Journal of Coastal Research SI 59 7-14 West Palm Beach, Florida 2011   Recent Capabilities of CMS-Wave: A Coastal Wave Model for Inlets and Navigation Projects Lihwa Lin†, Zeki Demirbilek†, and Hajime Mase‡ †U.S. Army Engineer Research & Development Center, ‡Disaster Prevention Research Institute 3909Halls Ferry Road Kyoto University, www.cerf-jcr.org Vicksburg, MS 39180-6199, USA Gokasho, Uji, Kyoto, 611-0011, Japan [email protected] ABSTRACT LIN, L.; DEMIRBILEK, Z., and MASE, H., 2011. Recent Capabilities of CMS-Wave: A Coastal Wave Model for Inlets and Navigation Projects. In: Roberts, T.M., Rosati, J.D., and Wang, P. (eds.), Proceedings, Symposium to Honor Dr. Nicholas C. Kraus, Journal of Coastal Research, Special Issue, No. 59, pp. 7-14. West Palm Beach (Florida), ISSN 0749-0208. The Coastal Inlets Research Program (CIRP) of the U.S. Army Engineer Research and Development Center (ERDC), Coastal and Hydraulics Laboratory (CHL) has developed a nearshore spectral wave transformation numerical model to address needs of the U.S. Army Corps of Engineers (USACE) navigation projects. The model is called CMS- Wave and is part of Coastal Modeling System (CMS) for wave estimates in the vicinity of coastal and estuarine navigation channels. It can simulate important wave processes at coastal inlets including wave diffraction, refraction, reflection, wave breaking and dissipation mechanisms, wave-current interaction, and wave generation and growth.  This paper describes recent improvements in CMS-Wave that include semi-empirical estimates of wave run-up and overtopping, nonlinear wave-wave interactions, and wave dissipation over muddy bottoms. CMS-Wave may be used with nested grids and variable rectangular cells in a rapid mode to assimilate full-plane wave generation for circulation and sediment transport models. A brief description of these recent capabilities is provided.  ADDITIONAL INDEX WORDS: Navigation, coastal inlets, numerical wave modeling, nearshore wave processes. INTRODUCTION The focus of this paper is to provide a brief description of some recent capabilities added to the model. Improved and practical wave models are needed for USACE CMS-Wave can represent important coastal wave processes navigation mission dealing with wave transformation in the including diffraction, refraction, reflection, wave breaking and vicinity of coastal inlets, estuaries and river mouths, harbors, dissipation mechanisms, wave-current interaction, and wave and navigation channels. Wave interaction with coastal jetties, generation and growth. The wave diffraction is calculated in the breakwaters and revetments requires modeling wave reflection, wave-action balance equation by an additional term. Recent diffraction, transmission and overtopping for accurate wave features incorporated for grid nesting, variable rectangle cells, estimates of channel infilling and potential breaching or flanking wave run-up and overtopping, and assimilation of full-plane of structures. Calculations are required for wave propagation wave generation are to support circulation and sediment across channels as well as over or through structures, where transport studies. Details of the theory and numerical combined wave diffraction and transmission are present implementation are presented in the CMS-Wave technical report simultaneously. Wave run-up and overtopping of structures are (Lin et al., 2008), including a number of examples of practical frequently needed. To address these needs, a spectral wave applications. In this paper, we provide validation for wave run- transformation model called CMS-Wave has been developed to up, transmission and overtopping of structures with laboratory support the operation and maintenance of coastal inlet and data, wave dissipation over muddy beds and nonlinear wave- navigation projects, also the risk and reliability assessment of wave interaction with the field and experiment data. shipping in inlets and harbors. It is a steady-state half-plane wave transformation model, where wave energy propagation is WAVE-ACTION BALANCE EQUATION independent of time and calculated from seaward towards the coastal boundary. Wave reflection off coastal structures and CMS-Wave calculates the spectral wave transformation based beaches is included in CMS-Wave. The workings and on the wave-action balance equation (Lin et al., 2008): performance of model have been described by Lin et al. (2006 and 2008), Seabergh et al. (2008), and Demirbilek et al. (2009). C N C N C N x  y    ____________________ x y  DM©O aCyIo: 2 a 01st10a0.l2 .E 11d2u/cSaIt5io9n-0 &02 R.1e s reeacrcehiv eFdo u2n8d Saetipotne m20b1er1 2009; accepted 18 2CCgcos2NyyCC2gcos2NyySinSdpSnl (1) Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 3. DATES COVERED 2011 2. REPORT TYPE 00-00-2011 to 00-00-2011 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Recent Capabilities of CMS-Wave: A Coastal Wave Model for Inlets and 5b. GRANT NUMBER Navigation Projects 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) 8. PERFORMING ORGANIZATION U.S. Army Engineer Research and Development Center,Coastal and REPORT NUMBER Hydraulics Laboratory,3909 Halls Ferry Road,Vicksburg,MS,39180 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT The Coastal Inlets Research Program (CIRP) of the U.S. Army Engineer Research and Development Center (ERDC) Coastal and Hydraulics Laboratory (CHL) has developed a nearshore spectral wave transformation numerical model to address needs of the U.S. Army Corps of Engineers (USACE) navigation projects. The model is called CMSWave and is part of Coastal Modeling System (CMS) for wave estimates in the vicinity of coastal and estuarine navigation channels. It can simulate important wave processes at coastal inlets including wave diffraction, refraction reflection, wave breaking and dissipation mechanisms, wave-current interaction, and wave generation and growth. This paper describes recent improvements in CMS-Wave that include semi-empirical estimates of wave run-up and overtopping, nonlinear wave-wave interactions, and wave dissipation over muddy bottoms. CMS-Wave may be used with nested grids and variable rectangular cells in a rapid mode to assimilate full-plane wave generation for circulation and sediment transport models. A brief description of these recent capabilities is provided. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF ABSTRACT OF PAGES RESPONSIBLE PERSON a. REPORT b. ABSTRACT c. THIS PAGE Same as 8 unclassified unclassified unclassified Report (SAR) Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 8 Lin, Demirbilek, and Mase _________________________________________________________________________________________________ where N = E / σ is the frequency and direction dependent wave- action density, defined as the wave energy-density E = E (x, y, σ, θ) divided by the intrinsic frequency . N and N denote the y yy first and second derivatives with respect to y; x and y are the horizontal coordinates;  is the wave direction measured counterclockwise from the x-axis; C and C are wave celerity g and group velocity; C, C, and C are the characteristic velocity x y  with respect to x, y, and , respectively.  is an empirical parameter representing the intensity of wave diffraction effect. The right-hand side terms respectively are: S is the source (e.g., in wind input), S is the sink (e.g., bottom friction, wave breaking, dp whitecapping, etc.), and S is the nonlinear wave-wave nl interaction. The first term on the right side of Equation 1 is the wave diffraction term formulated from a parabolic approximation wave theory (Mase, 2001). In applications, the diffraction intensity parameter  ( 0) needs to be calibrated and optimized for featured structures. The model omits the diffraction effect for  = 0 and calculates the diffraction for  > 0. In practice, the value of  may range from 0 (no diffraction) to 4 (strong diffraction) for calculating diffraction effects. A constant value of  = 2.5 has been used by Mase et al. (2001, 2005a, 2005b) to simulate wave diffraction for narrow and wide gap breakwater Figure 1. CMS-Wave grid and data-collection stations at Grays Harbor, applications. Lin et al. (2008) and Demirbilek et al. (2009) WA. USA. demonstrate that value of  = 4 is appropriate for semi-inifinite long breakwaters and also in narrow gaps (inlets) with openings equal or less than one wavelength. For wider gaps with the opening greater than one wavelength,  = 3 is recommended. The exact value of  in an application is dependent on the structure’s geometry, local bathymetry and incident wave conditions, and may need to be fine-tuned with data. The default value of = 4 is used in the model, corresponding to strong diffraction. Implementation of wave diffraction is approximate, and phase-resolving wave models (Holthuijsen et al., 2004) may be used to verify estimate of waves near structures, inlets and harbors. Figures 1 and 2 show an example of the CMS-Wave computational domain and calculated wave results at four different locations (HMB1 to HMB4), respectively, at Half- Moon Bay in Grays Harbor entrance, Washington, USA. Osborne and Davies (2004) described the field data collection in Grays Harbor. Numerical simulation is conducted for December 10 through 31, 2003. The input wind and wave data were obtained from the National Data Buoy Center (NDBC - http://www.ndbc.noaa.gov) Station 46029 and Coastal Data