Interaction of a free surface with a vortex patch

It is well known that most fluid flows feature vorticity. In order to avoid mathematical complexity, the study of surface waves is often carried out in the context of potential flow. In studies where vorticity is taken into account, it usually enters in a standard way, such as a background flow or in the boundary layer. In the current contribution, a numerical method for the simulation of the simultaneous evolution of a free-surface wave and an existing vortex patch is developed. The method uses the formulation of the free-surface problem due to Ablowitz et al. (2006) in connection with point-vortex methods and numerical tools based on asymptotic development of the Dirichlet-to-Neumann operator for the free surface. Simulations of shallow-water waves propagating over vortex patches of various strengths are then presented, and it is shown that the vortex patches can have strong, destabilizing effects on relatively low amplitude waves while their impact on surface profiles of larger amplitude is much weaker. It is also observed that very strong vortex patches are self-destabilizing when interacting with a free surface. (C) 2019 Elsevier B.V. All rights reserved.