BED GEOMETRY RESPONSE TO VARYING WAVE CONDITIONS September 26, 2013 Martin Anderson Home Institution: Lafayette College REU Institution: Oregon State University PI: Dr. Diane Foster Graduate Student Mentors: Meagan Wengrove, Emily Carlson
Abstract Understanding sediment transport on a small scale can enhance the understanding of larger scale bathymetry. As a part of the larger NEES Tsunami Induced Turbulent Coherent Structures Project at Oregon State University, this report examines formation and migration of ripples under different wave forcing conditions in a full-scale laboratory setting. A sand bed was installed in the large wave flume at the O.H. Hinsdale Wave Research Laboratory and instrumented to track wave height, pore water pressure, velocity, and sediment transport. A Bar Line Intensity Mapper (BLIM) was used to extract the bed geometry from Particle Imagery Velocimeter (PIV) images. These bedforms were plotted together to show ripple migration and changes in the bed over time. These images were plotted concurrently with a profile of the free stream velocity 50 cm above the sand bed. Plots were also made to demonstrate the ripple migration under various conditions. It was found that wave trains consisting of a variety of waves caused faster migration rates than wave trains consisting of waves with a regular height and period. This data can be used as a baseline for future tests involving ripple migration in different conditions. 2
Literature Review Most previous research pertaining to tsunamis focuses on the primary effects such as the initial run up and inundation (Foster et al., 2011). The secondary effects of a tsunami, or more generally, turbulent coherent structures (TCS), commonly called whirlpools by the public, have been observed for centuries in conjunction with tsunamis and are featured in carvings from tsunami prone areas (Lynett et al., 2012). More recently, these vortices have been observed to trap boats in harbors. A 285 meter ship in a harbor in Oman broke free of its moorings and drifted for hours as the result of tsunami secondary effects (Lynett et al., 2012). These TCS, specifically shallow TCS as observed in Oman, are mostly caused when a tsunami passes and is deformed by harbor structures such as a seawall, this deformation can cause whirlpools and scour of the harbor interior. Tsunami induced TCS can be split into three different categories: nearbed, shallow, and near-surface breaking. This project focuses on the nearbed TCS, specifically liquefaction and sediment transport (Foster et al., 2011). Shallow water sediment transport was first explored by looking at the formation and movement of ripples under steady oscillatory flow (Bagnold, 1946). The movement was broken down into rolling grain ripples and vortex ripples (Bagnold, 1946). Rolling grain ripples occur at lower velocities, while vortex ripples occur past a critical velocity, or when a ripple exceeds a critical height (Bagnold, 1946). It was later suggested by Dr. William James that sediment transport could also occur due to the pressure caused by a nearbreaking wave (Madsen, 1974). Madsen (1974) examined the horizontal pressure gradient caused by breaking waves and concluded that, under natural conditions, the horizontal pressure gradient induced by wave action could exceed a critical stability determined by the bed sediment and cause a momentary failure of the top portion of the bed. This momentary failure leaves the unstable sediment unable to resist any lateral motion and open to plug flow (Sleath, 1999). Plug flow can be broken down into two different types. In the first type, sediment made unstable by a pressure gradient is propelled as a block by the current and as it moves, a shear layer forms at the bottom of the plug and works upward (Sleath, 1999). The plug dilates during motion and increases in concentration again during the flow reversal (Sleath, 1999). The second type occurs as sediment above the bed falls while other sediment is pushed upward due to an increase in grain-grain boundary stress (Sleath, 1999). The two segments meet just above the bed and form a region of increased concentration. Plug flow is controlled by the Sleath parameter, and a sediment mobility parameter determined by fall velocity and height above the bed (Sleath, 1999). The first field confirmation of plug flow was provided by Foster et al. (2006). The observations support the involvement of pressure gradient induced incipient motion. Foster (2006) observed that vertical velocities not present in laboratory experiments played a role in raising sediment in a natural environment. The lack of concrete understanding of sediment transport under normal conditions is especially an issue when trying to understand tsunami induced conditions. Understanding near shore sediment transport starts by understanding the smaller scale (Brown, 2006). Once ripple formation and migration is understood, predictions can be made regarding the migration of larger bedforms and long-term bathymetric changes (Brown, 2006). 3
