Klein, R. and Majda, A. J. and McLaughlin, R.M.
(1992)
*Asymptotic Equations for the Stretching of Vortex Filaments by a Background Flow Field.*
Physics of Fluids A, 4
.
pp. 2271-2281.
ISSN 0899-8213

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## Abstract

Recently, two of the authors have derived [Physica D 49, 323 (1991)] and analyzed [Physica D 53, 267 (1991)] a new asymptotic equation for the evolution of small-amplitude short-wavelength perturbations of slender vortex filaments in high Reynolds number flows. This asymptotic equation differs significantly from the familiar local self-induction equation in that it includes some of the nonlocal effects of self-stretching of the filament in a simple fashion. Here, through systematic asymptotic expansions, the authors derive a modification of this asymptotic equation that incorporates the important additional effects of strain and rotation from a general background flow field. The main requirement on the background flow is that it does not displace the unperturbed background filament. The new asymptotic equations exhibit in a simple fashion the direct competition in filament dynamics between internal effects such as self-induction and self-stretching and external effects of background flows involving strain and rotation. Solutions of these asymptotic equations revealing various aspects of this competition are analyzed in detail through both theory and numerical simulation. An application is also presented for the nonlinear stability of a columnar vortex to suitable perturbations in a straining, rotating, background environment. Physics of Fluids A: Fluid Dynamics is copyrighted by The American Institute of Physics.

Item Type: | Article |
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Uncontrolled Keywords: | VORTEX FLOW, FILAMENTS, ASYMPTOTIC SOLUTIONS, STRAINS, ROTATION, STABILITY |

Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group |

ID Code: | 494 |

Deposited By: | Ulrike Eickers |

Deposited On: | 29 Jun 2009 10:26 |

Last Modified: | 29 Jun 2009 10:26 |

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