Geodesic
Singularity formation in the shape of a vortex sheet in three dimensions-numerical simulation
Takashi Ishihara1 ; Yukio Kaneda2
1 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
ESAIM. Proceedings, Tome 1 (1996), pp. 463-479.

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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.
DOI : 10.1051/proc:1996014

Takashi Ishihara 1 ; Yukio Kaneda 2

1 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 
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Takashi Ishihara; Yukio Kaneda. Singularity formation in the shape of a vortex sheet in three dimensions-numerical simulation. ESAIM. Proceedings, Tome 1 (1996), pp. 463-479. doi : 10.1051/proc:1996014. http://geodesic.mathdoc.fr/articles/10.1051/proc:1996014/

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