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Centripetal instabilities in two flows involving time-dependent Rayleigh layers on a rotating circular cylinder are examined. In one case we consider the stability of the flow induced in an infinite expanse of quiescent fluid when the cylinder is impulsively given a constant angular velocity; in the other problem the angular velocity increases as the square root of time so that the undisturbed flow has a constant wall shear. For both situations linear neutral stability curves for vortex motions are calculated by quasi-steady (or frozen-time) methods, with these results justified, where possible, by Wentzel-Kramers-Brillouin techniques. The topology of the neutral curve for the ramped angular velocity configuration allows a rigorous description of small wavelength, weakly and fully nonlinear vortex structures to be obtained. Our results are compared with the equivalent cases that arise in the study of unsteady thermal Rayleigh layers induced by the sudden heating of a horizontal flat plate.

Item Type:	Refereed Article
Research Division:	Mathematical Sciences
Research Group:	Applied mathematics
Research Field:	Theoretical and applied mechanics
Objective Division:	Expanding Knowledge
Objective Group:	Expanding knowledge
Objective Field:	Expanding knowledge in the mathematical sciences
UTAS Author:	Bassom, A (Professor Andrew Bassom)
ID Code:	107386
Year Published:	2002
Web of Science® Times Cited:	8
Deposited By:	Mathematics and Physics
Deposited On:	2016-03-11
Last Modified:	2016-08-11
Downloads:	141 View Download Statistics