Integration of Different Wave Forcing Formulations with Nearshore Circulation Models

Abstract

Wave-induced circulation in general coastal environments is simulated by coupling two widely-used finite-element models, namely, a refraction-diffraction-reflection model based on the elliptic mild-slope equation, and a two-dimensional (depth-averaged) shelf-scale circulation model. Such models yield wave-induced current-fields and set-up/down. This involves exploration of some numerical and practical issues, for example, the selection of appropriate boundary condition and grid resolution, numerical errors owing to higher-order derivatives, etc. Computations of the wave forcing from the elliptic wave model, and the wave-induced quantities from the circulation model, are validated with theoretical and published results. The coupled system is then used to simulate the wave-induced circulation in the domains where structures (e.g. breakwater, jetty, etc.) and bathymetric features (e.g. shoal, etc.) are present. In practice, usually an approximate form of the wave-induced forcing is used. This has certain limitations in some application, which have been poorly studied so far. Therefore, here we consider two alternative approaches. The performance of these wave forcing formulations is examined in the regions where the effects of wave reflection, diffraction and focusing are significant. It is observed that the “generalized approach” provides satisfactory results in most situations, provided a grid resolution of L/10 or more is achievable for the wave model domain. The widely-used simplified approach may produce a chaotic pattern of set-up/down and current field in the regions where the wave field is not purely progressive. The third approach ignores the effect of wave diffraction and reflection, and primarily simulates the effect of energy dissipation. Differences up to 25 percent are observed between the modeled current fields obtained with the generalized and the simplified approach. The results suggest that the generalized approach can be used with little practical difficulty and greater reliability.