Capillary modification of the singularity at a freestreamline separation point
Abstract
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 (1975) 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 the treatment in an attempt to deal with these singularities, and a local expansion having satisfactory properties is presented.
 Publication:

Quarterly Journal of Mechanics and Applied Mathematics
 Pub Date:
 August 1979
 Bibcode:
 1979QJMAM..32..303C
 Keywords:

 Capillary Flow;
 Cavitation Flow;
 Free Flow;
 Laminar Flow;
 Separated Flow;
 Boundary Conditions;
 Boundary Value Problems;
 Interfacial Tension;
 Linear Equations;
 Nonlinear Equations;
 Pressure Distribution;
 Singularity (Mathematics);
 Fluid Mechanics and Heat Transfer