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Instabilities of longitudinal rolls in the presence of Poiseuille flow

Published online by Cambridge University Press:  26 April 2006

R. M. Clever  and
F. H. Busse
R. M. Clever
Affiliation:
Institute of Geophysics and Planetary Physics, University of California at Los Angeles, CA 90024, USAand Institute of Physics, University of Bayreuth, 858 Bayreuth, Germany
F. H. Busse
Affiliation:
Institute of Geophysics and Planetary Physics, University of California at Los Angeles, CA 90024, USAand Institute of Physics, University of Bayreuth, 858 Bayreuth, Germany
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Abstract

Longitudinal rolls represent the preferred form of convection in a horizontal fluid layer heated from below in the presence of parallel shear flows for sufficiently low Reynolds numbers and for a finite range of the Rayleigh number above the critical value Rac. In this paper properties of the longitudinal rolls and their stability with respect to three-dimensional disturbances are investigated in the case of Poiseuille flow. While the convective heat transport is independent of the Reynolds number, the mass flux through the channel at a given Reynolds number decreases with increasing Rayleigh number. A wavy instability is found to set in at a finite Reynolds number and relatively low Rayleigh numbers, depending on the Prandtl number P. In particular, the stability region for longitudinal rolls is analysed for P = 0.025, 0.1, 0.71, 2.5, and 7. For sufficiently small Reynolds number the oscillatory, the skewed varicose or the knot instability can precede the wavy instability. For P = 7 the wavy instability is preceded by a modified knot instability throughout the Reynolds-number range that has been investigated. In spite of the difference hi symmetry, the results for Poiseuille flow resemble those obtained earlier hi the case of plane Couette flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 229 , August 1991 , pp. 517 - 529
Copyright
© 1991 Cambridge University Press

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