Introduction The project presented herein took place at Oregon State University in the summer of 2013. The experiments were run in the O.H. Hinsdale Wave Research Laboratory in the large wave flume (LFW). The LFW can be used to conduct large-scale tests under normal wave conditions and tsunami conditions. We installed a sand bed in order to examine the sediment transport in a near shore environment under different wave and tsunami conditions. This project will help further our understanding of sediment transport, which can, in turn, allow us to mitigate the hazards presented by tsunamis to ports. This project examines ripple migration under varying wave and tsunami conditions. Exploring the migration of ripples influenced by different wave conditions and the effects of plug flow can help us understand bathymetry changes that can affect coastal infrastructure (Brown, 2006). Over the course of the summer the bed response was recorded under variety of wave conditions. The project continued into the fall with the addition of a pipe at the surface of the sand bed to examine the scour caused by vortices shed off of the pipe. 4
Methods The large wave flume at Oregon State University s O.H. Hinsdale Wave Research Laboratory (Figure 1) is 104m long, 3.7m wide, and 4.6m deep. Waves are made by a wave maker at one end. The wave maker, constructed by MTS, is a paddle that spans the area of the vertical crosssection of the flume controlled by a pneumatic actuator. It has a movable concrete beach, which, for this experiment, was set up at a 1:12 slope. The project required the installation of a flat, fine grained sand beach between bays 9 and 11. The beach was two feet deep and has a slight slope leading up to it. For this project, the flume was filled to a level of 2.10 m making a water depth of 1.53 m above the sediment observational area. Figure 1: Large Wave Flume diagram of instrumentation. ADV ( ), ADCP ( ), wave gage ( ), PIV ( ). The sediment bed is located between bays 9 and 11 as shown. The flume was instrumented with sensors to measure water height, pore water pressure, and velocity. This portion of the project focuses on the velocity measurements as measured by a single point Acoustic Doppler Velocimeter (ADV), as well as bed geometry images taken with a Particle Imaging Velocity system. Velocity readings were taken at various points throughout the sampling area by Nortek s Vectrino I ADVs. These ADVs measure velocity at a single point using the Doppler Effect to calculate the velocity based upon a pair of reflected acoustic pulses. The pulses emanate from a central transducer and are reflected back to be measured by four receivers as shown in Figure 2. The ADVs measure x, y, and two components of z velocity, at a single point 5 cm from the transducer. The ADVs recorded data at a rate of 50 Hz. 5
Figure 2: Rendering Nortek Vectrino I ADV, a pulse pair is emitted from a central transducer and the signal reflection is recorded by a pair of biaxial receivers, giving a three dimensional estimate of velocity. The images used for this project were recorded using a Particle Image Velocimetry (PIV) system. The PIV cameras capture pairs of images with fine time constraints on the space between the first and second image. This space is used to resolve the particle velocities. These image sets can be analyzed to track particles over time and to indicate the two dimensional magnitude and direction of the particle velocity. The cameras recorded image pairs at a rate varying between 3 Hz and 5 Hz. For the purposes of this report, the primary use of the PIV is to monitor changes in bed geometry using the captured images, and does not utilize data from processed PIV velocity fields. A laser mounted on a platform on the side of the tank served as a flash lamp for the cameras (Figure 3). The laser is reflected down a pipe, where it passes through a lens system that expands the laser beam into a sheet that is used to illuminate a portion of the bed and the water column. 6
Figure 3: PIV laser mounting system. The laser is used as a flash lamp to illuminate the sediment and overlying water column for image collection (rendering courtesy of Jon Hunt of UNH). The bed shows up as a white line in the image from the PIV as seen in Figure 4. This is due to the reflected laser sheet. Once recorded, the images were converted to.jpg format and run through a bar-line intensity mapping (BLIM) toolbox in Matlab (This toolbox was developed by L. Pape at the Institute for Marine and Atmospheric Research in Utrecht in the Netherlands). BLIM examines the pixel intensity and draws a line through the pixels with the highest intensities and then allows the user to manipulate the defined line to best fit the visually accurate bar line, or in the case of this project, bed pattern and export this defined pattern to MATLAB (Figure 5). For this project, the lines from successive image pairs were used to create timestacks to study the relative rates and nature of ripple migration under varied wave conditions. Ripple migration provides insight into sediment transport and can have an impact on scour and instability in coastal infrastructure. The timestacks were paired with the corresponding velocity profile from an ADV located 50 cm above the sampling volume of the PIV cameras. Both the horizontal and vertical velocities are compared to the ripple patterns for each wave condition. The lines are also used to calculate the ripple migration rate by tracking the positions of the maximum and minimum points of the peaks and troughs of the ripples. The bed wavelength is measured as two times the horizontal distance from crest to trough of the ripple, and amplitude as half of the height measured from crest to trough. The amplitudes and wavelengths presented here are based upon captured images. Onshore 7
