Nonlinear energy fluxes and the finite depth equilibrium range in wave spectra

Results using a finite depth representation of Webb's [1978] transformation of Herterich and Hasselmann's [1980] equation for the rate of change of en ergy density in a random-phase, spatially homogeneous, finite depth wave sp ectrum show that the equilibrium range in finite depth preserves a k(-2.5) form consistent with Resio and Perrie's [1991] deepwater results and that t he relaxation time toward an equilibrium range in shallow water is consider ably faster than in deep water. Results from this finite depth nonlinear en ergy transfer representation compared to previously calculated results of a nalytical spectral situations show agreement, and the finite depth Zakharov [1968] and Herterich and Hasselmann [1980] forms are shown to be numerical ly equivalent. Spectral analyses of matching wave spectra sets at sites in 8 and 18 m depths at Duck, North Carolina, show a k(-2.5) shape in the equi librium range and show energy gains above the spectral peak and at high fre quencies with energy loss in the midrange of frequencies near the spectral peak, consistent with four-wave interactions. Spectral energy losses betwee n these two sites correlate with spectral energy fluxes to high frequencies , again consistent with four-wave interactions. The equilibrium range coeff icient shows strong dependence on friction velocity at both gages.