On the evolution of an angle in a vortex patch

The inviscid incompressible two-dimensional motion of some initially convex singular vortex patches is examined. The angle's evolution of a tangent-sl ope discontinuity on a singular contour is studied from a numerical and the oretical point of view. Different numerical examples show that the angle sh rinks for initial angle less than 90 degrees, and the angle widens when the initial angle is greater than 90 degrees or is "approximately" preserved f or initial angle 90 degrees for small time evolution. An asymptotic expansi on of the initial velocity field near a singularity for a class of singular vortex patches is performed to reinforce this result analytically. Some in itially nonconvex singular patches in which the evolution does not follow t his rule are shown.