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Energy decay of vortices in viscous fluids: an applied mathematics view

Published online by Cambridge University Press:  20 August 2012

Jan Nordström  and
Björn Lönn
Jan Nordström*
Affiliation:
Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden
Björn Lönn
Affiliation:
Department of Information Technology, Uppsala University, SE-75105 Uppsala, Sweden
*
†Email address for correspondence: jan.nordstrom@liu.se
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Abstract

The energy decay of vortices in viscous fluids governed by the compressible Navier–Stokes equations is investigated. It is shown that the main reason for the slow decay is that zero eigenvalues exist in the matrix related to the dissipative terms. The theoretical analysis is purely mathematical and based on the energy method. To check the validity of the theoretical result in practice, numerical solutions to the Navier–Stokes equations are computed using a stable high-order finite difference method. The numerical computations corroborate the theoretical conclusion.

JFM classification

Compressible Flows: Compressible Flows Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 709 , 25 October 2012 , pp. 593 - 609
Copyright
Copyright © Cambridge University Press 2012

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