Information Program (http://cdip.ucsd.edu) Buoy 036 (NDBC 46211), respectively. CMS-Wave was run in the coupled mode with a CMS-Flow model (Buttolph et al., 2006; http://cirp.usace.army.mil/products) that provided calculated water level and current input fields. The effect of current on waves (H shown in Figure 2 is the significant height defined as s the mean of the highest 1/3 wave height ) is pronounced at gauges HMB1 and HMB2 located closer to the navigation channel in relatively deep water. Comparison of simulation results with the field data shows that shallow water effects on Figure 2. Measured and calculated waves at HMB1 to 4, 10-31 wave diffraction, refraction, and breaking are evident at HMB3 December 2003. and HMB4. Journal of Coastal Research, Special Issue No. 59, 2011 Recent Capabilities of CMS-Wave  9 _________________________________________________________________________________________________ WAVE RUN-UP while Mase and Iwagaki (1984) specified the incident wave by JONSWAP spectrum (Hasselmann et al., 1973) as follows: The wave run-up consists of two components: (a) a rise of the mean water level resulting from wave breaking at the shore, E () J known as the wave setup η, and (b) swash oscillation of the  g2       ifnrocmid etnhte whoarvizeos.n tTalh em owmaevnet usmet uepq uiant ioCnMs bSy-W neagvlee citsi ncgo cmuprruetnetd, 5 exp1.25( m)4explnexp[0.5( mm)2] (9) surface wind drag and bottom stresses as where , are scale and shape parameters, and  ,  are     η 1 S S       (2)  m   xx  xy spectral peak frequency and peak-enhancement factor, x ρgh  x y  respectively. Incident waves in Ahrens and Titus are converted     η 1 Sxy Syy      (3)  to a JONSWAP spectrum as input to CMS-Wave using the y ρgh  x y  relationship of derived from Equations 8 and 9. 2(Q 3)3 p Figure 3 shows the calculated and measured R . Overall, where , g, h are the water density, gravitational acceleration 2% calculated run-up estimates agree with data; the correlation and water depth, respectively. Three radiation stress components coefficient for all cases is 0.83 (Lin et al., 2008). For steeper S , S , S are calculated using the linear wave theory (Dean xx xy yy slopes (1:1 to 2:3), the model tends to overpredict R and Dalrymple, 1984) as 2% suggesting Equation 7 is more accurate for mild slopes.  1 (4) Sxx En(cos2θ1)2dθdσ  1 (5) SyyEn(sin2θ1)2dθdσ S  Ensin2θdθdσ (6) xy 2 where and k is the wave number. The swash 1 kh n  2 sinh2kh oscillation of waves on the beach face is a random process. In engineering applications, the 2-percent runup defined as exceedance of the vertical level is commonly used and denoted as R (or R2). Komar (1998) gives an estimate of R on 2% 2% beaches, seawalls and jetties as R 2|η| (7) 2% The R is calculated using Equation 7 at the land-water 2% interface and averaged with the local depth to determine if water can flood the dry cells. If the wave run-up level is higher than elevation of adjacent dry land cells, these cells are flooded to simulate the overtopping and overwash at these cells. Wave run-up calculation in CMS-Wave is verified with data collected from two laboratory studies of random wave up-rush on plane smooth slopes (Ahrens and Titus, 1981; Mase and Figure 3. Measured and calculated 2% exceedence wave runup. Iwagaki, 1984). There are together a total of 395 run-up cases from these two studies covering a broad range of plane slope (1:1 to 1:30) and incident spectrum. Ahrens and Titus (1981) WAVE TRANSMISSION AND OVERTOPPING OF characterized the incident wave by the spectral peak frequency STRUCTURES and a wave group parameter (Goda, 1970) defined as Wave transmission over low-crested or submerged impermeable structures is exhibited by fall of the overtopping 2E2()d Q  , water mass. The ratio of structure crest elevation to incident p [E()d]2 wave height is a key parameter governing the wave transmission. CMS-Wave calculates the transmission coefficient where E()E(,)d (8) K, defined as the transmitted wave height divided by the t incident wave height, based on the simple expression (Goda, 2000): Journal of Coastal Research, Special Issue No. 59, 2011 10 Lin, Demirbilek, and Mase _________________________________________________________________________________________________ K 0.3 (1.5hc ), for 0 hc 1.25 (10) Wave overtopping rate is calculated using two different t H H methods. In a coupled CMS-Wave and CMS-Flow simulation i i (e.g., flow model gets radiation stresses from wave model and where h is the crest elevation of the breakwater above the still- c provides calculated current and water levels to wave model), the water level (hc is negative for a submerged breakwater), and Hi overtopping rate is the flow rate