University of South Florida Scholar Coons Geology Faculty Publications Geology 1-21 Liits of Wave Runup and Corresponding Beach- Profile Change fro Large-Scale Laboratory Data Tiffany M. Roberts University of South Florida, trober2@usf.edu Ping Wang University of South Florida, pwang@usf.edu Nicholas C. Kraus U.S. Ary Engineer Research and Developent Center, Coastal and Hydraulics Laboratory 399 Halls Ferry Road Vicksburg Follow this and additional works at: http://scholarcoons.usf.edu/gly_facpub Part of the Geology Coons Scholar Coons Citation Roberts, Tiffany M.; Wang, Ping; and Kraus, Nicholas C., "Liits of Wave Runup and Corresponding Beach-Profile Change fro Large-Scale Laboratory Data" (21). Geology Faculty Publications. Paper 192. http://scholarcoons.usf.edu/gly_facpub/192 This Article is brought to you for free and open access by the Geology at Scholar Coons. It has been accepted for inclusion in Geology Faculty Publications by an authorized adinistrator of Scholar Coons. For ore inforation, please contact scholarcoons@usf.edu.
Roberts, T. M., Wang, P., and Kraus, N. C. 27. Liits of Beach and Dune Erosion in Response to Wave Runup Elucidated Fro SUPERTANK. Proceedings Coastal Sedients 7 Conference, ASCE Press, Reston, VA, 1961-1974. LIMITS OF BEACH AND DUNE EROSION IN RESPONSE TO WAVE RUNUP ELUCIDATED FROM SUPERTANK Tiffany M. Roberts 1, Ping Wang 1, Nicholas C. Kraus 2 1. Departent of Geology, University of South Florida, 422 E. Fowler Ave., Tapa, FL 3362, USA. trobert@cas.usf.edu 2. U.S. Ary Engineer Research and Developent Center, Coastal and Hydraulics Laboratory, 399 Halls Ferry Road, Vicksburg, MS 3918-6199, USA. Nicholas.C.Kraus@erdc.usace.ary.il. Abstract: The unique dataset fro SUPERTANK is analyzed to exaine the upper liit of beach change in response to elevated water level caused by wave runup. Thirty SUPERTANK runs are investigated, including both erosional and accretionary wave conditions under rando and onochroatic waves. The upper liit of beach change approxiately equals the axiu vertical excursion of swash runup. Exceptions to this direct relationship are those with beach or dune scarps. The vertical extent of wave runup above ean water level on a non-scarped beach is approxiately equal to the significant breaking wave height. Scarps substantially liit the uprush of swash otion, resulting in a uch reduced axiu runup. Predictions of wave runup are not iproved by including a slope-dependent surf-siilarity paraeter. The liit of wave runup is substantially less for onochroatic waves than for rando waves, attributed to absence of low-frequency otion for onochroatic waves. INTRODUCTION Quantification of wave runup and its relationship to the upper liit of beach-profile change are required for understanding and predicting beach and dune erosion, especially during stors. Wave runup is coposed of wave setup, defined as a super-elevation of the ean water level, and swash runup, or fluctuations about that ean (Holan and Sallenger 1985; Nielsen 1988; Yaaoto et al. 1994; Holland et al. 1995). Nuerous studies on the liits of wave runup have been conducted, resulting in the developent of several predictive odels, fro three approaches.
