Observations of the directional spectrum relaxation of wavefields in slowly and rapidly turning winds

Abstract

INTRODUCTIONA representation of the wave energy as a function of frequency, the frequency spectrum, can easily be obtained since it can be extracted from a single record of the water surface elevation at one given location. But surface gravity water waves are not long-crested but rather propagate with appreciable angular spreading about their mean direction. The assumption of a single direction of propagation, common to most engineering applications can potentially lead to significant errors, especially in cases of mixed seas where energy peaks can come from different directions. The specification of wave direction of propagation is by no means simple and the physics leading to this angular spread of energy are not well understood, the main effects being the inherent variability of the source function, and the non-linear effects between wave components and those associated with wave breaking. A more accurate representation of the wave field in the frequency-direction domain will lead to a better understanding of the wave processes, which in turn * to whom all correspondence should be addressed e-mail: tsanis@water.eng.mcmaster.ca ABSTRACT A so called Exact Form of the Maximum Likelihood Method is used to obtain directional spectrum estimates from a 3-meter NDBC discus buoy, part of the Surface Wave Dynamics Experiment (SWADE) field array. The method was used to look at the response of wavefields to turning winds with various wind shift gradients. For slowly turning winds, the spectrum was found to smoothly adjust to the wind changes. As the wind shift gradient increased, a portion of the spectral energy was found to be decoupled from the wind while the bulk of the spectrum smoothly adjusted to the new wind direction. Finally, for even larger wind shift gradients, the preexisting spectrum was completely decoupled from the wind and decayed separately, as a new spectrum consistent with the wind direction was generated. These observations confirm theoretical results previously obtained from a third generation wave model. The relaxation of waves in turning winds was investigated using a simple relaxation model. Correlation coefficients obtained in this study are higher than previously published studies, especially for lower values of the wave age, and a relationship between the relaxation parameter and the wave age is observed.