Asymptotic equations for the stretching of vortex filaments in a background flow field

Rupert Klein, Andrew J. Majda, Richard M. McLaughlin

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)2271-2281
Number of pages11
JournalPhysics of Fluids A
Volume4
Issue number10
StatePublished - 1992

Fingerprint

vortex filaments
Stretching
Flow fields
flow distribution
Vortex flow
filaments
Reynolds number
Wavelength
induction
Computer simulation
perturbation
high Reynolds number
vortices
requirements
expansion
wavelengths
D 53

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Physics and Astronomy(all)
  • Mechanics of Materials
  • Computational Mechanics
  • Fluid Flow and Transfer Processes

Cite this

Asymptotic equations for the stretching of vortex filaments in a background flow field. / Klein, Rupert; Majda, Andrew J.; McLaughlin, Richard M.

In: Physics of Fluids A, Vol. 4, No. 10, 1992, p. 2271-2281.

Research output: Contribution to journalArticle

Klein, Rupert ; Majda, Andrew J. ; McLaughlin, Richard M. / Asymptotic equations for the stretching of vortex filaments in a background flow field. In: Physics of Fluids A. 1992 ; Vol. 4, No. 10. pp. 2271-2281.
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