Frequency Domain Wave Models in the Nearshore and Surf Zones
Abstract
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 (0(10) 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 = 0(1), where weak nonlinearity and weak dispersion are balanced.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2003
- Accession Number
- ADA526298
Entities
People
- James Kaihatu
Organizations
- United States Naval Research Laboratory