Phase Resolving Wave–Current Interactions with Improved Boussinesq-Type Equations

Abstract

A set of fully nonlinear Boussinessq-type equations with improved linear and nonlinear properties is considered for wave-current interaction analysis. These phase-resolving equations are so that the highest order of the derivatives is three. We implement a new source function for the wave-current generation within the domain, which allows to generate a wide range of wave-current conditions. The set of equations is solved using a fourth order explicit numerical scheme which semi-discretizes the equations in space and then integrates in time using an explicit Runge-Kutta scheme. A novel treatment of the boundaries, which uses radiative boundary conditions for the current and damps the waves, is used to avoid boundary reflections. Several validation tests are presented to demonstrate the capabilities of the new model equations for wave-current interaction. © 2015 World Scientific Publishing Company and Japan Society of Civil Engineers