Fully nonlinear wave-current interactions and kinematics by a BEM-based numerical wave tank

Abstract

A numerical wave tank (NWT) with fully nonlinear free-surface boundary conditions is developed to investigate nonlinear wave–wave and wave–current interactions and the resulting kinematics. In the present paper, the variation of wave amplitude and wave length of a monochromatic wave under several different speeds of steady uniform currents is studied through direct numerical simulations in the time domain. The nonlinear wave–current interactions are solved using a boundary integral equation method (BIEM) and a Mixed Eulerian–Lagrangian (MEL) time marching scheme. Both a semi-Lagrangian approach and Lagrangian (material-node) approach are employed and their performance is compared. A regridding algorithm based on cubic spline fitting is devised for updating the free-surface moving boundary in a stable and accurate manner. The incident waves are generated by feeding prescribed analytical waves on the input boundary. An efficient artificial numerical beach is devised and applied to dissipate wave energy and minimize wave reflections from the downstream wall. Nonlinear wave kinematics as a result of nonlinear wave–current interactions is calculated and the results are compared with a multi-layer Boussinesq model. The spatial variation of nonlinear wave profiles and kinematics affected by currents are also addressed and discussed.