Onshore Figure 4: PIV image showing bed geometry. The white line near the bottom of the image is the bed, illuminated by the laser sheet. Results The results presented are products of a single submersed camera. Timestacks of bed geometry are produced from sampling over a defined period of time for a given wave condition, finding the bed geometry for equally spaced images within the sampling window, and then merging the geometries to create a representation of bed evolution based upon wave forcing. The resolution of these time stacks is a direct result of the number of images recorded for a given wave condition. The length of the records vary from 01:40 (mm:ss) to 05:33. Regular waves Regular waves are waves with a constant period (T) and wave height (H). Onshore Figure 5: PIV Image, regular waves, H=10 cm T= 4 sec, BLIM line is shown as the purple line along the bed. The timestack of regular waves with wave height of 10 cm and wave period of 4 sec, shows the bed elevation has a variation of 5 mm, which is characteristic of low amplitude, high wavelength ripples (Figure 6). The sediment transport is influenced by the wave velocity; lower velocities cause less sediment to be kicked up into the water column and tend to roll sediment along the bed. Higher velocity waves create more of a vortex, which causes faster ripple migration. For this wave condition the ADV record is noisy due to low energy waves in this train and very low suspended sediment concentrations. As a result, the ADV had few reflectors in the water column. Higher amounts of particulate matter in the water improve the quality of the ADV data. 8
Onshore Time (sec) Bed Amplitude (mm) Velocity (m/s) Figure 6: timestack, regular waves, H=10 cm, T= 4 sec. To the left is the ADV data, horizontal velocity shown in blue and vertical velocity shown in red. To the right is the bed geometry time stack, where bed geometry is shown in mm. The bedform geometry over time with the color intensity decreasing from black to white with increasing time is shown in Figure 7a. The red and green lines in Figure 7b represent the on/offshore position in the image of the ripple trough (red) and crest (green) respectively. The ripple migration rate is shown in Figure 7c, with this example showing no evident migration due to relatively low energy waves. a. b.. d. 9
Figure 7: Migration plot, regular waves, h=10 cm, T=4 sec. a) BLIM lines shown by decreasing color intensity (black to white) with increasing time, b) The velocity corresponding to the x vs. t and dx vs. t plots. c) The X position of the trough (red) and crest (green) of the ripple, d) The change in the X position of the trough and crest of the ripple. A slightly higher energy wave type of 30 cm high waves with a period of 4 seconds is presented in Figure 8. The timestack (Figure 9) shows much higher ripples as well as a steady rate of onshore migration. The dx vs. t plots show the migration of the minimum and maximum points throughout the data collection period. The minimum in Figure 9d is shown to maintain a stable position, while the maximum displays a little more fluctuation. The ripples presented an average amplitude of 17.5 mm and an average wavelength of 100.2 mm. Onshore Figure 8: PIV Image, regular waves, H=30 cm T= 4 sec. The BLIM line is shown in purple. Onshore Time (sec) Bed Amplitude (mm) Velocity (m/s) Figure 9: timestack, regular waves, h= 30 cm, T= 4 sec. To the left is the ADV data, horizontal velocity shown in blue and vertical velocity shown in red. To the right is the bed geometry time stack, where bed geometry is shown in mm. 10
a. b. c. d. Figure 10: migration plot, regular waves, h= 30 cm, T= 4 sec, a) BLIM lines shown by decreasing color intensity (black to white) with increasing time, b) The velocity corresponding to the x vs. t and dx vs. t plots, c) The X position of the trough (red) and crest (green) of the ripple, d) The change in the X position of the trough and crest of the ripple. 10 b and c show only slightly more variation than 7 b and c. There is a gradual shift that is more apparent in 10b than 10c. Bichromatic Waves A bichromatic wave train is the addition of two regular waves with two different periods. The wavemaker paddle moved in a sinusoidal pattern dictated by the two periods of the waves, 3.7 sec and 4.3 sec. The combination of waves creates wave groups through constructive and destructive interference. The nominal wave height was 12 cm, but the nature of the way the waves are run creates areas of constructive and destructive interference that make larger or smaller waves. The ripples from the bichromatic waves are similar to those caused by the 30 cm regular waves with an amplitude of 20.0 mm and a wavelength of 131.6 mm (Figure 11). The peak velocities in the wave groups correspond to times of ripple migration (Figure 12). The increased peak velocity found in the bichromatic waves indicates higher energy waves that cause higher ripple migration rates (Figure 13). The dx vs. t plot shows migration rate peaks at the peak velocity of the wave groups. 11