Report Docuentation Page For Approved OMB No. 74-188 Public reporting burden for the collection of inforation is estiated to average 1 hour per response, including the tie for reviewing instructions, searching existing data sources, gathering and aintaining the data needed, and copleting and reviewing the collection of inforation. Send coents regarding this burden estiate or any other aspect of this collection of inforation, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Inforation Operations and Reports, 1215 Jefferson Davis Highway, Suite 124, Arlington VA 2222-432. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to coply with a collection of inforation if it does not display a currently valid OMB control nuber. 1. REPORT DATE 27 2. REPORT TYPE 3. DATES COVERED --27 to --27 4. TITLE AND SUBTITLE Liits of Beach and Dune Erosion in Response to Wave Runup Elucidated fro Supertank 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) U.S. Ary Engineer Research and Developent Center,Coastal and Hydraulics Laboratory,399 Halls Ferry Road,Vicksburg,MS,3918-6199 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 1. SPONSOR/MONITOR S ACRONYM(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unliited 11. SPONSOR/MONITOR S REPORT NUMBER(S) 13. SUPPLEMENTARY NOTES Proceedings Coastal Sedients 7 Conference, 13-17 May 27, New Orleans, LA, ASCE Press, 1961-1974 14. ABSTRACT The unique dataset fro SUPERTANK is analyzed to exaine the upper liit of beach change in response to elevated water level caused by wave runup. Thirty SUPERTANK runs are investigated, including both erosional and accretionary wave conditions under rando and onochroatic waves. The upper liit of beach change approxiately equals the axiu vertical excursion of swash runup. Exceptions to this direct relationship are those with beach or dune scarps. The vertical extent of wave runup above ean water level on a non-scarped beach is approxiately equal to the significant breaking wave height. Scarps substantially liit the uprush of swash otion, resulting in a uch reduced axiu runup. Predictions of wave runup are not iproved by including a slope-dependent surf-siilarity paraeter. The liit of wave runup is substantially less for onochroatic waves than for rando waves, attributed to absence of low-frequency otion for onochroatic waves. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Sae as Report (SAR) 18. NUMBER OF PAGES 14 19a. NAME OF RESPONSIBLE PERSON Standard For 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18
The earliest physics-based approach is developed upon a theoretical derivation for onochroatic waves. Bowen et al. (1968) derived a wave setup slope inside the surf zone for onochroatic (sinusoidal) waves as: η h 2 1 = K K = (1 + 2.67 γ ) (1) x x where h = still-water depth, η = wave setup, x = cross-shore coordinate, γ = H/( η + h) and H = wave height. Based on both theory and laboratory easureents, the axiu set-up under a onochroatic wave, η M, was found to occur at the shoreline: ηm =.3γ (2) H b where H b = breaking wave height (Battjes 1974). The above equations concern only the wave setup portion of the runup. The second approach is based ainly on field easureents ade on dissipative beaches. Guza and Thornton (1981) suggested that the setup at the shoreline, η sl, is linearly proportional to the significant deepwater wave height H o : η sl =.17Ho (3) In a following study, Guza and Thornton (1982) found that the significant wave runup, R s, (including both wave setup and swash runup) is also linearly proportional to the significant deepwater wave height: Rs = 3.48 +.71 Ho (units of centieters) (4) Coparing Eqs. (3) and (4), the entire wave runup is approxiately 4 ties the wave setup, i.e., swash runup constitutes a significant portion of the total elevated water level. According to Huntley et al. (1993), Eq.