Wave number spectrum and mean square slope of intermediate‐scale ocean surface waves

Abstract

This paper presents an analysis of the wave number spectra of intermediate‐scale waves (wavelengths between 0.02 and 6 m) covering a wide range of wind and background wave conditions under various sea‐state conditions. The main result of the analysis is that the dependence of the dimensionless wave spectrum on the dimensionless wind friction velocity follows a power law function. The coefficient and exponent of the power law function vary systematically with the wave number. The wave number dependence of the coefficient and exponent serves as an empirical parameterization for computing the wave number spectra of intermediate‐scale waves at different wind speeds. Calculation of the mean square slope from the resulting wave number spectrum confirms that intermediate‐scale waves are the dominant contributor of the ocean surface roughness. A simple formula is presented for calculating the band‐pass filtered mean square slope of the ocean surface for remote sensing applications.