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Three-dimensional tertiary motions in a plane shear layer

Published online by Cambridge University Press:  20 April 2006

M. Nagata  and
F. H. Busse
M. Nagata
Affiliation:
Department of Earth and Space Sciences, University of California at Los Angeles
F. H. Busse
Affiliation:
Department of Earth and Space Sciences, University of California at Los Angeles
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Abstract

The nonlinear evolution of instabilities of a plane-parallel shear flow with an inflection-point profile is studied. The particular example of the cubic-profile flow generated in an inclined layer heated from above and cooled from below is chosen because it exhibits supercritical bifurcations for secondary and tertiary flows. Since the limit of small Prandtl number is assumed, buoyancy effects caused by temperature perturbations are negligible. The analysis describes first the transition to transverse roll-like vortices which become unstable at slightly supercritical Grashof numbers to a vortex-pairing instability with alternating pairing in the spanwise direction. Three-dimensional finite-amplitude solutions for this tertiary mode of motion are computed and discussed. Finally the question of the stability of the tertiary flow is addressed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 135 , October 1983 , pp. 1 - 26
Copyright
© 1983 Cambridge University Press

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