(4) is the best choice for predicting wave runup on dissipative beaches. Based on field easureents on highly dissipative beaches, Ruessink et al (1998) and Ruggiero (24) also found linear relationships, but with different epirical coefficients. The third and ore recent approach, proposed by Holan (1986) and several siilar studies (Holan and Sallenger 1985; Ruggiero et al. 24; Stockdon et al. 26), argued that ore accurate predictions can be obtained by including the surf siilarity paraeter, ξ: ξ = β 1/2 ( Ho / Lo) (5) where L o is the deepwater wavelength, and β is the beach slope. Holan (1986) found a dependence of the 2% exceedence of runup R 2 on the deepwater significant wave height and the surf siilarity paraeter: R2 = (.83ξ o +.2) Ho (6) Stockdon et al. (26) expanded upon the Holan (1986) analysis and developed the epirical equation: 2
1 2 1 2 HL o o(.563β f +.4) 2 R2 = 1.1.35 β f ( HoLo) + (7) 2 Realizing the variability of beach slope in ters of both definition and easureent, Stockdon et al. (26) define the foreshore beach slope as the average slope over a region of two ties the standard deviation of continuous water level record. Most field studies were conducted on gentle sloping dissipative beach and found wave runup within the swash zone to be doinated by infragravity frequency coponents, or surf beat. Mechaniss for generating low-frequency otion at the shoreline include 1) obliquely incident wave groups (Gallagher 1971; Bowen and Guza 1978), 2) tievarying wave breaking (Syonds et al. 1982; List 1992), and 3) bound long wave generated by periodical variations of ean water level due to wave groupiness outside the surf zone (Longuet-Higgins and Stewart 1962). In contrast to nuerous studies on wave runup, little data are available relating the liit of wave runup with that of the beach-profile change. In this paper, data fro the prototype-scale SUPERTANK experient (Kraus et al 1992; Kraus and Sith 1994) are exained to study the liit of wave runup and corresponding liit of beach dune erosion. Specifically, this study exaines 1) the level of swash runup and wave setup; 2) tie-series beach-profile changes under erosional and accretionary waves; 3) the relationship between the above two phenoena; and 4) the accuracy of existing wave runup prediction ethods. A new epirical forula predicting the liits of wave runup and that of beach change is proposed based on the SUPERTANK data. SUPERTANK EXPERIMENTS One of the largest and ost densely instruented laboratory ovable-bed studies to date is the SUPERTANK experient. This ulti-institutional effort sponsored by the Corps of Engineers was conducted at the O.H. Hinsdale Wave Research Laboratory at Oregon State University fro July 29 to Septeber 2, 1991 (Fig. 1). This facility is the largest wave channel in the United States that can contain a sandy beach through which experients coparable to the agnitude of naturally occurring waves can be conducted (Kraus et al. 1992). Fig. 1. Layout of SUPERTANK experients. Diensions are in feet and inches. 3
The SUPERTANK experient easured total-channel hydrodynaics and sedient transport along with the resulting beach-profile changes. The wave channel was 14 long, 3.7 wide, and 4.6 deep (the still water level was typically 1.5 below the top) with a constructed sandy beach extending 76 offshore (Fig. 1). The beach was coposed of 6 3 of fine, well-sorted quartz sand with a edian size of.22 and a fall speed of 3.3 c/s. The wave generator and wave channel were equipped with a sensor to absorb the energy of reflected waves. The water-level fluctuations were easured with 16 resistance and 1 capacitance gauges. These 26 gauges, spaced 3.7 apart, provided detailed wave propagation patterns, especially in the swash zone. The beach profile was surveyed following each wave run. The initial profile was constructed based on the equilibriu beach profile developed by Dean (1977) and Bruun (1954) as: 2 3 hx ( ) = Ax (8) where h = still-water depth, x = horizontal distance fro the shoreline, and A = a shape paraeter corresponding to a ean grain size of.3. The initial beach was built steeper with a greater A-value to ensure adequate water depth in the offshore area (Wang and Kraus 