On the modeling of wave–current interaction using the elliptic mild-slope wave equation

Abstract

Methods to incorporate the effect of ambient currents in the prediction of nearshore wave transformation are developed. This is accomplished through the construction of a finite-element coastal/harbor wave model based on an extended mild-slope wave–current equation that includes wave breaking. Improved boundary conditions are used to provide more accurate forcing and to minimize spurious wave reflections from the boundaries. Multiple nonlinear mechanisms, appearing both in the governing equations and in the boundary conditions, are handled successfully and efficiently with iterative techniques. The methods are tested against results from other types of models based on parabolic approximations or Boussinesq equations for three wave–current problems of common interest and varying complexity. While indicating good agreement in general, the analysis also highlights the limitations of parabolic approximation models in case of strong local currents and velocity shear. We also consider the harbor engineering problem pertaining to waves approaching an inlet with a jettied entrance, where wave–current interaction can create a complex wave pattern that adversely affects small craft navigation and causes scouring. The role of ebb and flood currents on wave transformation and on breaking in the vicinity of the inlet is investigated using the model in conjunction with hydraulic laboratory data. It is found that although the ebb currents cause larger waves outside the inlet, much of the wave energy is soon dissipated due to breaking; during the flood tide, in contrast, more wave energy can penetrate into the inlet throat.