Onshore Figure 11: PIV Image, bichromatic waves, h=12 cm, T 1 =3.7 sec, T 2 =4.3 sec. The BLIM line is shown in purple. Onshore Time (sec) Bed Amplitude (mm) Velocity (m/s) Figure 12: timestack, bichromatic waves, h=12 cm, T 1 =3.7 sec, T 2 =4.3 sec. To the left is the ADV data, horizontal velocity shown in blue and vertical velocity shown in red. To the right is the bed geometry time stack, where bed geometry is shown in mm. 12
a. b. c.c d. Figure 13: migration plot, bichromatic waves, h=12 cm, T 1 =3.7 sec, T 2 =4.3 sec, a) BLIM lines shown by decreasing color intensity (black to white) with increasing time, b) The velocity corresponding to the x vs. t and dx vs. t plots, c) The X position of the trough (red) and crest (green) of the ripple, d) The change in the X position of the trough and crest of the ripple. Irregular Waves An irregular wave train is a set of waves with random wave heights and a constant period. The ripples caused by the varying waves have an amplitde of 9.8 mm and a wavelength of 102.5 mm (Figure 14). Again, it is apparent that the wave velocity peaks in Figure 15 are congruent with the regions of greatest migration. The migration rate plot (Figure 16) spikes in migration rate at 150 seconds and 325 seconds. There is a drastic shift in the ripples at the end of the collecition that could be attributed to plug flow. The spikes in Figures 16b and 16c correspond to the boundaries visible in the timestack where the migration rate changes drastically. The change in minimum/maximum position is most affected when the wave velocity shifts upward very quickly. This is most evident around 550 seconds. Onshore 13
Figure 14: PIV Image, irregular waves, T= 4 sec. The BLIM line is shown in purple. Onshore Time (sec) Bed Amplitude (mm) Velocity (m/s) Figure 15: timestack, irregular waves, T= 4 sec. To the left is the ADV data, horizontal velocity shown in blue and vertical velocity shown in red. To the right is the bed geometry time stack, where bed geometry is shown in mm. 14
a. b. c. d. Figure 16: migration plot, irregular waves, T= 4 sec, a) BLIM lines shown by decreasing color intensity (black to white) with increasing time, b) The velocity corresponding to the x vs. t and dx vs. t plots, c) The X position of the trough (red) and crest (green) of the ripple, d) The change in the X position of the trough and crest of the ripple. Solitary Tsunami Wave A solitary wave with a wave height of 50 cm was generated by the wave paddle and is used to simulate a tsunami. The tsunami disturbs a large amount of sediment, as shown in Figure 17, that obscures the bed from view during the wave event. The timestack in Figure 18 displays a red bar during the tsunami to account for the lack of usable data at that time. The tsunami significantly flattens out any ripples in the bed prior to the wave. Onshore Onshore Onshore Before During After Figure 17: PIV Images before, during and after a tsunami, h=50 cm. The BLIM lines are shown in purple. The 15
Onshore Time (sec) Bed Amplitude (mm) Velocity (m/s) Figure 18: timestack, tsunami, h=50 cm. To the left is the ADV data, horizontal velocity shown in blue and vertical velocity shown in red. To the right is the bed geometry time stack, where bed geometry is shown in mm. Solitary Tsunami Wave plus Regular and Bichromatic Waves A set of regular or bichromatic waves is run to set up the bed geometry, then one solitary wave is generated, and another set of regular or bichromatic waves are generated to understand how the bed reforms and evolves after a tsunami occurs. Here, the regular wave train is comprised of waves with a 20 cm wave height and a 4 second period with a tsunami with a wave height of 50 cm (Figure 19). The timestack shows the ripple migration prior to the tsunami as well as the rebuilding of ripples after the tsunami. 16
Onshore Time (sec) Bed Amplitude (mm) Velocity (m/s) Figure 19: timestack, tsunami with regular waves, h T =50 cm, h W =20 cm, T W =4 sec. To the left is the ADV data, horizontal velocity shown in blue and vertical velocity shown in red. To the right is the bed geometry time stack, where bed geometry is shown in mm. Figure 20 shows a train of bichromatic waves interrupted by a tsunami. The dark red lines in the timestacks are collection periods when the location of the bed is not clear due to very high sediment concentrations in the water column coinciding with the peak velocities of the wave train. 17