25). For efficiency, ost SUPERTANK tests were initiated with the final profile of the previous run. Approxiately 35 surveys were conducted using an autotracking, infrared Geodieter targeting pris attached to a survey rod ounted on a carriage pushed by researchers. Although three lines, two along the wave-channel wall and one in the center, were surveyed, only the center line is exained in this study. Wave-processing procedures are discussed in Kraus and Sith (1994). To separate incident-band wave otion fro low-frequency otion, a non-recursive, low-pass filter was applied. The period cutoff for the filter was set to twice the peak period of the incident waves. After inspection of all 2 SUPERTANK tests, 5 tests with 3 wave runs were selected for analysis in the present study. The selection was based on the particular purpose of the wave run, the trend of net sedient transport, and easured beach change. Tieseries beach-profile changes and cross-shore distribution of wave height and ean water level were analyzed. The breaker point is defined at the location with a sharp decrease in wave height (Wang et al. 22). The axiu runup is defined by the location and beach elevation of the swash gauge that contained a value larger than zero wave height, i.e., water reached that particular gauge. There ay be soe differences in the runup easured in this study as copared to the video ethod (e.g., Holland et al. 1995) and horizontally elevated wires (e.g., Guza and Thornton 1982). The differences are not expected to be significant. RESULTS AND DISCUSSION The subject 3 wave runs are suarized in Table 1. The thirty cases are coposed of 12 erosional rando wave runs (ER), 3 erosional onochroatic wave runs (EM), 7 accretionary rando wave runs (AR), 3 accretionary onochroatic wave runs (AM), and 5 dune erosion rando wave runs (DE). The first two nubers in the Wave Run ID 1A_6ER indicate the ajor data collection test, the letter A indicates a particular wave condition, and 6 describes the inutes of wave action. The erosional and accretionary cases are designed based on the Dean nuber N, 4
H b N = (9) wt where w = fall speed of the sedient, and T = wave period. Table 1. Suary of Selected Wave Runs and Input Wave and Beach Conditions (Notation is explained at the botto of the table). Wave Run ID H o T p s L o n N H b β s ξ H b _ h M H b _ l H sl _ h H sl _ l 1A_6ER.78 3. 14. 2 6.4.68.1.42.66.15.13.24 1A_13ER.78 3. 14. 2 6.8.68.9.38.67.15.1.23 1A_27ER.78 3. 14. 2 6.9.68.1.42.65.16.1.24 1B_2ER.71 3. 14. 3.3 6.6.65.14.58.63.17.1.23 1B_6ER.73 3. 14. 3.3 6.8.67.11.44.65.17.11.24 1B_13ER.72 3. 14. 3.3 7..69.9.36.67.18.12.25 1E_13ER.69 4.5 31.6 2 4.9.72.11.69.71.15.15.16 1E_2ER.69 4.5 31.6 2 5..74.12.77.72.15.15.18 1E_27ER.69 4.5 31.6 2 5.1.76.9.58.74.15.16.2 1F_11ER.66 4.5 31.6 3.3 5.1.75.9.58.72.18.15.26 1F_13ER.68 4.5 31.6 3.3 5.1.76.8.48.74.18.13.21 1F_17ER.69 4.5 31.6 3.3 5.1.76.8.5.73.2.12.24 G_6EM 1.5 3. 14. M 1. 1.18.1.43 1.18.1.11.3 G_14EM 1.4 3. 14. M 1.5 1.4.1.41 1.4.4.8.1 G_21EM 1.15 3. 14. M 1.8 1.7.9.39 1.7.4.11.2 3A_6AR.34 8. 99.9 3.3 1.6.41.14 2.24.4.6.24.8 3A_13AR.33 8. 99.9 3.3 1.6.39.13 2.9.38.6.24.9 3A_2AR.34 8. 99.9 3.3 1.6.41.13 2.2.4.6.25.1 3C_13AR.31 9. 126.4 2 1.4.4.13 2.36.4.4.18.5 3C_2AR.31 9. 126.4 2 1.4.39.15 2.31.38.4.19.6 3C_27AR.31 9. 126.4 2 1.4.39.15 2.6.38.4.2.6 3D_4AR.37 9. 126.4 2 1.4.41.13 2..42.5.17.7 I_8AM.6 8. 99.9 M 2.9.76.2 2.78.76.1.38.3 I_29AM.63 8. 99.9 M 3.1.81.17 2.35.81.1.34.2 I_59AM.6 8. 99.9 M 2.7.72.12 1.64.73.1.25.3 6A_4DE.69 3. 14. 3.3 6.2.61.12.55.58.14.16.24 6A_6DE.69 3. 14. 