A new approach for nonparallel flow stability
Abstract
The paper develops a new stability approach for conical flows of a viscous incompressible fluid. We study whether conical flows are robust with respect to steady three-dimensional disturbances given at outer or inner boundaries of the similarity region. A special transformation of the Navier-Stokes equations allows the exact reduction of this stability problem to a system of ordinary differential equations. There is no quasi-parallel approximations despite the conical flows are strongly nonparallel. Disturbances decay as one moves away from the boundaries into the similarity region when Reynolds number Re is small. The disturbances grow if Re exceeds a critical value. This causes a variety of bifurcations including: appearance of folds related to (a) hysteretic transitions between the primary solutions and (b) jump flow separation from the cone, (c) initiation of radially oscillating regimes, (d) development of swirl in primarily swirl-free flows, and (e) azimuthal symmetry breaking. Bifurcations (a)-(c) are new and (d)-(e) have been found in our prior works. Here the instability nature of all these bifurcations is clarified. The outer disturbances are found to be responsible for (a) hysteresis and (d) swirl generation. The jump flow separation (b) and loss of the azimuthal symmetry (e) occur due to the inner disturbances. The radial oscillations (c) develop due to global disturbances influenced by both boundaries.
- Publication:
-
APS Division of Fluid Dynamics Meeting Abstracts
- Pub Date:
- November 1996
- Bibcode:
- 1996APS..DFD..HH01S