Onshore Time (sec) Bed Amplitude (mm) Velocity (m/s) Figure 20: timestack, tsunami with bichromatic waves, h T =50 cm, h W =12 cm, T 1 =3.7 sec, T 2 =4.3 sec. To the left is the ADV data, horizontal velocity shown in blue and vertical velocity shown in red. To the right is the bed geometry time stack, where bed geometry is shown in mm. Discussion/Conclusions Waves of larger height and higher velocity are capable of causing much larger ripples. These higher energy waves also cause faster ripple migration rates. Not only does higher energy influence migration, but regularity plays a role as well. The bichromatic and irregular waves, while having peak velocities not much larger than the 30 cm high regular waves, caused much faster migration on the order of.025 cm/s for the bichromatic case, compared to.02 cm/s for the 30 cm height regular wave case. This could be attributed to the variation in velocity affecting how the sediment moves along the bed, whether it was rolled over the crest of a ripple or picked up in a vortex and deposited on the next crest. Lower velocities facilitate rolling grain ripples, which have smaller amplitudes and longer wavelengths, while higher velocities result in vortex ripples with larger amplitudes. The differences in wave heights and velocities for the trials containing bichromatic and irregular waves prevent the bed from developing a stable ripple pattern. This instability facilitates sediment transport. The change between conditions facilitating rolling grain and vortex ripples cause sediment to migrate in both patterns, which results in faster migration than one pattern alone. In the bichromatic and irregular trains the ripples migrate in jumps outlined by the wave groups with distinct boundaries visible in the timestacks. This could be attributed to plug flow or to the settling of larger amounts of sediment between wave groups and filling in ripple troughs. In the tsunami trials, the tsunami effectively flattened the bed from its previous setup condition. For the solitary wave trains, irregular waves were run for 12 minutes between tsunamis to reset 18
the ripples. In all of the tsunami trials, there was a fluctuation in velocity after the tsunami. This is caused by the backflow from the tsunami and is the predominant cause of TCS. After the tsunami in the bichromatic trial, the ripples were quick to reform, taking approximately 25 seconds after the tsunami occurs. The ripples in the regular wave trial did not reform as quickly, taking approximately 60 seconds to reform after the tsunami occurred. This information can be used as full-scale observations of sediment transport under various wave and tsunami conditions. Observations of sediment transport are valuable for making model predictions about how a tsunami can potentially affect harbor bathymetry after a tsunami occurs. As the larger project progresses, this data can be used as a baseline comparison for the next phase of the project examining bed scour. A three-inch diameter steel pipe was installed across the width of the flume below the PIV system. The normal bed conditions can then be compared to the conditions caused by the vortices shed off of the pipe. Contact Information Martin Anderson Lafayette College, Class of 2014 Civil Engineering andersom@lafayette.edu martinanderso@gmail.com Dr. Diane Foster Associate Professor, University of New Hampshire diane.foster@unh.edu Acknowledgements Special thanks to Emily Carlson, Meagan Wengrove, and Professor Diane Foster. This project was partially supported by the National Science Foundation through the Research Experience for Undergraduates program (EEC-1263155) and the George E. Brown Jr. Network for Earthquake Engineering Simulation (NEES) Cooperative Agreement CMMI-0927178. This project was partially supported by the National Science Foundation through EEC-1263155 and CMMI- 0927178. Additional funding came from CMMI-1135026. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. I would also like to acknowledge the staff at the Oregon State University O.H. Hinsdale Wave Research Laboratory. References Bagnold, R. A. (1946), Motion of waves in shallow water, interaction between waves and sand bottoms. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 187(1008), 1 18 Brown, Jennifer, A. (2006) Sea-Bed Response to Non-Breaking Waves. B.S. Ohio State University: USA. 19
Foster, D. L., A. J. Bowen, R. A. Holman, and P. Natoo. (2006). Field evidence of pressure gradient induced incipient motion. J. Geophys. Res., 111. Foster, D., Lynett, P., and Hsu, T. (2011). Tsunami Induced Coherent Structures." NSF Proposal. Lynett, P. J., J.C. Borrero, R. Weiss, S. Son, D. Greer, and W. Renteria. (2012). Observations and modeling of tsunami-induced currents in ports and harbors. Earth and Planetary Science Letters, 327-328, 768-74. Madsen, O. S. (1974). Stability of a sand bed under breaking waves, 14th Conference on Coastal Engineering in New York, pp. 776 794. Sleath, J. F. A. (1999). Condition for plug formation in oscillatory flow. Cont. Shelf Res., 19, 1643-1664. 20