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Optimal linear growth in magnetohydrodynamic duct flow

Published online by Cambridge University Press:  16 April 2010

DMITRY KRASNOV ,
OLEG ZIKANOV ,
MAURICE ROSSI  and
THOMAS BOECK
DMITRY KRASNOV*
Affiliation:
Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, Postfach 100565, 98684 Ilmenau, Germany
OLEG ZIKANOV
Affiliation:
Department of Mechanical Engineering, University of Michigan–Dearborn, 4901 Evergreen Road, Dearborn, MI 48128-1491, USA
MAURICE ROSSI
Affiliation:
UPMC Univ Paris 06, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France
THOMAS BOECK
Affiliation:
Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, Postfach 100565, 98684 Ilmenau, Germany
*
†Email address for correspondence: [email protected]
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Abstract

Transient linear growth in laminar magnetohydrodynamic duct flow is analysed. The duct is straight with rectangular cross-section and electrically insulating walls. The applied uniform magnetic field is oriented perpendicular to the mean flow direction and parallel to one of the walls. Optimal perturbations and their maximum amplifications over finite time intervals are computed. The optimal perturbations are increasingly damped by the magnetic field, localized in the boundary layers parallel to the magnetic field irrespective of the duct aspect ratio. Typically, the optimal perturbations have non-vanishing streamwise wavenumber as found in magnetohydrodynamic channel flow with spanwise magnetic field. The Hartmann boundary layers perpendicular to the magnetic field do not contribute to the transient growth.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 653 , 25 June 2010 , pp. 273 - 299
Copyright
Copyright © Cambridge University Press 2010

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