Singularity Formation in the Shape of a Vortex Sheet in Three Dimensions|numerical Simulation

The evolution of a small but nite three-dimensional disturbance on a at uniform vortex sheet is studied numerically on the basis of a Lagrangian representation of the motion. The numerical simulations connrm the asymptotic analysis by Ishihara and Kaneda (1995; J. Fluid Mech., 300, 339-366) for the spontaneous singularity formation in the shape of the vortex sheet. They also suggest that the singularities appear along curves, which have a rather simple dependence on the spanwise-coordinate. Reeecting the three-dimensionality of the vortex dynamics, the singularity-curve is not along any of the vortex lines.