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.