Spectral Wave Modeling in Very Shallow Water at Southern Coast of Caspian Sea

Abstract

This study evaluates the capability of the Simulating WAves Nearshore (SWAN) wave model (version 41.01) in predicting significant wave height and spectral peak energy content for swell waves in very shallow water of surf zone during depth-induced wave breaking and dissipation. The model results were compared with field measurements at five nearshore stations. The results demonstrated that some breaker index formulations were successful for significant wave height prediction in surf zones. However, an incorrect shape of the energy spectrum and overestimated near spectral peak energy content at shallow water stations were obtained using all of the embedded depth-induced wave breaking formulations in SWAN. The dependent breaker index on relative depth (K _p d) formulation, which was successful in predicting near spectral peak energy content, resulted in an average error of 30%. Finally, this formulation was modified to enhance the model performance in reproducing the spectral peak energy content.

Keywords

Caspian Sea / Shallow water / SWAN / Spectral peak energy / Coastal processes

References

[1] Alsina J, Baldock T. Improved representation of breaking wave energy dissipation in parametric wave transformation models. Coast Eng, 2007, 54(10): 765-769

[2] Baldock T, Holmes P, Bunker S, Van Weert P. Cross-shore hydrodynamics within an unsaturated surf zone. Coast Eng, 1998, 34(3): 173-196

[3] Battjes J, Janssen J (1978). Energy loss and set-up due to breaking of random waves. Coastal Eng Proc, 1(16). https://doi.org/10.1061/9780872621909.034

[4] Battjes J, Stive M. Calibration and verification of a dissipation model for random breaking waves. J Geophys Res: Oceans (1978–2012), 1985, 90(C5): 9159-9167

[5] Becq F (1998). Extension de la modélisation spectrale des états de mer vers le domaine côtier

[6] Becq-Girard F, Forget P, Benoit M. Non-linear propagation of unidirectional wave fields over varying topography. Coast Eng, 1999, 38(2): 91-113

[7] Beji S, Battjes J. Experimental investigation of wave propagation over a bar. Coast Eng, 1993, 19(1): 151-162

[8] Benit M (2009). Formulation and quantification of the distributed collinear triad approximation TU Delft, M.Sc. thesis, Delft University of Technology UUID:2d1720e2-f4ce-4c6b-8e3d-1bd7d9f7cfa1

[9] Booij N, Ris R, Holthuijsen LH. A third-generation wave model for coastal regions: 1. Model description and validation. J Geophys Res: Oceans (1978–2012), 1999, 104(C4): 7649-7666

[10] Bottema M, van Vledder GP. A ten-year data set for fetch-and depth-limited wave growth. Coast Eng, 2009, 56(7): 703-725

[11] Dong G, Ma Y, Perlin M, Ma X, Yu B, Xu J. Experimental study of wave–wave nonlinear interactions using the wavelet-based bicoherence. Coast Eng, 2008, 55(9): 741-752

[12] Eldeberky Y (1996). Nonlinear transformation of wave spectra in the nearshore. Ph.D thesis, TU Delft, Delft University of Technology

[13] Eldeberky Y, Battjes J. Parameterization of triad interactions in wave energy models. Proc Coastal Dynamic, 1995, 95: 140-148

[14] Elgar S, Freilich M, Guza R. Model–data comparisons of moments of nonbreaking shoaling surface gravity waves. J Geophys Res: Oceans (1978–2012), 1990, 95(C9): 16055-16063

[15] Elgar S, Guza R, Freilich M. Observations of nonlinear interactions in directionally spread shoaling surface gravity waves. J Geophys Res: Oceans, 1993, 98(C11): 20299-20305

[16] Elgar S, Herbers T, Chandran V, Guza R. Higher-order spectral analysis of nonlinear ocean surface gravity waves. J Geophys Res: Oceans (1978–2012), 1995, 100(C3): 4977-4983

[17] Fenton J. Nonlinear wave theories. Sea, Ocean Eng Sci, 1990, 9: 3-25

[18] Goda Y. A 2-D random wave transformation model with gradational breaker index. Coast Eng J, 2004, 46(01): 1-38

[19] Goda Y. A performance test of nearshore wave height prediction with CLASH datasets. Coast Eng, 2009, 56(3): 220-229

[20] Goda Y. Reanalysis of regular and random breaking wave statistics. Coast Eng J, 2010, 52(01): 71-106

[21] Goda Y, Morinobu K. Breaking wave heights on horizontal bed affected by approach slope. Coast Eng J, 1998, 40(04): 307-326

[22] Gorrell L, Raubenheimer B, Elgar S, Guza R. SWAN predictions of waves observed in shallow water onshore of complex bathymetry. Coast Eng, 2011, 58(6): 510-516

