Free access article

ESAIM: Proc., 1996, Vol. 1, pp. 463-479
DOI: 10.1051/proc:1996014

Singularity formation in the shape of a vortex sheet in three dimensions-numerical simulation

Takashi Ishihara¹ and Yukio Kaneda<sup>2

1</sup>  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

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.

© EDP Sciences, ESAIM 1996

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