Singularity formation in the shape of a vortex sheet in three dimensions-numerical simulation
Department of Mathematics Faculty of Science Toyama University Gofuku, Toyama 930, Japan
2 Department of Applied Physics Faculty of Engineering Nagoya University Chikusa-ku, Nagoya 464-01, Japan
The evolution of a small but finite three-dimensional disturbance on a flat uniform vortex sheet is studied numerically on the basis of a Lagrangian representation of the motion. The numerical simulations confirm 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. Reflecting the three-dimensionality of the vortex dynamics, the singularity-curve is not along any of the vortex lines.
© EDP Sciences, ESAIM, 1996