calculated by CMS-Flow. is the incident wave height. For a composite breakwater, Without coupling, CMS-Wave calculates the average protected by a mound of armor units at its front, K is calculated overtopping rate using the empirical formula of Hughes (2008) t (Goda, 2000) as given by  h 1.58 (13) Kt 0.3 (1.1Hhc ), for 0Hhc 0.75 (11) q gHi30.03360.53Hci  i i Table 2 provides comparison of the calculated average For permeable rubble-mound breakwaters, the transmission is overtopping rates obtained with decoupled and coupled CMS calculated using d’Angremond et al. (1996) formula as runs performed for laboratory measurements of Hughes (2008) for four incident irregular waves and two steady storm surges (cid:2022) (cid:1828) (cid:1860) (cid:1837) (cid:3404)0.64(cid:3428)1(cid:3398)exp(cid:3436)(cid:3398) (cid:3440)(cid:3432)(cid:4666) (cid:4667)(cid:2879)(cid:2868).(cid:2871)(cid:2869)(cid:3398)0.4 (cid:3030),for (cid:1828)(cid:3407)10 (cid:1834) overtopping a levee. In the simulation of higher surge (water (cid:3047) 2 (cid:1834)(cid:3036) (cid:1834)(cid:3036) (cid:3036) level = 1.3 m) and larger waves (incident wave height = 2.3 m), (12) the calculated overtopping rates from the CMS-Wave alone agree better with data than results from the coupled run. This where B is the crest width and  is the Iribarren parameter suggests that empirical formulas used in CMS-Wave for defined as the fore-slope of the breakwater divided by the overtopping, runup and transmission need further verification square-root of deepwater incident wave steepness. In practice, with data to determine appropriateness of each formula. Equations 10 to 12 are applicable to both monochromatic and random waves. Figure 4 shows the calculated transmission coefficients and data curves compiled by Goda (2000) for a Table 1. Comparison of transmission coefficients, Kt vertical breakwater. In these simulations, CMS-Wave was forced by a monochromatic wave of 1 m and 6 sec for a vertical h (m) Vertical Breakwater Composite Breakwater c breakwater with h = 10 m, d = 5 m, and B = 20 m. Table 1 Data (Goda, 2000) Eq. 10 CMS-Wave Eq. 11 CMS-Wave shows comparison of calculated transmission coefficients and -2 1.02 1.02 laboratory data compiled by Goda (2000), and Equations 10 and -1.5 1.03 1.03 11 for monochromatic incident waves. -1 0.76 0.78 0.78 -0.5 0.60 0.63 0.63 0 0.42 0.45 0.46 0.33 0.34 0.5 0.26 0.30 0.27 0.18 0.18 1 0.13 0.15 0.15 0.03 0.04 1.5 0.06 0.10 0.024 2 0.05 0.07 0.018  Table 2. Comparison of average overtopping rate (m2/sec) Exp No. Surge Wave Wave Measured Calculated Level Height Period (Hughes, 2008) (m) (m) (sec) CMS CMS-Wave R128 0.29 - - 0.27 0.28 - 0.82 6.1 0.38 0.38 0.39 R109 0.29 - - 0.26 0.28 - 2.48 13.7 0.70 0.85 0.92 R121 1.3 - - 2.55 2.57 - 2.3 6.1 2.67 2.93 2.76 R127 1.3 - - 2.54 2.57 - 2.3 14.4 2.84 2.98 2.81 WAVE-WAVE INTERACTIONS Figure 4. Measured and calculated transmission coefficients for a vertical breakwater. The exact solution of wave-wave interaction requires solving computationally expensive six-dimensional integral (Resio and Tracy, 1982). The wave-wave interactions in CMS-Wave are Journal of Coastal Research, Special Issue No. 59, 2011 Recent Capabilities of CMS-Wave  11 _________________________________________________________________________________________________ calculated using a modified method of Jenkins and Phillips (2001). They proposed a simple formula to represent wave-wave interactions as a second-order diffusion operator of the isotropic form that conserves the wave action. CMS-Wave implements this formula directly in the wave-action balance equation such that no additional integration is required to calculate wave-wave interactions. By keep only the first and second-order terms in the Jenkins-Phillips formulation, wave-wave interactions in finite water depth can be expressed as F 2F S a b (14) nl  2 where 1 is a function of kh, a , a [1(2n1)2cosh2kh]1 b 2n2 n and n4  3 (15) Fk35 ( m)4E (2)2g   The variation of a and b as functions of kh is shown in Figure 5. Nonlinear wave-wave interaction coefficients a and bσ as Figure 5, indicating that wave-wave interactions are more functions of kh. significant in the intermediate water depths and diminish in the shallow water. This is because wave-wave interactions initially take place in the deepwater, continue to evolve in the intermediate depth, and gradually diminish in shallow water. The effect of interactions on wave evolution is greater over long fetches in a large ocean domain and less in a local coastal region. Figure 6 shows the comparison of directionally integrated S from Equation 14 and exact computations in the nl examples of Hasselmann et al. (1985). These calculations are for the