Interaction of waves with non-colinear currents

The present paper reports on a study of the interaction of a current-free monochromatic surface wave field with a wave-free uniform current field in a three-dimensional flow frame. The wave and the current fields are not necessarily collinear with each other. The formulation of the wave–current field is done under the assumption of irrotational and inviscid flow. We have developed the three dimensional expressions describing the characteristics of the combined flow in terms of mass, momentum and energy transport conservation. These equations are found efficient to describe the sought-for combined wave–current field. The parameters describing the wave–current field after the interaction are the surface disturbance amplitude and length, mean water depth, mean current-like parameter and direction of the combined flow, which would be calculated from a set of equations that satisfy conservation of mean mass, momentum and energy flux and a dispersion relation on the free surface before and after the interaction. The results are shown in terms of relative changes in wave heights and lengths, current-like parameters and final directions obtained for the combined wave–current field with respect to current-free wave and wave-free current pre-interaction parameters.