3.3 6.2.61.1.46.6.14.12.24 6B_2DE.64 4.5 31.6 3.3 4.4.66.11.74.63.15.18.24 6B_4DE.63 4.5 31.6 3.3 4.4.66.11.76.62.16.18.25 6B_6DE.65 4.5 31.6 3.3 4.4.66.12.79.63.17.18.3 n = spectral peakedness; β s. = beach slope defined as the slope of the section approxiately 1 landward and 1 seaward of the shoreline; H b _ h = incident band wave height at the breaker line; H b _ l = low frequency band wave height at the breaker line; H sl _ h = incident band wave height at the shoreline; H sl _ l = low-frequency band wave height at the shoreline. Beach Profile Change Typically, erosion is defined as a net offshore transport of sand resulting in a loss of beach volue above the ean water line. Accretion is defined as a total net onshore transport of sand, building the beach above ean water level. As expected, a larger Dean nuber N resulted in erosion, and a saller N induced accretion (Table 1). Significant profile change occurred during the first erosional wave run case, 1A, over the onotonic initial profile (Eq. 8). Substantial shoreline recession occurred along with the developent of an offshore bar (Fig. 2A). Initially, the foreshore exhibited a convex shape while the end profile was concave. The 27-in profile was substantially steeper near the shoreline than the initial profile. A bar fored after 6 in of wave action. 5
After 27 in, the bar oved 4 further offshore. The axiu beach-face recession occurred at the +.37 contour line. The subsequent wave runs were conducted over the barred beach. The beach-profile changes are detectable, but uch ore subtle. Fig. 2B shows an exaple of shoreline accretion and onshore bar oveent. Elevation relative to MWL () A 1.8 1.2.6 -.6-1.2-1.8 1A: Equilibriu Erosion (Rando) initial 6 in 13 in. 27 in. Ho =.8 Tp = 3 s n = 2 5 1 15 2 25 3 35 Distance () Elevation relative to MWL () B 1.8 1.2.6 -.6-1.2-1.8 3D: Equilibriu Accretion (Rando) initial 4 in Ho =.5 Tp = 9 s n = 2 5 1 15 2 25 3 35 Distance () Fig. 2. (A) Bar developent over onotonic equilibriu beach-profile, and (B) profile developed under accretionary rando waves In soe of the erosional wave runs, a scarp developed (Fig 3A). Beach slope iediately seaward of the scarp tends to be steeper than on a non-scarped beach. The nearly vertical scarp had significant influence on the wave runup, liiting the swash uprush abruptly. Monochroatic waves tend to create erratic and undulating profiles (Fig 3B), in contrast to the sooth profiles under rando waves, likely because of wave reflection. The erratic profile evolution did not see to approach a stable equilibriu 6
shape. In addition, the profile shape developed under onochroatic waves does not represent profiles typically easured in the field (Wang and Davis 1998). Elevation relative to MWL () 1.8 1.2.6 -.6-1.2 6A: Scarp initial 4 in. 6 in. Ho =.7 Tp = 3 s n = 3.3 Elevation relative to MWL () -1.8 A 1.8 1.2.6 -.6-1.2 5 1 15 2 25 3 35 Distance () I: Equilibriu Accretion (Monochroatic) Ho =.5 Tp = 8 s MON B -1.8 initial 8 in 29 in 59 in 5 1 15 2 25 3 35 Distance () Fig. 3. (A) Scarp developent, and (B) beach profiles under onochroatic waves. The tie-series of beach profiles (e.g., Figs. 2 and 3) were exained to deterine the trend of erosion or accretion, and the upper and lower liits of change during each wave run (Table 2). Table 2 also suarizes the easured and predicted liits of wave runup, discussed in the following section. For the scarped cases, the upper liit of profile change was at the top of the scarp. Thus, it is controlled by the height of the beach ber or dune, and does not directly represent the extent of wave action. In 7
Table 2, the listed upper liit used for the scarped cases was the elevation of the scarp toe. The purpose is to link toe erosion or accretion to the wave condition. For the studied 3 wave runs, the incident breaking wave height ranged fro.39 to 1.18 (Table 2). The easured upper liit of profile change, including the scarped cases, ranged fro.27 to.7. The lower liit of beach change ranged fro.65 to 1.61. Relationship between the profile change and wave condition is discussed in the following sections. Table 2. Suary of Upper and Lower Liit of Beach Changes and Measured and Predicted Wave Runup Equations. Wave Run ID H b R ax UL LL Scarp Eq 4 Eq 6 M Eq 7 Eq 1 1A_6ER.68.6.66 1.29 No.59.43.31.68 1A_13ER.68.6.66 1.29 No.59.4.29.68 1A_27ER.68.7.66 1.29 No.59.43.31.68 1B_2ER.65.33.67 1.35 No.54.49.38.65 1B_6ER.67.7.67 1.35 No.55.42.31.67 1B_13ER.69.64.67 1.35 No.55.36.26.69 1E_13ER.72.77.74 1.52 