On the Generation of Vorticity at a Free Surface

The mechanism for the generation of vorticity at a viscous free surface is described This is a free surface analogue of Lighthill s strategy for determining the vorticity ux at solid boundaries In this method the zero shear stress and pressure boundary conditions are transformed into a boundary integral formulation suitable for the velocity vorticity description of the ow A vortex sheet along the free surface is determined by the pressure boundary condition while the condition of zero shear stress determines the vorticity at the surface In general vorticity is generated at free surfaces whenever there is ow past regions of surface curvature It is shown that vorticity is conserved in free surface viscous ows Vorticity which ows out of the uid across the free surface is gained by the vortex sheet the integral of vorticity over the entire uid region plus the integral of surface vorticity over the free surface remains constant The implications of the present strategy as an algorithm for numerical calculations are discussed