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Symmetry breaking in vortex-source and Jeffery—Hamel flows

Published online by Cambridge University Press:  26 April 2006

M. Goldshtik ,
F. Hussain  and
V. Shtern
M. Goldshtik
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX 77204–7492, USA Permanent address: Institute of Themophysics, Novosibirsk 630090, USSR.
F. Hussain
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX 77204–7492, USA
V. Shtern
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX 77204–7492, USA Permanent address: Institute of Themophysics, Novosibirsk 630090, USSR.
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Abstract

The stability and bifurcations associated with the loss of azimuthal symmetry of planar flows of a viscous incompressible fluid, such as vortex-source and Jeffery–Hamel flows, are studied by employing linear, weakly nonlinear and fully nonlinear analyses, and features of new solutions are explained. We address here steady self-similar solutions of the Navier–Stokes equations and their stability to spatially developing disturbances. By considering bifurcations of a potential vortex-source flow, we find secondary solutions. They include asymmetric vortices which are generalizations of the classical point vortex to vortical flows with non-axisymmetric vorticity distributions. Another class of solutions we report relates to transition trajectories that connect new bifurcation-produced solutions with the primary ones. Such solutions provide far-field asymptotes for a number of jet-like flows. In particular, we consider a flow which is a combination of a jet and a sink, a tripolar jet, a jet emerging from a slit in a plane wall, a jet emerging from a plane channel and the reattachment phenomenon in the Jeffery–Hamel flow in divergent channels.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 232 , November 1991 , pp. 521 - 566
Copyright
© 1991 Cambridge University Press

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