Chapter 2: Frequency Domain Wave Models in the Nearshore and Surf Zones

摘要

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 (cot, k1) and (c02, k2) excite secondary waves at (cot + co2, k1 + k2), 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.