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Physics of Fluids / Volume 12 / Issue 6 / ARTICLES

Phys. Fluids 12, 1535 (2000); http://dx.doi.org/10.1063/1.870402 (9 pages)

A model for the turbulent Hartmann layer

T. Alboussière and R. J. Lingwood

Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom

(Received 25 March 1999; accepted 9 February 2000)

Here we study the Hartmann layer, which forms at the boundary of any electrically-conducting fluid flow under a steady magnetic field at high Hartmann number provided the magnetic field is not parallel to the wall. The Hartmann layer has a well-known form when laminar. In this paper we develop a model for the turbulent Hartmann layer based on Prandtl’s mixing-length model without adding arbitrary parameters, other than those already included in the log-law. We find an exact expression for the displacement thickness of the turbulent Hartmann layer [also given by Tennekes, Phys. Fluids 9, 1876 (1966)], which supports our assertion that a fully-developed turbulent Hartmann layer of finite extent exists. Leading from this expression, we show that the interaction parameter is small compared with unity and that therefore the Lorentz force is negligible compared with inertia. Hence, we suggest that the turbulence present in the Hartmann layer is of classical type and not affected by the imposed magnetic field, so justifying use of a Prandtl model. A major result is a simple implicit relationship between the Reynolds number and the friction coefficient for the turbulent Hartmann layer in the limit of large Reynolds number. By considering the distance over which the stress decays, we find a condition for the two opposite Hartmann layers in duct flows to be isolated (nonoverlapping). © 2000 American Institute of Physics.

© 2000 American Institute of Physics

KEYWORDS and PACS

Keywords

turbulence, magnetohydrodynamics, boundary layer turbulence, pipe flow

PACS

  • 47.27.-i

    Turbulent flows

  • 47.65.-d

    Magnetohydrodynamics and electrohydrodynamics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.870402

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    R. J. Lingwood and T. Alboussière, "On the stability of the Hartmann layer," Phys. Fluids 11, 2058 (1999)PHFLE6000011000008002058000001.

    G. Talmage, J. S. Walker, S. H. Brown, N. A. Sondergaard, H. Branover, and S. Sukoriansky, "Liquid-metal flows in sliding electrical contacts with arbitrary magnetic-field orientations," Phys. Fluids A 3, 1657 (1991)PFADEB000003000006001657000001.

    H. Tennekes, "Turbulent magnetohydrodynamic channel flow," Phys. Fluids 9, 1876 (1966)PFLDAS000009000009001876000001.

    P. S. Lykoudis and E. C. Brouillette, "Magneto-fluid-mechanics channel flow. II. Theory," Phys. Fluids 10, 1002 (1967)PFLDAS000010000005001002000001.

    E. C. Brouillette and P. S. Lykoudis, "Magneto-fluid-mechanics channel flow. I. Experiment," Phys. Fluids 10, 995 (1967)PFLDAS000010000005000995000001.

    Y. Shimomura, "Large eddy simulation of magnetohydrodynamic turbulent channel flows under a uniform magnetic field," Phys. Fluids A 3, 3098 (1991)PFADEB000003000012003098000001.


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