Myths, Math, and Physics of Free-Surface Vorticity

Abstract

The boundary equations for the production of vorticity are examined in the case of a free surface. Mathematical manipulation of the equations leads to interesting results which are given physical interpretation through examination of three flows: a surface wave, an accelerated free-surface channel flow, and the vortex ring interaction with a free surface. The predicted phenomena are unusual, and require abandonment of preconceptions regarding the notion that vorticity is angular momentum. The flux and appearance of vorticity in free-surface flows is shown to be a consequence of necessary viscous accelerations at the boundary even for otherwise irrotational subsurface flow. The deformation of the free surface is the critical factor separating the free-surface problem from the vortex image analogy.