On the evolution of a singular vortex patch in a two-dimensional incompressible fluid flow

The angle evolution of a tangent-slope discontinuity on a singular vortex p atch, i.e. a patch of vorticity with tangent discontinuities in its boundar y, is studied from a numerical and theoretical point of view. Different num erical examples show that the angle shrinks for an initial angle less than 90 degrees, the angle widens when the initial angle is greater than 90 degr ees or is approximately preserved for 90 degrees for small time evolution. An asymptotic expansion of the initial velocity field near a singularity is performed for a class of singular vortex patches to reinforce analytically these results. (C) 1999 Elsevier Science B.V. All rights reserved.