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Physics of Fluids / Volume 10 / Issue 4 / ARTICLES

Phys. Fluids 10, 850 (1998); doi:10.1063/1.869608 (9 pages)

Bifurcation analysis of double-diffusive convection with opposing horizontal thermal and solutal gradients

Shihe Xin, Patrick Le Quéré, and Laurette S. Tuckerman

LIMSI-CNRS, BP 133, 91403 Orsay Cedex, France

(Received 1 July 1997; accepted 29 December 1997)

The onset of convection in double diffusion with equal and opposite thermal and solutal buoyancy forces is studied. Numerical linear stability analyses and integration of the full Boussinesq equations are performed in an infinite vertical fluid layer and in closed rectangular cavities bounded by rigid walls. Detailed study of the subsequent nonlinear evolution is carried out for Le = 1.2 and Pr = 1. In the infinite vertical layer, the onset of convection is found to correspond to a subcritical circle pitchfork bifurcation. The finite-amplitude branch of steady states in turn loses stability to traveling waves via a supercritical drift pitchfork bifurcation. In a square cavity the bifurcation is transcritical and the full branch of stable and unstable solutions is constructed. With increasing cavity aspect-ratio, we observe alternating transcritical and pitchfork bifurcations, depending on the symmetry of the most unstable eigenvector. © 1998 American Institute of Physics.

© 1998 American Institute of Physics

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KEYWORDS and PACS

Keywords

bifurcation, convection, diffusion, flow instability, waves, confined flow

PACS

  • 47.20.Ky

    Nonlinearity, bifurcation, and symmetry breaking

  • 47.27.T-

    Turbulent transport processes

  • 47.35.-i

    Hydrodynamic waves

  • 47.60.-i

    Flow phenomena in quasi-one-dimensional systems

ARTICLE DATA

Permalink
http://link.aip.org/link/doi/10.1063/1.869608

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.
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    C. K. Mamun and L. S. Tuckerman, "Asymmetry and Hopf bifurcation in spherical Couette flow," Phys. Fluids 7, 80 (1995)PHFLE6000007000001000080000001.

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