FRF Spectrum: TMA with Kitaigorodskii's f-4 Scaling

Abstract

This paper describes the development of a mathematical function which represents the spectrum of wind-generated gravity waves in water of arbitrary depth. The derivation parallels that of the TAM spectrum. The primary difference is that Philips' (1958) model for saturation at high frequencies is replaced by Kitaigorodskii's (1983) model. This spectrum incorporates wind speed directly into the formulation and is consistent with an fE-4 power law scaling for deep water. In its raw form the new model requires four internal constraints (gravity, depth, wind speed and peak frequency), and has four model coefficients. Values for the coefficients are determined for 1,022 observations of wave spectra made at the Corps of Engineers Field Research Facility (FRF) in depths of 19, 8.5 and 6m. The coefficients are then correlated with dimensionless combinations of the physical parameters associated with the spectrum to see if the number of coefficients can be reduced. If three of the coefficients are held constant at their mean values, a direct relationship to wave steepness is obtained for the forth coefficient that is related to the peakedness of the spectrum.