Directional Distributions and Mean Square Slopes in the Equilibrium and Saturation Ranges of the Wave Spectrum

Abstract

Field observations show that the crosswind component constitutes a significant portion of the ocean surface mean square slope. The average ratio between the crosswind and upwind mean square slope components is 0.88 in slick-covered ocean surfaces. This large crosswind slope component cannot be explained satisfactorily based on our present models of a unimodal directional distribution function of ocean waves. Two-dimensional spectral analysis of the 3D ocean surface topography reveals that a bimodal directional distribution is a common feature for wave components shorter than the peak wavelength. The calculated result of the upwind and crosswind mean square slope components using a bimodal directional distributions yields substantial improvement in agreement with field measurements. Also discussed in this paper is the transition of the spectral function from an equilibrium form to a saturation form. Through comparison with the mean square slope data of the slick cases under which short waves are suppressed and calculation of the range of wavenumbers influenced by nonlinear wave?wave interaction, it is found that the transition from the equilibrium range to saturation range occurs at a wavenumber in the neighborhood of 6.5 times the peak wavenumber.