Three-dimensional wave effects on a steady current

Abstract

Measurements in a laboratory flume have shown unexpected wave-induced changes in the vertical profile of the mean horizontal velocity. Two theoretical explanations for these changes have been proposed so far. One is based on a local force balance in the longitudinal direction and the other relies on secondary circulations in the cross-sectional plane. In this study, a two-dimensional (2DV lateral) model based on the so-called generalized Lagrangian mean (GLM) formulation has been developed to investigate the three-dimensional effect of waves on the steady current and in particular to investigate the validity of the two fundamentally different explanations. Formulations for the three-dimensional wave-induced driving force have been implemented in an existing 2DV non-hydrostatic numerical flow model. Computations for regular waves following and opposing a turbulent current over a horizontal bed have been carried out and the results are compared with both experimental results and results from an existing numerical model. The results clearly indicate predominance of the longitudinal component of the wave-induced driving force over the cross-sectional components. Although the 2DV model has only been applied to and verified with measurements in wave–current systems in a laboratory flume, the approach followed here is relevant for a wider class of problems of wave–current interactions.