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Coaxial scattering of Euler-equation translating V-states via contour dynamics

Published online by Cambridge University Press:  20 April 2006

Edward A. Overman  and
Norman J. Zabusky
Edward A. Overman
Affiliation:
Institute for Computational Mathematics and Applications, Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15261
Norman J. Zabusky
Affiliation:
Institute for Computational Mathematics and Applications, Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15261
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Abstract

The robustness of localized states that transport energy and mass is assessed by a numerical study of the Euler equation in two space dimensions. The localized states are the translating ‘V-states’ discovered by Deem & Zabusky. These piecewise- constant dipolar (i.e. oppositely-signed ± or ±) vorticity regions are steady translating solutions of the Euler equations. A new adaptive contour-dynamical algorithm with curvature-controlled node insertion and removal is used. The evolution of one V-state, subject to a symmetric-plus-asymmetric perturbation is examined and stable (i.e. non-divergent) fluctuations are observed. For scattering interactions, coaxial head-on (or ± on ±) and head-tail (or & on ±) arrangements are studied. The temporal variation of contour curvature and perimeter after V-states separate indicate that internal degrees of freedom have been excited. For weak interactions we observe phase shifts and the near recurrence to initial states. When two similar, equal-circulation but unequal-area V-states have a head-on interaction a new asymmetric state is created by contour ‘exchange’. There is strong evidence that this is near to a V-state. For strong interactions we observe phase shifts, ‘breaking’ (filament formation) and, for head-tail interactions, merger of like-signed vorticity regions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 125 , December 1982 , pp. 187 - 202
Copyright
© 1982 Cambridge University Press

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