[23] Groeneweg J, van der Westhuysen A, van Vledder GP, Jacobse S, Lansen J, van Dongeren A (2009). Wave modelling in a tidal inlet: performance of SWAN in the Wadden Sea. Proc. 31th Int. Conf. Coastal Eng., ASCE, City, 411–423. doi https://doi.org/10.1142/9789814277426_0035

[24] Hanson JL, Phillips OM. Automated analysis of ocean surface directional wave spectra. J Atmos Ocean Technol, 2001, 18(2): 277-293

[25] Hasselmann K. On the non-linear energy transfer in a gravity-wave spectrum part 1. General theory. J Fluid Mech, 1962, 12(04): 481-500

[26] Herbers T, Russnogle N, Elgar S. Spectral energy balance of breaking waves within the surf zone. J Phys Oceanogr, 2000, 30(11): 2723-2737

[27] Janssen T, Battjes J. A note on wave energy dissipation over steep beaches. Coast Eng, 2007, 54(9): 711-716

[28] Katsardi V, De Lutio L, Swan C. An experimental study of large waves in intermediate and shallow water depths. Part I: wave height and crest height statistics. Coast Eng, 2013, 73: 43-57

[29] Lippmann T, Brookins A, Thornton E. Wave energy transformation on natural profiles. Coast Eng, 1996, 27(1): 1-20

[30] Mahmoudof SM, Badiei P, Siadatmousavi SM, Chegini V. Observing and estimating of intensive triad interaction occurrence in very shallow water. Cont Shelf Res, 2016, 122: 68-76

[31] Marshall RJ, Stephenson WJ. The morphodynamics of shore platforms in a micro-tidal setting: interactions between waves and morphology. Mar Geol, 2011, 288(1): 18-31

[32] Masselink G. Field investigation of wave propagation over a bar and the consequent generation of secondary waves. Coast Eng, 1998, 33(1): 1-9

[33] Najafi-Jilani A, Nik-Khah A. Development of integrated marine monitoring network on southern coastline of Caspian Sea. Int J Naval Architect Ocean Eng, 2011, 3(2): 136-140

[34] Nelson RC. Design wave heights on very mild slopes―an experimental study. Transactions of the Institution of Engineers, Australia. Civ Eng, 1987, 29(3): 157-161

[35] Rattanapitikon W, Vivattanasirisak T, Shibayama T. A proposal of new breaker height formula. Coast Eng J, 2003, 45(01): 29-48

[36] Ris R, Holthuijsen L, Booij N. A third-generation wave model for coastal regions: 2. Verification. J Geophys Res: Oceans (1978–2012), 1999, 104(C4): 7667-7681

[37] Robertson B, Hall K, Zytner R, Nistor I. Breaking waves: review of characteristic relationships. Coast Eng J, 2013, 55(01): 1350002

[38] Ruessink B, Walstra D, Southgate H. Calibration and verification of a parametric wave model on barred beaches. Coast Eng, 2003, 48(3): 139-149

[39] Rusu E. Wave energy assessments in the Black Sea. J Mar Sci Technol, 2009, 14(3): 359-372

[40] Rusu E, Onea F. Evaluation of the wind and wave energy along the Caspian Sea. Energy, 2013, 50: 1-14

[41] Salmon J, Holthuijsen L, Zijlema M, van Vledder GP, Pietrzak J. Scaling depth-induced wave-breaking in two-dimensional spectral wave models. Ocean Model, 2015, 87: 30-47

[42] Sénéchal N, Bonneton P, Dupuis H. Field experiment on secondary wave generation on a barred beach and the consequent evolution of energy dissipation on the beach face. Coast Eng, 2002, 46(3): 233-247

[43] The Wamdi Group The WAM model-a third generation ocean wave prediction model. J Phys Oceanogr, 1988, 18(12): 1775-1810

[44] Thornton EB, Guza R. Transformation of wave height distribution. J Geophys Res: Oceans (1978–2012), 1983, 88(C10): 5925-5938

[45] Ting FC. Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone. Coast Eng, 2001, 43(3): 183-208

[46] Van Vledder GP, Groeneweg J, van der Westhuysen A (2009). Numerical and physical aspects of wave modelling in a tidal inlet. Proc. 31th Int. Conf. Coastal Eng., ASCE, City, 424–436. https://doi.org/10.1142/9789814277426_0036

[47] Zijlema M, van der Westhuysen AJ. On convergence behaviour and numerical accuracy in stationary SWAN simulations of nearshore wind wave spectra. Coast Eng, 2005, 52(3): 237-256