Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-19T00:42:57.908Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional stability of a Burgers vortex

Published online by Cambridge University Press:  03 February 2004

PETER J. SCHMID  and
MAURICE ROSSI
PETER J. SCHMID
Affiliation:
Laboratoire de Modélisation en Mécanique (LMM), Université Paris VI, 4 place Jussieu, F-75252 Paris, Cedex 05, France Permanent address: Department of Applied Mathematics, University of Washington, Seattle, WA 98195-2420, USA.
MAURICE ROSSI
Affiliation:
Laboratoire de Modélisation en Mécanique (LMM), Université Paris VI, 4 place Jussieu, F-75252 Paris, Cedex 05, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The evolution of infinitesimal three-dimensional perturbations superimposed on a Burgers vortex is studied. By a sequence of variable transformations and scalings this linear evolution problem is reduced to a time-dependent system which is nearly identical to the stability equations governing a Lamb–Oseen vortex. The maximum amplification reached by perturbations over a finite time interval is computed through an iterative scheme based on the direct and adjoint governing equations, and results on the asymptotic stability of the Burgers vortex are deduced. The Burgers vortex is shown to be asymptotically stable, although significant short-term amplification may occur.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 500 , April 2004 , pp. 103 - 112
Copyright
© 2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)