Numerical Simulation of Oblique Wave Breaking and Wave-Induced Currents in the Surf Zone

Abstract

In the present study, the three-dimensional, incompressible, turbulent, free-surface flow, developing by the propagation and breaking of nonlinear gravity waves over a constant-slope beach, is numerically simulated. The main objective is to investigate the flow structure in the surf zone as a result of the interaction between the longshore and the undertow current, induced by spilling wave breaking, oblique to the shoreline. The simulations are performed employing the so-called large-wave simulation (LWS) method coupled with a numerical solver for the Navier-Stokes equations. According to the employed LWS methodology, large velocity and free-surface scales are fully resolved, while the effect of subgrid scales is modeled by eddy-viscosity stresses, similar to large-eddy simulation (LES) methodology. In order to validate our model, the case of incoming Stokes waves with wavelength to inflow depth ratio λ/dI ≈ 6.6 and wave steepness H/λ ≈ 0.025, propagating normal to the shore over a bed of constant slope 1/35, is investigated. Our results are compared to published experimental measurements, and it is found that the LWS model predicts adequately the wave breaking parameters — breaking height and depth — and the distribution of the undertow current in the surf zone. Two cases of oblique breaking waves, with inflow angles φI = 20° and 30°, and all other parameters identical to that of the validation case, are considered. The gradual breaking of the refracted waves is captured, as well as the three-dimensional structure of the flow in the surf zone. LWS-predicted profiles of the undertow and the longshore current at several positions in the surf zone, are presented. It is indicated that the undertow prevails in the outer surf zone, while the longshore current becomes stronger in the inner surf zone and reaches its maximum magnitude close to the shore.