SINGULARITIES ON FREE SURFACES OF FLUID-FLOWS

Isolated singularities on free surfaces of two-dimensional and axially symmetric three-dimensional steady potential flows with gravity are c onsidered. A systematic study is presented, where known solutions are recovered and new ones found. In two dimensions, the singularities fou nd include those described by the Stokes solution with a 120 degrees a ngle, Craya's flow with a cusp on the free surface? Gurevich's flow wi th a free surface meeting a rigid plane at 120 degrees angle, and Daga n and Tulin's flow with a horizontal free surface meeting a rigid wall at an angle less than 120 degrees. In three dimensions, the singulari ties found include those in Garabedian's axially symmetric flow about a conical surface with an approximately 130 degrees angle, flows with axially symmetric cusps, and flows with a horizontal free surface and conical stream surfaces. The Stokes, Gurevich, and Garabedian flows ar e exact solutions. These are used to generate local solutions, includi ng perturbations of the Stokes solution by Grant and Longuet-Higgins a nd Fox, perturbations of Gurevich's flow by Vanden-Broeck and Tuck, as ymmetric perturbations of Stokes flow and nonaxisymmetric perturbation s of Garabedian's flow. A generalization of the Stokes solution to thr ee fluids meeting at a point is also found.