JONSWAP spectra with =2 and =5. Figure 7 shows the calculated nonlinear wave energy transfer rate S in the nl frequency and direction domain for a JONSWAP spectrum with =5. These calculated results are consistent with the observed and theoretical results that the nonlinear wave-wave interactions cause wave energy to transfer from high to low frequencies (downshifting). Figure 8 shows the calculated wave height fields with and without nonlinear wave-wave interactions at the Louisiana coast Figure 6. Comparison of directionally integrated S for JONSWAP in the north central Gulf of Mexico. The input wind and incident spectrum with γ =2 and 5. nl wave data are supplied by NDBC Buoy 42041 located approximately in the middle of offshore boundary. Figure 9 shows the corresponding wave period fields with and without the nonlinear wave energy transfer. The simulation is for the wave interaction can be rather small and insignificant in growth of an incident deepwater southeast wave of 0.3 m and 4 magnitude without the wind input. sec under a moderate 15-kt wind from southeast. With the The wave transformations near inlet jetties and in the wave nonlinear wave-wave interactions, the calculated wave height diffraction zone can be improved with the nonlinear wave-wave along the coast is about 10 percent higher than without the interactions. Figure 2 shows the comparison of calculated waves nonlinear energy transfer effect. The nonlinear wave-wave with and without the nonlinear energy transfer in Grays Harbor. interactions also increase wave periods over a larger coverage The calculated wave height with the nonlinear energy transfer is area, which is a consequence of wave energy transfer from about 5 percent higher than without the nonlinear energy higher to lower frequencies. Wind input was triggered in these transfer. This change is small and in practical applications can simulations. It should be noted that wind input can reveal better be neglected. More importantly, we note that the proposed new wave-wave interaction result because more wave energy from formulation that extends the Jenkins-Phillips original wind input can transfer from high to low frequencies. The wave- formulation from deepwater to finite depth should be Journal of Coastal Research, Special Issue No. 59, 2011 12 Lin, Demirbilek, and Mase _________________________________________________________________________________________________ Figure 7. Calculated non-linear energy transfer for a directional JONSWAP spectrum with γ =5. Figure 9. Calculated wave period field (a) with and (b) without non- linear wave energy transfer. viscous effect, the wave dissipation over a muddy bed can be expressed as (Lamb, 1932) S 4( )k2E (16) dp k t where  is the kinematic viscosity and  is the turbulent eddy k t viscosity. In the present study, is formulated by a maximum t viscosity  representing the wave breaking condition times the tb ratio of wave height over depth as   Hs . The value of tb t tb h is set to 0.04 m2/sec for the muddy bed and 0.01 m2/sec for the primary sand area based on model comparison with data. As an example, wave fields affected by muddy beds for the Louisiana coast are calculated and shown in Figures 8 and 9. In Figure 10, Figure 8. Calculated wave height field (a) with and (b) without non- CSI3 is the location of muddy bed, and CSI5 is for the primary linear wave energy transfer. sandy bed. These wave gauges were deployed by the Coastal Studies Institute (CSI) at Louisiana State University (Sheremet and Stone, 2003; Sheremet et al., 2005). Figure 11 shows the comparison of calculated and measured wave heights at gauges extensively tested in different depths with different wave and CSI3 and CSI5. The calculated wave heights at the muddy bed wind conditions. The robustness and consistency of our CSI3 using Equation 16 agree better with measurements as proposed formula must be validated with laboratory and field compared to those without the muddy bed effect included. For data and confirmed against other formulations. the more sandy location CSI5 away from the muddy area, the calculated wave heights are less affected by inclusion of the WAVE DISSIPATION OVER MUDDY BOTTOMS muddy bed effect .The present treatment of muddy bed does address the potential affect of mud on dynamics of waves as The wave dissipation over muddy beds in CMS-Wave is reported by other researchers (Sheremet, 20005; Kaihatu, calculated based on the assumption that the turbulent eddy 2008). The goal in the present study is to provide viscosity is several orders of magnitude greater than the approximate estimate of mud on spectral wave dissipation, kinematic viscosity of sea water. By neglecting the kinematic without