Vortex Flows and Related Numerical Methods II
ESAIM: Proceedings,
Vol. 1, 1996, pp. 463-479
Singularity Formation in the Shape of a Vortex Sheet
in Three Dimensions-Numerical Simulation
Takashi Ishihara
Department of Mathematics
Faculty of Science
Toyama University
Gofuku, Toyama 930, Japan
Yukio Kaneda
Department of Applied Physics
Faculty of Engineering
Nagoya University
Chikusa-ku, Nagoya 464-01, Japan
Abstract
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.
Vortex Flows and Related
Numerical Methods II
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