Energy balance of wind waves as a function of the bottom friction formulation

Abstract Four different expressions for wave energy dissipation by bottom friction are intercompared. For this purpose, the SWAN wave model and the wave data set of Lake George (Australia) are used. Three formulations are already present in SWAN (ver. 40.01): the JONSWAP expression, the drag law friction model of Collins and the eddy–viscosity model of Madsen. The eddy–viscosity model of Weber was incorporated into the SWAN code. Using Collins' and Weber's expressions, the depth- and fetch-limited wave growth laws obtained in the nearly idealized situation of Lake George can be reproduced. The wave model has shown the best performance using the formulation of Weber. This formula has some advantages over the other formulations. The expression is based on theoretical and physical principles. The wave height and the peak frequency obtained from the SWAN runs using Weber's bottom friction expression are more consistent with the measurements. The formula of Weber should therefore be preferred when modelling waves in very shallow water.

[1]  J. A. Putnam,et al.  The dissipation of wave energy by bottom friction , 1949 .

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

[3]  R. C. Ris,et al.  Spectral Modelling of Wind Waves in Coastal Areas , 1997 .

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

[5]  Ying Poon,et al.  SPECTRAL WAVE ATTENUATION BY BOTTOM FRICTION: THEORY , 1988 .

[6]  Gerbrand J. Komen,et al.  On the Balance Between Growth and Dissipation in an Extreme Depth-Limited Wind-Sea in the Southern North Sea , 1983 .

[7]  Klaus Hasselmann,et al.  Nonlinear and linear bottom interaction effects in shallow water , 1978 .

[8]  M. W. Dingemans,et al.  Water Wave Propagation Over Uneven Bottoms: Part 1 , 1997 .

[9]  N. Booij,et al.  A third‐generation wave model for coastal regions: 2. Verification , 1999 .

[10]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[11]  C. L. Bretschneider.  REVISED WAVE FORECASTING RELATIONSHIPS , 2000 .

[12]  L. Cavaleri,et al.  Wind wave prediction in shallow water: Theory and applications , 1981 .

[13]  I. Young,et al.  The growth of fetch limited waves in water of finite depth. Part 1. Total energy and peak frequency , 1996 .

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

[15]  C. Willmott.  ON THE VALIDATION OF MODELS , 1981 .

[16]  N. Weber.  Bottom friction for wind sea and swell in extreme depth-limited situations , 1991 .

[17]  J. Collins.  Prediction of shallow‐water spectra , 1972 .

[18]  Ivar G. Jonsson,et al.  WAVE BOUNDARY LAYERS AMD FRICTION FACTORS , 1966 .

[19]  Jaak Monbaliu,et al.  Effects of the bottom friction formulation on the energy balance for gravity waves in shallow water , 1994 .

[20]  Hans C. Graber,et al.  A Finite-Depth Wind-Wave Model. Part I: Model Description , 1988 .

[21]  A. Davies,et al.  A numerical model of the combined wave and current bottom boundary layer , 1988 .