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 language | English (US) |
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Pages (from-to) | 521-566 |
Number of pages | 46 |
Journal | Journal of Fluid Mechanics |
Volume | 232 |
Issue number | 14 |
DOIs | |
State | Published - Jan 1 1991 |
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering