A fully nonlinear numerical method for modeling wave-current interactions

On this basis, the recently developed Enhanced Spectral Boundary Integral (short as ESBI) method is further enhanced to be able to model the wave-current interactions using the new equations, by developing the appropriate procedure for dealing with the extra terms related to nonlinear wave-current interactions. The new equations are used as the prognostic equations for updating the free surface in time domain, and a fast converging iterative technique is employed to solve them. The robustness of the newly developed method is demonstrated through comparing with experimental data available in literature and good agreements are observed in the several different cases, including the 3D fully nonlinear interactions between ocean waves and horizontally varying current. A comparison with the Higher-Order Spectrum (HOS) method based on weak-nonlinear formulations of wave-current interactions is also made to confirm larger error does appear if the wave steepness is high by using the HOS. The method presented in the paper can be employed to simulate the real evolution of ocean waves on current in a phase-resolved way to give deep insights to the dynamics of wave-current interactions, which may not be done correctly by the existing methods so far.