Vorticity Interactions with a Free Surface

The study of vorticity interactions with a free surface is concerned with the dynamics of a vorticity field bounded by a deformable surface. The surface deforms to satisfy the conditions that the tangential stress be equal to zero and the normal stress be equal to a constant at all times. The form of the vorticity field is arbitrary. For example, the vorticity field can be distributed, as in a shear flow, or concentrated, as in a vortex ring. The free-surface stress conditions are satisfied on the external side of the surface, which is the side opposite that of the vorticity field. Hence, the free surface is actually a boundary of the fluid domain containing the vorticity field; the effect of the dynamic evolution of fluid on the external side of the surface is negligible. Because the surface is free to deform during the interaction with the vorticity, its position in space evolves with time. The interaction is characterized by both the vorticity and the flux of vorticity at the free surface, the deformation of the free surface, and the dynamic behavior of the vorticity field.