CAPILLARY MODIFICATION OF THE SINGULARITY AT A FREE-STREAMLINE SEPARATION POINT

The classical solution for cavitating flow past a body is singular where the free streamline separates from a sharp edge, predicting infinite curvature there. Ackerberg (1) includes surface tension to resolve the difficulty, but his solution contains capillary waves. It is observed here that this is possible only if the waves have energy supplied from downstream. Solutions not containing waves are possible if a modified singular behaviour is allowed at the edge. Nonlinear terms in the boundary conditions are included in our treatment in an attempt to deal with these singularities, and a local expansion having satisfactory properties is presented. © 1979 Oxford University Press.