No.52.53.46.72 1E_2ER.74.78.84 1.52 No.52.58.51.74 1E_27ER.76.45.84 1.52 No.52.47.41.76 1F_11ER.75.4.43 1.52 Yes.5.45.4.75 1F_13ER.76.38.42 1.52 Yes.52.41.36.76 1F_17ER.76.45.48 1.52 Yes.52.42.36.76 G_6EM 1.18.28.38 1.61 No.78.58.36 1.18 G_14EM 1.4.18.25 1.61 Yes.77.56.35 1.4 G_21EM 1.7.32.27 1.61 Yes.85.6.35 1.7 3A_6AR.41.41.31 1.36 No.28.7.72.41 3A_13AR.39.43.31 1.36 No.27.64.66.39 3A_2AR.41.42.31 1.36 No.28.64.66.41 3C_13AR.4.4.39 1.1 No.25.67.73.4 3C_2AR.39.42.42 1.1 No.25.73.79.39 3C_27AR.39.42.42 1.1 No.25.73.79.39 3D_4AR.41.23.43.65 No.3.69.76.42 I_8AM.76.27.46 1.82 No.46 1.51 1.27.76 I_29AM.81.16.53 1.82 No.48 1.35 1.12.81 I_59AM.72.35.53 1.82 Yes.46.94.8.72 6A_4DE.61.17.28 1.16 Yes.52.45.34.61 6A_6DE.61.17.28 1.16 Yes.52.4.29.61 6B_2DE.66.16.38.99 Yes.49.52.45.66 6B_4DE.66.16.38.99 Yes.48.52.45.66 6B_6DE.66.17.38.99 yes.5.56.48.66 R ax = easured axiu wave runup; UL, LL = upper and lower liit of beach change, respectively. Wave Runup Measured and predicted wave runup is suarized in Table 2. Three exaples, a rando wave run without scarp (Fig. 4A), a rando case with scarp (Fig. 4B), and a onochroatic case (Fig. 4C), are given. The non-scarp rando wave cases are ost copatible with existing field studies. The easured wave runup for the scarp cases are uch lower than that for the non-scarp cases, apparently liited by the steep scarp. Wave runup generated by onochroatic waves is also uch saller than that by rando waves with siilar statistical wave height and period. 8
ean water level ().8.6.4.2 -.2 A 1A_ER 2 4 6 8 distance () 6 in 13 in 27 in ean water level ().2.1 6A_DE B -.1 2 4 6 8 distance () 4 in 6 in ean water level ().4.3.2.1 I_AM C -.1 2 4 6 8 distance () 8 in 29 in 59 in Fig. 4. Exaples of wave runup under rando wave (A), over a scarped beach, and (B) under onochroatic waves (C). 9
A direct relationship between the easured runup height on non-scarp beach and breaker height as developed with the SUPERTANK data is: Rax = 1. Hb (1) Copared to the various existing epirical forulas, Eq. (1) adopts the approach introduced by Guza and Thornton (1982) and is siple, involving only the breaking wave height. Except for three wave runs, the observed wave runup equals the breaking wave height. Eq. (1) reproduced the easured values closely (Fig. 5). Agreeent between easured and predicted values was reduced by including the surf siilarity paraeter, ξ. Eqs. (6) and (7) under-predicted the easured wave runup significantly for the erosional cases with steep waves, while over-predicted for accretionary cases. Loss of predictive capability is caused by the substantially greater ξ for the gentle long-period accretionary waves than the steep short-period erosional waves (Table 1)..9.8 Swash Runup ().7.6.5.4.3.2.1 3D_4AR 3C_27AR 3C_2AR 3C_13AR 3A_2AR 3A_13AR 3A_6AR 1E_27ER 1E_2ER 1E_13ER 1B_13ER 1B_6ER 1B_2ER 1A_27ER 1A_13ER 1A_6ER Wave Run No. easured Eq. 1 Eq. 6 Eq. 7 Fig. 5. Coparison of easured and predicted wave runup by three equations. Douglass (1992) re-analyzed the Holan (1986) data set and found no correlation between runup and beach-face slope. He further argued that beach slope is a dependent variable that is free to respond to the incident wave energy and should not be included in a runup prediction. In practice, beach face slope is a difficult paraeter to define and deterine. Except for Stockdon et al. (26), a clear definition of beach slope is not given in ost studies. However, the Stockdon et al. definition of beach slope is difficult to utilize. In the present paper, the slope is defined over that portion of the beach extending roughly 1 landward and seaward fro the shoreline. The accretionary cases tend to have greater slope,.13 to.2, whereas the erosional case have slopes of.8 to.14 (Table 1). Exaination of Fig. 3 indicates that the beach face is curved instead of planar. Therefore, substantially different beach slopes can be obtained by iposing different definitions. Including the beach slope thus adds abiguity in applying the 1