using any complicated approaches. Journal of Coastal Research, Special Issue No. 59, 2011 Recent Capabilities of CMS-Wave  13 _________________________________________________________________________________________________ Other features can also be important concerning wave asymmetry in shallow water, infra-gravity waves for seiching in harbors, and surface roughness of breakwaters. Future companion papers in this series will address a more complete description of these nearshore wave processes. ACKNOWLEDGMENTS The authors are grateful to Dr. Nicholas C. Kraus for his continual support and encouragement for many years towards development and improvement of the capabilities of CMS-Wave to increase reliability of wave modeling in coastal inlets and navigation applications. The authors wish to thank the Coastal Studies Institute, Louisiana State University of U.S.A., for providing directional wave and current measurements off the Figure 10. Location of muddy bed, NDBC 42041, and CSI wave gauges. Louisiana coast. Permission was granted by the Chief, U. S. Army Corps of Engineers to publish this information. LITERATURE CITED Ahrens, J. P. and Titus, M. F., 1981. Laboratory data report: irregular wave runup on plane smooth slopes. Coastal Engineering Research Center unpublished Laboratory Report. Vicksburg, Mississippi: U.S. Army Engineer Waterways Experiment Station. Buttolph, A. M.; Reed, C. W.; Kraus, N. C.; Ono, N.; Larson, M.; Camenen, B.; Hanson, H.; Wamsley, T., and Zundel, A. K., 2006. Two-Dimensional Depth-Averaged Circulation Model CMS-M2D: Version 3.0, Report 2, Sediment Transport and Morphology Change. Coastal and Hydraulics Laboratory Technical Report ERDC/CHL-TR-06-7. Vicksburg, Mississippi: US Army Engineer Research and Development Center. Dean, R. G. and Dalrymple, R. A., 1984. Water wave mechanics for engineers and scientists. Englewood Cliffs, New Jersey: Figure 11. Measured (+) and Calculated (---) waves on muddy bed along Louisiana coast. Prentice-Hall, Inc. Demirbilek, Z.; Lin, L., and Seabergh, W.C., 2009. Laboratory and numerical studies of hydrodynamics near jetties. Coastal CONCLUSIONS Engineering Journal 51(2):143-175 JSCE. d’Angremond, K.; Van der Meer, J.W., and de Jong, R.J., 1996. This paper introduces some recent capabilities that have been Wave transmission at low-crested structures. Proceedings 25th added to CMS-Wave model. Due to space limitation, only a International Conference on Coastal Engineering, Orlando, brief description of the added features is provided and details of Florida, USA: ASCE, 2418-2427. these will be reported soon in technical reports and notes. Goda, Y., 1970. A synthesis of Breaker Indices. Transactions of Examples provided for the new capabilities are simply the Japan Society of Civil Engineers 2(2):227-230. comparisons to analytical solutions, other models and available Goda, Y., 2000. Random seas and design of maritime structures. data. The comparisons include wave run-up, wave transmission 2d ed. Singapore: World Scientific Publishing. over and through structures, wave-wave interactions, and wave Hasselmann, K.; Barnett, T. P.; Bouws, E.; Carlson, H.; energy dissipation on muddy beds. These new features Cartwright, D. E.; Enke, K.; Ewing, J. A.; Gienapp, H.; implemented in CMS-Wave may not be essential, but often are Hasselmann, D. E.; Kruseman, P.; Meerbrug, A.; Muller, P.; needed for wave estimates in coastal engineering applications Olbers, D. J.; Richter, K.; Sell, W., and Walden, H., 1973. near structures and in navigation channels, where wave-current Measurements of wind-wave growth and swell decay during and wave-structure interactions can become important and the Joint North Sea Wave Project (JONSWAP). Deutsche significant. Additional research is in progress to further evaluate Hydrographische Zeitschrift A80(12), 95p. the appropriateness of the proposed capabilities, which require Hasselmann, S.; Hasselmann, K.; Allender, J.H., and Barnett, extensive validation and verification before these new features T.P., 1985. Computations and parameterizations of the can be confidently used in the engineering practice. Once nonlinear energy transfer in a gravity wave spectrum. Part II. completed, a comprehensive mathematical description of these Parameterizations of the nonlinear energy transfer for new added features will be provided with validation examples. Journal of Coastal Research, Special Issue No. 59, 2011 14 Lin, Demirbilek, and Mase _________________________________________________________________________________________________ application in wave models. Journal of Physical Mase, H.; Amamori, H., and Takayama, T., 2005a. 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