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Instability of vertically stratified horizontal plane Poiseuille flow

Published online by Cambridge University Press:  20 November 2020

P. Le Gal Open the ORCID record for P. Le Gal [Opens in a new window] ,
U. Harlander Open the ORCID record for U. Harlander [Opens in a new window] ,
I. D. Borcia Open the ORCID record for I. D. Borcia [Opens in a new window] ,
S. Le Dizès Open the ORCID record for S. Le Dizès [Opens in a new window] ,
J. Chen  and
B. Favier Open the ORCID record for B. Favier [Opens in a new window]
P. Le Gal*
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, 49 rue F. Joliot Curie, 13384 Marseille, CEDEX 13, France
U. Harlander
Affiliation:
Department of Aerodynamics and Fluid Mechanics, Brandenburg University of Technology, Cottbus-Senftenberg, Germany
I. D. Borcia
Affiliation:
Department of Aerodynamics and Fluid Mechanics, Brandenburg University of Technology, Cottbus-Senftenberg, Germany Institute of Physics, Brandenburg University of Technology, Erich-Weinert-Strasse 1, 03046 Cottbus, Germany
S. Le Dizès
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, 49 rue F. Joliot Curie, 13384 Marseille, CEDEX 13, France
J. Chen
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, 49 rue F. Joliot Curie, 13384 Marseille, CEDEX 13, France
B. Favier
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, 49 rue F. Joliot Curie, 13384 Marseille, CEDEX 13, France
*
†Email address for correspondence: legal@irphe.univ-mrs.fr
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Abstract

We present here the first study on the stability of plane Poiseuille flow when the fluid is stratified in density perpendicularly to the plane of horizontal shear. Using laboratory experiments, linear stability analyses and direct numerical simulations, we describe the appearance of an instability that results from a resonance of internal gravity waves and Tollmien–Schlichting waves carried by the flow. This instability takes the form of long meanders confined in thin horizontal layers stacked along the vertical axis.

JFM classification

Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Internal waves

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JFM Rapids
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Journal of Fluid Mechanics , Volume 907 , 25 January 2021 , R1
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© The Author(s), 2020. Published by Cambridge University Press

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References

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