Frequency Domain Wave Models in the Nearshore and Surf Zones
NAVAL RESEARCH LAB STENNIS SPACE CENTER MS OCEAN DYNAMICS AND PREDICTION BRANCH
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In deep water kh 1, where k is the wave number and h the water depth, second-order wave nonlinearity can be described as a small correction to the underlying linear wave. Perturbation expansions in wave steepness E ka, where a is the wave amplitude, are used Phillips, 1960, and at second-order only non-resonant bound waves are possible among triads of wave frequencies. Thus the interacting waves with the frequency-vector wave number combination wI,kl and wZ,kz excite secondary waves at WI wz, ki kz, but these secondary wave amplitudes always remain small relative to the primary amplitudes. At the next order, resonant interaction occurs between quartets of waves, with the resultant slow energy exchange between the interacting waves. In shallow water kh 1 waves become less dispersive and more collinear, and triads of waves at second-order begin to more closely satisfy the resonant conditions for wave interaction. The perturbation solutions of finite depth do not apply in the nearshore, since significant energy transfer occurs over much shorter distances 010 wavelengths than in deep water. The Ursell number Ur aj kZh3 Ursell, 1953 is the typical measure for the validity of these perturbation solutions, which are only applicable if Ur 1. Though the resonant conditions between triads are only exactly satisfied in the collinear, non-dispersive limit, the nonlinearity inherent in shoaling waves in the nearshore is strong enough for significant energy transfer to occur at near-resonance Bryant, 1973. Recourse is often made to the Boussinesq equations Peregrine, 1967 for simulation of nonlinear energy transfer in shallow water, as they are valid for Ur 01, where weak nonlinearity and weak dispersion are balanced.
- Physical and Dynamic Oceanography