FREE-SURFACE DEFORMATION AND FORMATION OF CUSPS AT LOW REYNOLDS NUMBER FLOW

摘要

Free surface deformation and cusp formation are analyzed by considering a viscous flow due to a vortex dipole below the free surface where the direction and the strength of vortex dipole are given arbitrarily. In the analysis, the Stokes' approximation is used and surface tension effects are included, but gravity is neglected. The solution is obtained analytically by using conformal mapping and complex variable techniques. From the solution, the deformation of the free surface and the formation of a cusp on the free surface are discussed. For some typical directions and strengths of vortex dipole, the deformations of free surface shape are shown.