Boussinesq-type equations for wave–current interaction

Abstract A new formulation of Boussinesq-type equations for wave–current interaction is presented by means of a perturbation method and in terms of a computation velocity. The research focuses on inclusion of the mean water depth change caused by the presence of a current and the wave–current interaction. Strong and moderate current cases are considered for the derivation, and this allows a perturbation method to be used for the derivation and can reveal the effect of the current on the vertical distributions of the wave velocity and the pressure explicitly. The derived model is enhanced to include the higher accuracy dispersion of Pade [4, 4] expansion and a fully nonlinear property. Numerical simulations are performed to show the effect of the mean water depth change caused by the presence of a current on wave motions.