The observation of singularities in the boundary of patches of constant vorticity

The equations of motion describing inviscid fluid flow are solved numerically in two dimensions for the case where the flow can be described by patches of constant vorticity. The case where the vorticity is described initially by two circular patches is studied in detail. The numerical evidence indicates that when the minimum distance between the two patches is initially less than the radius of the patches a singularity forms in finite time on the boundary curves of the patches. The singularity appears to be a jump discontinuity in the tangent vector of the boundary curve.