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

The angle evolution of a tangent-slope discontinuity on a singular vortex patch, i.e. a patch of vorticity with tangent discontinuities in its boundary, is studied from a numerical and theoretical point of view. Different numerical examples show that the angle shrinks for an initial angle less than 90°, the angle widens when the initial angle is greater than 90° or is approximately preserved for 90° 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.