Vortex ring interaction with a free surface.

Abstract

The interaction between a vortex ring and a free surface is studied experimentally and numerically. Three separate, but related subjects are discussed. First, a head-on collision of a large vortex ring with the free surface is investigated experimentally. Three different free surface patterns, that depend on the strength of the vortex ring and the elapsed time, are observed: a single circular depression of the free surface for weak vortex rings, axisymmetric outward propagating waves in the early stage of a strong vortex ring interaction, and fully three-dimensional waves in the later stages for both weak and strong rings. The early stage of the interaction is well predicted by an inviscid, axisymmetric numerical model. Secondly, the generation of surface waves due to a vortex reconnection at the free surface is investigated numerically. Guided by experimental observations, the Froude number is assumed to be small and hence the free surface motion is assumed to be linear. The ring is modeled as a collection of "essentially inviscid" vortons and the free surface evolution is solved by using a spectral method. The proposed model successfully captures the reconnection and the wave generation, and the results are comparable to available experimental observations. Short waves are generated due to rapid pressure changes when the vortex ring changes its topology. Thirdly, effects of a surface contaminant on the oblique collision of a vortex ring with a flat surface are studied numerically. The Froude number is assumed to be so small that the surface remains fiat. The full viscous Navier-Stokes equations and a conservation equation for the contaminant are solved by a finite difference method. For a clean surface, simulations at two Reynolds numbers (200 and 400) are done. For the contaminated surface, simulations with varying contamination parameter at the lower Reynolds number are performed. The results show a considerable modification of the underwater vortical flows due to the surface vorticity generated by the contaminant gradient. The distribution of the contaminant during the interaction depends on the strength of the contamination. Results are also compared to a collision with a no-slip surface.