Numerical simulations of vortex interactions with a free surface.

Abstract

The vortex interactions with a free surface is studied numerically using a combined vortex/boundary integral technique. The interaction is controlled by a Froude number, based on the vortical motion, and the geometric parameters describe the initial vortex configuration. In the interaction of two-dimensional vortex flows with a free surface Two problems are studied in considerable detail, the head-on collision of a vortex pair with a free surface and the large amplitude Kelvin-Helmholtz instability of a submerged shear-layer. The interaction is controlled by a Froude number and by the geometric parameters describing the initial vortex configuration. In the large Froude number limit, the surface motion follows the vortical flow, but depends only weakly on the actual value of the Froude number. For low Froude numbers, the free surface remains almost flat, and the disturbances caused by the vortical flow decrease rapidly with Froude number. The interaction of two-dimensional vortex flows with a free surface and the interaction of surface waves with a vortex generated current are studied numerically using a combined vortex/boundary integral technique. The interaction is controlled by a Froude number, based on the vortical motion, and the geometric parameters describe the initial vortex configuration. In the first type of problem, the head-on collision of a vortex pair with the free surface and the large amplitude Kelvin-Helmholtz instability of a submerged shear-layer below the free surface are studied in considerable detail. Here the vorticity is modeled as point vortices, vortex sheets and finite area vortex regions. In the large Froude number limit, the surface motion follows the vortical flow, but depends only weakly on the actual value of the Froude number. For low Froude numbers, the free surface remains almost flat, and the disturbances caused by the vortical flow decrease rapidly with Froude number. The second physical circumstance, in which the surface wave is generated by a time dependent pressure load, is studied numerically with the Multipole Expansion Technique (MET). For the strong interaction, which depends on both Froude number and the initial depth of the vortex, the current generally stops the waves from passing; for the weak interaction, the current has only a small effect on the waves.