Repository: Freie Universität Berlin, Math Department

An Asymptotic Theory for the Nonlinear Instability of Anti- Parallel Pairs of Vortex Filaments

Klein, R. and Majda, A. J. (1993) An Asymptotic Theory for the Nonlinear Instability of Anti- Parallel Pairs of Vortex Filaments. Physics of Fluids A, 5 . pp. 369-379. ISSN 0899-8213

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Simplified asymptotic equations describing the nonlinear dynamics of perturbed pairs of parallel vortex filaments are derived and analyzed here. The derivations are general enough to allow for vortices of unequal strength, but emphasis here is on the antiparallel vortex pair. The simplified asymptotic equations account for both the internal effects of self-induction and self-stretching for each filament and also the external effects of mutual induction that lead to a nontrivial coupling of the perturbations of the two filaments. When these nonlinear equations are linearized at the unperturbed filament pair, the linearized stability theory of Crow [AIAA J. 8, 2172 (1970)] is recovered in a systematic fashion. The asymptotic equations are derived in a novel singular limit at high Reynolds numbers through assumptions similar to the authors' recent theories [Physica D 49, 323 (1991); ibid. 53, 267 (1991); Phys. Fluids A 4, 2271 (1992)] for the dynamics of a single perturbed vortex filament. Through the Hasimoto transform [J. Fluid Mech. 51, 477 (1972)], these equations become two coupled perturbed nonlinear Schrödinger equations for a pair of filament functions. A series of numerical solutions of the asymptotic equations exhibits several new phenomena in the nonlinear instability of pairs of antiparallel vortex filaments. Physics of Fluids A: Fluid Dynamics is copyrighted by The American Institute of Physics.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:493
Deposited By: Ulrike Eickers
Deposited On:29 Jun 2009 10:15
Last Modified:29 Jun 2009 10:15

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