Nonlinear saturation-based whitecapping dissipation in SWAN for deep and shallow water

This study investigates the effectiveness of a revised whitecapping source term in the spectral wind wave model SWAN (Simulating WAves Nearshore) that is local in frequency space, nonlinear with respect to the variance density and weakly dependent on the wave age. It is investigated whether this alternative whitecapping expression is able to correct the tendency towards underprediction of period measures that has been identified in the default SWAN model. This whitecapping expression is combined with an alternative wind input source term that is more accurate for young waves than the default expression. The shallow water source terms of bottom friction, depth-induced breaking and triad interaction are left unaltered. It is demonstrated that this alternative source term combination yields improved agreement with fetch- and depth-limited growth curves. Moreover, it is shown, by means of a field case over a shelf sea, that the investigated model corrects the erroneous overprediction of wind-sea energy displayed by the default model under combined swell-sea conditions. For a selection of field cases recorded at two shallow lakes, the investigated model generally improves the agreement with observed spectra and integral parameters. The improvement is most notable in the prediction of period measures.

[1]  David M. Farmer,et al.  Multiscale Measurements of Ocean Wave Breaking Probability , 2002 .

[2]  Y. Eldeberky,et al.  Nonlinear transformation of wave spectra in the nearshore , 1996 .

[3]  I. Young,et al.  A review of the central role of nonlinear interactions in wind—wave evolution , 1993, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[4]  Yoshiaki Toba,et al.  Local balance in the air-sea boundary processes , 1973 .

[5]  R. Long,et al.  Array measurements of atmospheric pressure fluctuations above surface gravity waves , 1981, Journal of Fluid Mechanics.

[6]  Klaus Hasselmann,et al.  On the spectral dissipation of ocean waves due to white capping , 1974 .

[7]  M. Longuet-Higgins.  A nonlinear mechanism for the generation of sea waves , 1969, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[8]  Jose-Henrique G. M. Alves,et al.  Performance of a Saturation-Based Dissipation-Rate Source Term in Modeling the Fetch-Limited Evolution of Wind Waves , 2003 .

[9]  M. Donelan,et al.  Wave-Follower Field Measurements of the Wind-Input Spectral Function. Part II: Parameterization of the Wind Input , 2006 .

[10]  S. Badulin,et al.  Self-similarity of wind-driven seas , 2005 .

[11]  J. A. Battjes,et al.  A reanalysis of the spectra observed in JONSWAP , 1987 .

[12]  S. Hsiao,et al.  Measurements of wind velocity and pressure with a wave follower during Marsen , 1983 .

[13]  David W. Wang,et al.  Investigation of Wave Growth and Decay in the SWAN Model: Three Regional-Scale Applications , 2003 .

[14]  Miguel C. Teixeira,et al.  On the distortion of turbulence by a progressive surface wave , 2002, Journal of Fluid Mechanics.

[15]  W. Kendall Melville,et al.  Distribution of breaking waves at the ocean surface , 2002, Nature.

[16]  Jin Wu.  Wind‐stress coefficients over sea surface from breeze to hurricane , 1982 .

[17]  P. Janssen.  Quasi-linear Theory of Wind-Wave Generation Applied to Wave Forecasting , 1991 .

[18]  M. S. Longuet-Higgins,et al.  Measurement of breaking waves by a surface jump meter , 1983 .

[19]  John Trinder,et al.  Wavenumber spectra of short gravity waves , 1989, Journal of Fluid Mechanics.

[20]  K. Hasselmann,et al.  On the Existence of a Fully Developed Wind-Sea Spectrum , 1984 .

[21]  Fabrice Ardhuin,et al.  Swell and Slanting-Fetch Effects on Wind Wave Growth , 2007 .

[22]  Marcel Zijlema.  Chapter 26 – Parallelization of a nearshore wind wave model for distributed memory architectures , 1996 .

[23]  L. Holthuijsen,et al.  FOUR-WAVE INTERACTIONS in SWAN , 2003 .

[24]  J. A. Battjes,et al.  ENERGY LOSS AND SET-UP DUE TO BREAKING OF RANDOM WAVES , 1978 .

[25]  M. Bottema,et al.  IMPROVED MODELLING OF NONLINEAR FOUR-WAVE INTERACTIONS IN SHALLOW WATER , 2003 .

[26]  M. Longuet-Higgins,et al.  Periodicity in Whitecaps , 1972, Nature.

[27]  Paul A. Hwang,et al.  An empirical investigation of source term balance of small scale surface waves , 2004 .

[28]  T. Barnett,et al.  Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP) , 1973 .

