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10/02/01 Colloquium
DR. FRANCISCO MARQUES
DEPARTMENT OF APPLIED PHYSICS
POLYTECHNIC UNIVERSITY OF CATALONIA, SPAIN
DEPARTMENT OF APPLIED PHYSICS
POLYTECHNIC UNIVERSITY OF CATALONIA, SPAIN
Instabilities, Symmetry Breaking and Mode Interactions in an Enclosed Swirling Flow.
Abstract: The flow in a cylinder with a rotating endwall has continued to attract much attention since Vogel (1968) first observed the vortex breakdown of the central core vortex that forms. Recent experiments have observed a multiplicity of unsteady stats the coexist over a range of the governing parameters. In spite of numerous numerical and experimental studies, there continues to be considerable controversy with fundamental aspects of this flow, particularly with regards to symmetry breaking. Also, it is not well understood where these oscillatory states originate from, how they are interrelated, nor how they are related to the steady, axisymmetric basic state. The basic state loses stability via a supercritical Hopf bifurcation as the rotation rate is increased. For a certain range of cylinder aspect ratio, the Hopf bifurcation does not break the SO(2) symmetry (axisymmetry), while outside the range it does, leading to a rotating wave solution. These two bifurcation scenarios are explored, using an efficient and accurate numerical scheme for the three-dimensional Naviers-Stokes equations in primitive variables in a cylinder.
