Journal of Fluid Mechanics

Distortions of inertia waves in a rotating fluid cylinder forced near its fundamental mode resonance

Richard  Manasseh a1c1
a1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK

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A series of experimental observations is presented of a flow in which inertial oscillations are excited. The homogeneous fluid is contained in a completely filled right circular cylinder. The cylinder is spun about its axis of symmetry and a small ‘forced precession’ (or coning motion) is impulsively started. The flow is visualized by an electrolytic dyeline method. The mathematical problem for linear inviscid inertial oscillations in this system, although ill-posed in general, admits a solution in terms of wave modes for the specific boundary conditions considered here. The experiments show that while this linear inviscid theory provides some facility for predicting the flow structure at early times, the flow rapidly and irreversibly distorts away from the predicted form. This behaviour is seen as a precursor to some of the more dramatic breakdowns described by previous authors, and it may be pertinent to an understanding of the breakdowns reported in experiments on elliptical flow instabilities.

(Published Online April 26 2006)
(Received March 4 1993)
(Revised October 19 1993)

c1 Current affiliation: School of Mathematics, University of New South Wales, P.O. Box 1, Kensington, NSW 2033, Australia