Singularity Formation in a Cylindrical and a Spherical Vortex Sheet

The evolutions of the planar and axisymmetric vortex sheets generated by the impulsive motion of a cylinder and a sphere, respectively, are compared numerically. The numerical method addresses difficulties that occur in the axisymmetric case near the axis of symmetry. The planar vortex sheet is known to develop a branch point singularity in finite time. Comparison of the planar and axisymmetric solutions indicates that the axisymmetric sheet develops a branch point singularity as well, and that it is of the same order p as the planar singularity. The value of p is consistent with 3/2.