Evolution of the Bimodal Directional Distribution of Ocean Waves

Abstract

Recent results of numerical wave models have shown that the presence of a bimodal directional spreading is a robust feature at wavenumbers above the spectral peak. This directional bimodality is controlled mainly by directional transfer of energy through nonlinear wave?wave interactions. The bimodal feature has also been observed in the directional spectra derived from the spatial topography of ocean surface waves acquired by stereo-photography, image radars, and an airborne scanning lidar system. In this study, a comprehensive data analysis of the evolution of the wave directional distribution during two active wave growth periods in Lake Michigan is conducted. The wind and wave measurements are acquired by two heave?pitch?roll buoys moored at a nearshore and an offshore station. An empirical method averaging the results of the maximum likelihood method and maximum entropy method is used to estimate the directional distribution from buoy measurements. The study shows that the bimodal distribution is a distinctive and persistent feature over a broad frequency range throughout the wave growth process. The characteristics of directional bimodality are quantified by parameters related to the separation angles and the amplitudes of the sidelobes. In general, the values of the parameters are smallest near the peak frequency and increase toward both lower and higher frequencies. This frequency-dependent pattern appears to be invariant to the change of wave age throughout the wave growth process. The persistent nature of the directional bimodality indicates that the nonlinear wave?wave interaction mechanism not only actively moves wave energy away from the peak frequency into both higher and lower frequency components but also constantly redistributes wave energy into directions oblique to the wind direction. At the offshore buoy site when the wind and peak wave directions align closely, the bimodal distribution is symmetric about the wind direction. At the nearshore buoy site when the local wind and the peak wave are not moving in the same direction or the wind field is less homogeneous, the bimodal distribution is asymmetric.