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RESEARCH PAPERS

Nonlinear Spin-Up of a Rotating Stratified Fluid: Theory

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

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

Michael R. Foster

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

Peter A. Davies

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

J. Fluids Eng 120(4), 662-666 (Dec 01, 1998) (5 pages) doi:10.1115/1.2820719 History: Received November 05, 1997; Revised July 30, 1998; Online December 04, 2007

Abstract

We consider the boundary layer that forms on the wall of a rotating container of stratified fluid when altered from an initial state of rigid body rotation. The container is taken to have a simple axisymmetric form with sloping walls. The introduction of a non-normal component of buoyancy into the velocity boundary-layer is shown to have a considerable effect for certain geometries. We introduce a similarity-type solution and solve the resulting unsteady boundary-layer equations numerically for three distinct classes of container geometry. Computational and asymptotic results are presented for a number of parameter values. By mapping the parameter space we show that the system may evolve to either a steady state, a double-structured growing boundary-layer, or a finite-time breakdown depending on the container type, rotation change and stratification. In addition to extending the results of Duck et al. (1997) to a more general container shape, we present evidence of a new finite-time breakdown associated with higher Schmidt numbers.

Copyright © 1998 by The American Society of Mechanical Engineers
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