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RESEARCH PAPERS

Nonlinear Spin-Up of a Rotating Stratified Fluid: Experimental Method and Preliminary Results

[+] Author and Article Information
Richard E. Hewitt, Peter W. Duck

Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

Peter A. Davies, Fraser W. Smith

Department of Civil Engineering, The University, Dundee, DD1 4HN, United Kingdom

Michael R. Foster

Department of Aerospace Engineering, Applied Mechanics and Aviation, The Ohio State University, Columbus, OH 43210

J. Fluids Eng 120(4), 667-671 (Dec 01, 1998) (5 pages) doi:10.1115/1.2820720 History: Received November 05, 1997; Revised July 30, 1998; Online December 04, 2007

Abstract

We consider the nonlinear spin-up of a rotating stratified fluid in a conical container. An analysis of similarity-type solutions to the relevant boundary-layer problem (Duck et al, 1997) has revealed three types of behavior for this geometry. In general, the boundary-layer evolves to either a steady state, a growing boundary-layer, or a finite-time singularity depending on the initial to final rotation rate ratio, and a “modified Burger number.” We emphasize the experimental aspects of our continuing spin-up investigations and make some preliminary comparisons with the boundary-layer theory, showing good agreement. The experimental data presented is obtained through particle tracking velocimetry. We briefly discuss the qualitative features of the spin-down experiments which, in general, are dominated by nonaxisymmetric effects. The experiments are performed using a conical container filled with a linearly stratified fluid, the generation of which is nontrivial. We present a general method for creating a linear density profile in containers with sloping boundaries.

Copyright © 1998 by The American Society of Mechanical Engineers
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