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 energy density in a random-phase, spatially homogeneous, finite depth wave spectrum 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 the relaxation time toward an equilibrium range in shallow water is considerably faster than in deep water. Results from this finite depth nonlinear energy transfer representation compared to previously calculated results of analytical spectral situations show agreement, and the finite depth Zakharov [1968] and Herterich and Hasselmann [1980] forms are shown to be numerically 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 equilibrium range and show energy gains above the spectral peak and at high frequencies with energy loss in the midrange of frequencies near the spectral peak, consistent with four-wave interactions. Spectral energy losses between these two sites correlate with spectral energy fluxes to high frequencies, again consistent with four-wave interactions. The equilibrium range coefficient shows strong dependence on friction velocity at both gages.