) is given in (B-6). rj = // cos(a:v)-i- n- cos(2/cv) (B-6) A B-l

74 The second order model of the particle velocity components is shown in (B-7) and (B-8). gcoshk(h + z) 3 H 2 a-kcosh2k(h + z) v x =ij cos# + - cos26> (B-7) c cosh kh 16 sinh kh e sinhk(h + z).. 3 H'a ksinh2k(h + z). v 2 =rj 0 ^sin^^- ^-sin2^ (B-8) c cosha7? 16 sinh kh The derivation of these eqations can also be fond in standard textbooks (sch as Dean and Dalrymple, 1984). The presence of the 2nd-order term increases the particle velocities, which are varied along the wave de to the phase fnction. For example, horizontal velocities are increased at the wave crest bt are redced at the wave trogh. B-2

75 APPENDIX C: IRREGULAR WAVE TIME HISTORIES Hrricane Camille Camille 30th Scale: #42 Spot Time, seconds a E TO Time, seconds ih Figre C\. Hrricane Camille, 30 ' Scale, wave grop 42

76 -O E CO Camille 30th Scale: #43 /\jl/vv^^ Time, seconds Spot Time, seconds Figre C2. Hrricane Camille, 30 lh Scale, wave grop 43. C-2

77 Camille 46th Scale: #44 Spot 49 Grop Time, seconds 120 Spot 51 Grop 60 Time, seconds Figre C3. Hrricane Camille, 30 lh Scale, wave grop 44. C-3

78 Bretschneider Sea State 8 (BS -SS8) BS-SS8, #37 re V a E ra Time, seconds Time, seconds Figre C4. BS-SS8, wave grop 37. C-4

79 0.1 BS-SS8: # CO I 0 to Time, seconds Time, seconds 100 Figre C5. BS-SS8, wave grop 38. C-5

80 This page intentionally left blank. C-6

81 Distribtion List Nmber of Copies Office Individal Total Copies 1 NAVSEA05D1 J. Webster 1 1 ONR33I L. Patrick Prtell 2 1 NAVSEA 05D3 R. Dean 3 1 DTIC 4 Nmber of Copies NSWCCD Code Individal Total Copies 3452 (Library) (pdf only) 0120 J. Barkyomb 5 50 J. Etxegoien A. Reed T. F D. Walden v 5500 T. Applebce M. Dipper T. Smith J. Hickok (pdf only) 5500 D. Hayden (pdf only) 5500 J. Hoyt (pdf only) 5500 C. Bassler S. Percival In 5500 L. Hanyok V. Belenky W. Belknap( pdf only) 5500 B. Campbell (pdf only) 5500 T. Carrico (pdf only) 5500 S. Lee (pdf only) 5500 D. Wndrow (pdf only) L. Minnick D. Drazen (pdf only) 5600 P. Atsavapranee D.Walker (pdf only) 5800 R. Hrwitz (pdf only)