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Axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation

Published online by Cambridge University Press:  21 April 2006

M. V. Melander ,
J. C. Mcwilliams  and
N. J. Zabusky
M. V. Melander
Affiliation:
National Center for Atmospheric Research, PO Box 3000, Bulder, CO 80307, USA Present address: Institute for Computational Mathematics and Applications, Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
J. C. Mcwilliams
Affiliation:
National Center for Atmospheric Research, PO Box 3000, Bulder, CO 80307, USA
N. J. Zabusky
Affiliation:
National Center for Atmospheric Research, PO Box 3000, Bulder, CO 80307, USA Present address: Institute for Computational Mathematics and Applications, Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
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Abstract

We consider the evolution of an isolated elliptical vortex in a weakly dissipative fluid. It is shown computationally that a spatially smooth vortex relaxes inviscidly towards axisymmetry on a circulation timescale as the result of filament generation. Heuristically, we derive a simple geometrical formula relating the rate of change of the aspect ratio of a particular vorticity contour to its orientation relative to the streamlines (where the orientation is defined through second-order moments). Computational evidence obtained with diagnostic algorithms validates the formula. By considering streamlines in a corotating frame and applying the new formula, we obtain a detailed kinematic understanding of the vortex's decay to its final state through a primary and a secondary breaking. The circulation transported into the filaments although a small fraction of the total, breaks the symmetry and is the chief cause of axisymmetrization.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 178 , May 1987 , pp. 137 - 159
Copyright
© 1987 Cambridge University Press

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