A fully nonlinear numerical method for modeling wave-current interactions

摘要

The presence of current in the ocean can significantly modify the characteristics of ocean waves, and it is considered as an important factor responsible for the occurrence of extreme waves, e.g., rogue waves, which are well known as great threats to ocean engineering practices. The magnitude and direction of ocean current normally vary spatially and ocean waves can become very large and steep. Accurate and efficient phasere-solved numerical methods of fully nonlinear wave-current interactions on a large scale in three dimensions (3D) are required to understand their properties, but the existing phase-resolved methods are all based on the assumption of linear or weakly nonlinear interactions. This paper will address the issues and present a fully nonlinear numerical method to model the 3D interactions between waves and varying current on a large scale using a phase-resolved formulation. A new set of equations describing the three-dimensional, fully nonlinear interactions between waves and horizontally shearing current is proposed. They are derived by making no assumption on wave steepness or the order of wave-current interactions. The resulting new equations correctly describe the free surface boundary conditions by representing the fully nonlinear wave-current interactions, removing the limitation to the small wave steepness of the existing formulations in literature.