[29]  K. Katsaros,et al.  Dependence of Wave-Breaking Statistics on Wind Stress and Wave Development , 1992 .

[30]  Alexander V. Babanin,et al.  Breaking probabilities for dominant surface waves on water of finite constant depth , 2001 .

[31]  K. Hasselmann.  On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory , 1962, Journal of Fluid Mechanics.

[32]  S. Hasselmann,et al.  Computations and Parameterizations of the Nonlinear Energy Transfer in a Gravity-Wave Spectrum. Part I: A New Method for Efficient Computations of the Exact Nonlinear Transfer Integral , 1985 .

[33]  Donald T. Resio,et al.  Nonlinear energy fluxes and the finite depth equilibrium range in wave spectra , 2001 .

[34]  Gerbrant Ph. van Vledder,et al.  The WRT method for the computation of non-linear four-wave interactions in discrete spectral wave models , 2006 .

[35]  J. P. Hansen,et al.  High Range Resolution Radar Measurements of the Speed Distribution of Breaking Events in Wind-Generated Ocean Waves: Surface Impulse and Wave Energy Dissipation Rates , 2001 .

[36]  M. Donelan,et al.  Dynamics and Modelling of Ocean Waves , 1994 .

[37]  D Hurdle,et al.  Improved Spectral Wave Modelling of White-Capping Dissipation in Swell Sea Systems , 2004 .

[38]  Jens Bösenberg,et al.  Field measurements of wave-induced pressure over wind-sea and swell , 1991, Journal of Fluid Mechanics.

[39]  Donald T. Resio,et al.  Equilibrium‐range constant in wind‐generated wave spectra , 2004 .

[40]  W. Pierson,et al.  A proposed spectral form for fully developed wind seas based on the similarity theory of S , 1964 .

[41]  I. Young,et al.  The growth of fetch limited waves in water of finite depth. Part 2. Spectral evolution , 1996 .

[42]  S. A. Kitaigordskii,et al.  On Phillips' Theory of Equilibrium Range in the Spectra of Wind-Generated Gravity Waves , 1975 .

[43]  Alexander V. Babanin,et al.  Breaking Probability for Dominant Waves on the Sea Surface , 2000 .

[44]  Vladimir E. Zakharov,et al.  Statistical theory of gravity and capillary waves on the surface of a finite-depth fluid , 1999 .

[45]  On the mass and momentum transfer between short gravity waves and larger-scale motions , 1971 .

[46]  O. Phillips.  Spectral and statistical properties of the equilibrium range in wind-generated gravity waves , 1985, Journal of Fluid Mechanics.

[47]  C. Linwood Vincent,et al.  FRF Spectrum: TMA with Kitaigorodskii's f-4 Scaling , 1990 .

[48]  W. Rosenthal,et al.  Similarity of the wind wave spectrum in finite depth water: 1. Spectral form , 1985 .

[49]  H. Mitsuyasu,et al.  The Effect of Swell on the Growth of Wind Waves , 1991 .

[50]  Michael Selwyn Longuet-Higgins,et al.  On wave breaking and the equilibrium spectrum of wind-generated waves , 1969, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[51]  M. Banner,et al.  Modeling Spectral Dissipation in the Evolution of Wind Waves. Part I: Assessment of Existing Model Performance , 1994 .

[52]  Kimmo K. Kahma,et al.  Reconciling Discrepancies in the Observed Growth of Wind-generated Waves , 1992 .

[53]  Alexander V. Babanin,et al.  Spectral Distribution of Energy Dissipation of Wind-Generated Waves due to Dominant Wave Breaking , 2006 .

[54]  Yoshiaki Toba,et al.  Local balance in the air-sea boundary processes , 1972 .

[55]  N. Booij,et al.  A third-generation wave model for coastal regions-1 , 1999 .

[56]  M. Donelan,et al.  Directional spectra of wind-generated ocean waves , 1985, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[57]  Robert N. Swift,et al.  Airborne Measurements of the Wavenumber Spectra of Ocean Surface Waves. Part II: Directional Distribution* , 2000 .

[58]  Fabrice Ardhuin,et al.  On the Interaction of Surface Waves and Upper Ocean Turbulence , 2006 .

[59]  W. Plant.  A relationship between wind stress and wave slope , 1982 .

[60]  Leo H. Holthuijsen,et al.  Statistics of Breaking Waves Observed as Whitecaps in the Open Sea , 1986 .

[61]  W. Perrie,et al.  A numerical study of nonlinear energy fluxes due to wave-wave interactions Part 1. Methodology and basic results , 1991, Journal of Fluid Mechanics.