epirical forulas. Deterining offshore wave height ay also cause uncertainty. In ost field studies, the offshore wave height was taken to be that easured at a wave gage in the study area. Siilarly, here it is taken as that fro the offshore-ost gauge. Under extree stor conditions, estiating the offshore wave height ay not be straightforward (Wang et al. 26). One of the first epirical forulas (Eq. 4) predicting the significant runup height R was developed by Guza and Thornton (1982) based on field easureents. As discussed previously, wave runup height easured here is expected to approxiate the axiu runup R ax. If a Raleigh distribution of wave height is assued, the axiu wave height should be 1.4 ties the significant height. Multiplying the proportional constant of.71 in Eq. (4) by 1.4 yields approxiately 1, which is the epirical coefficient obtained here. Therefore, the siple forula found in this study agrees with the for found by Guza and Thornton (1982). It has been docuented in any field studies perfored on gently sloping beach that the swash otion and, therefore runup, is doinated by low-frequency wave energy. Typically, the low-frequency energy is defined as that carried by the wave coponents exceeding twice the incident peak period. The agnitudes of the incident and lowfrequency energy are copared at the breaker line, H b _ h and H b _ l, and at shoreline, H sl _ h and H sl _ l (Table 1). For onochroatic waves, little low-frequency energy was easured at the breaker line and the shoreline. Lack of low-frequency odulation ay explain the relatively low swash runup easured during the regular wave cases (Table 2). For the rando wave cases, energy fro the incident band doinates at the breaker line (Table 1). The incident-band energy decreased significantly at the shoreline, whereas the low-frequency energy increased. This is readily apparent for the short-period steep erosional waves, where low-frequency energy doinated at the shoreline. The wave spectral peakedness n does not see to have great influence on this trend. For the longer period gentle accretionary waves, the decrease of incident-band energy was not as rapid and low-frequency energy did not becoe the doinant band at the shoreline (Table 1). The low-frequency coponent is defined dynaically here as exceeding twice the incident peak period. For the erosional waves, the low-frequency coponent starts at 6 or 9 s, whereas for the longer accretionary waves, it starts at 16 or 18 s. Relationship between Wave Runup and Liit of Beach-Profile Change A ajor goal of studying the axiu wave runup is to predict the upper liit of beach changes. Knowledge of the axiu runup is valuable in evaluating the liit of storinduced beach or dune erosion. For the rando wave runs without scarps, the easured upper liit of beach-profile change roughly equals the easured wave runup (Fig. 6). Thus, the wave runup, predictable using significant breaking wave height, can be directly used to calculate the upper liit of beach erosion. For cases with beach or dune scarps, the upper liit of the beach change is controlled by the elevation of the backbeach ber or dune (Fig. 3A). Once a scarp fors, the overlying sedient will eventually collapse under gravity and cause significant change above the upward liit of 11
water excursion. The easured wave runup is subdued by the nearly vertical scarp and the steep beach slope directly seaward of the scarp; and it cannot be predicted by known epirical forulas. Beach-profile change under onochroatic waves differs greatly fro that under the ore realistic rando waves. Both wave runup and upper liit of beach-profile change are significantly saller than those under rando waves with siilar statistical wave height and period. Findings fro laboratory onochroatic ovable-bed studies are not directly applicable to field conditions, as also discussed by Wang and Kraus (25). Although not a focus of this study, the lower liit of beach changes was also easured and is listed in Table 2. Typically, the lower liit of beach-profile change is 1.5 to 3 ties the significant breaking wave height. Longer period waves see to influence beach change in deeper water (~ 3 ties H s ), as copared to shorted period waves (~ 2 ties H s ). It was beyond the scope of this paper to exaine factors controlling the lower liit of the beach change. 