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 flux
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 flow. 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 flow past regions of surface curvature. It is shown that vorticity
is conserved in
free-surface viscous flows. Vorticity which flows out of the fluid across
the free surface
is gained by the vortex sheet; the integral of vorticity over the entire
fluid 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.
Numerical solution of compressible viscous flows at high Reynolds numbers
