Shallow water wave modelling with nonlinear dissipation

In this paper a new shallow water wave model is described which uses nonlinear dissipation derived from turbulent diffusion as damping mechanism. The source functions of the model are presented in detail. Analytical results of the dynamical equation for simple cases illustrate basic features of the model. Academic test runs in deep and shallow water are performed. The designed cases are identical to the ones used in previous wave model intercomparison studies and thus allow comparison with other wave models. Results of a hindcast of a North Sea storm event illustrate the model behaviour in nonuniform real shallow water systems. In this case we can compare with field data and with the community wave model WAM cy. 4, which has been run parallel to our model. Our study shows that the concept of wave modelling with nonlinear dissipation is consistent with common knowledge of wave evolution in oceanic and shelf sea applications.

[1]  G. Burgers,et al.  Boundary-Layer Model Results for Wind-Sea Growth , 1993 .

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

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

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

[5]  J. A. Battjes,et al.  Parameterisation of Triad Interactions in Wave Energy Models , 1996 .

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

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

[8]  J. A. Battjes,et al.  Spectral modeling of wave breaking: Application to Boussinesq equations , 1996 .

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

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

[11]  Hendrik L. Tolman,et al.  Effects of Numerics on the Physics in a Third-Generation Wind-Wave Model , 1992 .

[12]  W. Rosenthal.  Derivation of Phillips α-Parameter from Turbulent Diffusion as a Damping Mechanism , 1989 .

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

[14]  L. Bender.  Modification of the Physics and Numerics in a Third-Generation Ocean Wave Model , 1996 .

[15]  J. Miles.  On the generation of surface waves by shear flows , 1957, Journal of Fluid Mechanics.

[16]  O. Phillips.  On the generation of waves by turbulent wind , 1957, Journal of Fluid Mechanics.

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

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

[19]  W. Plant.  A two-scale model of short wind-generated waves and scatterometry , 1986 .

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

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

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