Moments-Based Reduced Spectral Wave Modeling of Frequency-and-Directional Spreading Effects on Wave-Induced Longshore Currents

Abstract

Often, nearshore radiation stresses are approximated using the monochromatic wave assumption, although this can have significant errors when the incident waves have finite frequency and/or directional spread. Consequently, the resulting wave-driven currents could be predicted erroneously or, when fitting to observations, biased model parameters such as the bottom friction coefficient may result. We develop and test a moments-based reduced spectral wave model which includes the leading order effects of wave frequency and directional spreading. This model solves the evolution equations of wave moments, which are integrations of the wave action balance equation multiplied by weighting functions over frequencies and directions. An assumption of analytical Gaussian distribution for the frequency-direction spectrum is made to develop a simple five-parameter system that contains information on the wave height, period, direction, frequency bandwidth, and directional bandwidth. Using this model, we investigate the finite bandwidth effects on the wave field and radiation stresses. The directional spreading is found to have a strong impact on the radiation stress, with a larger directional bandwidth resulting in smaller radiation stresses. However, the frequency spreading has much less impact. The spectral wave breaking based on the roller concept is considered in this wave model. After coupling with a circulation model based on the shallow water equations, simulation results compare favorably with the DUCK94 field data for waves and longshore currents but show strong dependence on the directional bandwidth.