Symmetry breaking in vortex-source and Jeffery—Hamel flows

M. Goldshtik, F. Hussain, V. Shtern

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28 Scopus citations

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.

Original languageEnglish
Pages (from-to)521-566
Number of pages46
JournalJournal of Fluid Mechanics
Volume232
Issue number14
DOIs
StatePublished - Nov 1991

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