Boussinesq modeling of a rip current system

TLDR

The study investigates surface wave transformation and breaking‑induced nearshore circulation using a fully nonlinear extended Boussinesq model. A time‑domain numerical model based on the fully nonlinear extended Boussinesq equations incorporates an eddy‑viscosity term for wave‑breaking dissipation, a moving shoreline technique for run‑up, and quasi‑fourth‑order finite‑difference schemes to solve the equations. Numerical results agree with laboratory measurements, reproducing wave height, mean water level, and longshore/cross‑shore velocities, and reveal the temporal‑spatial variability and instability of rip currents, as well as vorticity and wave‑diffraction effects by underlying vortices.

Abstract

In this study, we use a time domain numerical model based on the fully nonlinear extended Boussinesq equations [ Wei et al. , 1995] to investigate surface wave transformation and breaking‐induced nearshore circulation. The energy dissipation due to wave breaking is modeled by introducing an eddy viscosity term into the momentum equations, with the viscosity strongly localized on the front face of the breaking waves. Wave run‐up on the beach is simulated using a moving shoreline technique. We employ quasi fourth‐order finite difference schemes to solve the governing equations. Satisfactory agreement is found between the numerical results and the laboratory measurements of Haller et al. [1997], including wave height, mean water level, and longshore and cross‐shore velocity components. The model results reveal the temporal and spatial variability of the wave‐induced nearshore circulation, and the instability of the rip current in agreement with the physical experiment. Insights into the vorticity associated with the rip current and wave diffraction by underlying vortices are obtained.