1.4 1.2 Breaking Wave Height Beach Change Wave Runup Monochroatic Wave Cases Upper Liit () 1.8.6.4 Non-scarped Rando Wave Cases Scarped Rando Wave Cases.2 1A_6ER 1A_27ER 1B_6ER 1E_13ER 1E_27ER 3A_13AR 3C_13AR 3C_27AR Wave Run No. 1F_13ER 6A_4DE 6B_2DE 6B_6DE G_6EM G_21EM I_29AM Fig. 6. Coparison of wave runup, upper liit of beach change, and breaking wave height. CONCLUDING DISCUSSION SUPERTANK s unique dataset was analyzed to exaine the effects of elevated water level caused by wave setup and swash runup on the upper liit of beach and dune change. Thirty SUPERTANK wave runs were investigated. The investigated runs deonstrate that the Dean Nuber is a reliable indicator for predicting the general trend of beach erosion and accretion. In fact, the SUPERTANK experients were designed in this way (Kraus and Sith 1992). The SUPERTANK data indicate that the vertical extent of wave runup above ean water 12
level on a non-scarped beach is approxiately equal to the significant breaking wave height. A siple epirical forula for predicting the axiu wave runup, Rax: Rax = 1. Hb, is therefore developed. This forula agrees with the original runup forula concept of Guza and Thornton (1982). The reliability of the calculated wave runup decreased, as copared to easured values, by including the surf siilarity paraeter. An exception to the direct relationship between breaking wave height and runup concerns dune or beach scarping. The steep scarp substantially liits the uprush of swash otion, resulting in a uch reduced axiu level, as copared with the non-scarping situation. For onochroatic waves, the easured wave runup is uch saller than the breaking wave height. The lack of low-frequency odulation liits the wave runup for onochroatic waves. Based on the SUPERTANK experients, the upper liit of beach-profile change was found to be approxiately equal to the axiu vertical excursion of swash runup. Therefore, the liit of swash runup can serve as an estiate of the landward liit of beach change. Physical situations that are exceptions to this direct relationship are those with beach or dune scarping. For the scarping cases, the upper liit of beach change is uch higher than the axiu swash runup and is controlled by the elevation of backbeach/ber or dune. ACKNOWLEDGEMENTS This study was jointly funded by the Coastal Inlets Research Progra (CIRP) conducted by the U.S Ary Corps of Engineers (USACE), and by the University of South Florida. Perission was granted by Headquarters, USACE, to publish this inforation. REFERENCES Battjes, J.A. 1974. Coputations of set-up, longshore currents, run-up overtopping due to wind-generated waves. Rep. 74-2, Delft Univ. Technol., Delft, The Netherlands. Bowen, A.J., Inan, D.L., and Sions, V.P. 1968. Wave set-down and set-up. J. Geophys. Res., 73(8), 2569-2577. Bowen, A.J., and Guza, R.T. 1978. Edge waves and surf beat. J. Geophys. Res., 83(4), 1913-192. Bruun, P. 1954. Coastal erosion and the developent of beach profiles. Tech. Meo. No. 44, Beach Erosion Board, U.S. Ary Corps of Engineers. Dean, R.G. 1977. Equilibriu beach profiles: U.S. Atlantic and Gulf coasts. Ocean Engineering Rep. No. 12, Dept. of Civil Eng., Univ. of Delaware, Newark, DE. Douglass, S.L. 1992. Estiating extree values of run-up on beaches. J. Waterway, Port, Coastal and Ocean Eng., 118, 22-224. Gallagher, B. 1971. Generation of surf beat by non-linear wave interactions. J. Fluid Mech., 49(1), 1-2. Guza, R.T., and Thornton, E.B. 1981. Wave set-up on a natural beach. J. Geophys. Res., 86(C5), 4133-4137. Guza, R.T., and Thornton, E.B. 1982. Swash oscillations on a natural beach. J. Geophys. Res. 87(C1), 483-49. Holland, K.T., Raubenheier, B., Guza, R.T., and Holan, R.A. 1995. Runup 13
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