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Source-sink flows of a stratified fluid in a rotating annulus

Published online by Cambridge University Press:  20 April 2006

Jae Min Hyun
Jae Min Hyun
Affiliation:
Department of Mechanical Engineering, Clarkson College of Technology, Potsdam, New York 13676
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Abstract

We examine the steady axisymmetric source–sink flows of a stably stratified fluid in a rotating annulus, for which S ∼ O(1), E [Lt ] 1. Numerical methods are used to integrate the unsteady Navier–Stokes equations to obtain the approximate steady solutions. Results on the radial and vertical structures of the flow and temperature-field details are presented. Specific comparisons of the relative sizes of the terms in the equations are conducted to reveal the balance of the dynamic effects. The profiles of the vorticity components are displayed. In the linear flow regime of a homogeneous fluid, the transport of fluid in the meridional plane takes place entirely via boundary layers. As stratification increases, the meridional flows are less concentrated in the boundary layers, and an appreciable portion of the meridional fluid transport is carried through the main body of fluid. The distinction between the sidewall layers and the interior becomes less clear. The flows in the main body of fluid develop vertical velocity shear, resulting in a thermal-wind relation. In the nonlinear case, the source sidewall layer thickens and the sink layer thins. As stratification increases, the meridional fluid transport through the main body of fluid is more pronounced than in the linear case. The balance of terms indicates that the bulk of the flow field is still characterized by the thermal-wind relation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 145 , August 1984 , pp. 111 - 125
Copyright
© 1984 Cambridge University Press

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References

Allen, J. S. 1973 Upwelling of a stratified fluid in a rotating annulus: steady state. Part 2. Numerical solutions. J. Fluid Mech. 59, 337–368.Google Scholar
Babcilon, V. 1968 Stewartson layers in transient rotating fluid flows. J. Fluid Mech. 33, 815–825.Google Scholar
Bakcilon, A., Latt, J., Piacsek, S. & Warn-Varnas, A. 1975 Numerical experiments on stratified spin-up. Geophys. Fluid Dyn. 7, 29–42.Google Scholar
Bennetts, D. A. & Hocking, L. M. 1973 On nonlinear Ekman and Stewartson layers in a rotating fluid. Proc. R. Soc. Lond. A 333, 469–489.Google Scholar
Bennetts, D. A. & Jackson, W. D. N. 1974 Source—sink flows in a rotating annulus: a combined laboratory and numerical study. J. Fluid Mech. 66, 689–705.Google Scholar
Hide, R. 1968 On source—sink flows in a rotating fluid. J. Fluid Mech. 32, 737–764.Google Scholar
Hyun, J. M., Fowlis, W. W. & Warn-Varnas, A. 1982 Numerical solutions for the spin-up of a stratified fluid. J. Fluid Mech. 117, 71–90.Google Scholar
Pedlosky, J. 1971 Geophysical fluid dynamics. In Mathematical Problems in the Geophysical Sciences (ed. W. H. Reid). American Mathematical Society.
Warn-Varnas, A., Fowlis, W. W., Piacsek, S. & Lee, S. M. 1978 Numerical solution and laser-Doppler measurements of spin-up. J. Fluid Mech. 85, 609–639.Google Scholar
Wedemeyer, E. H. 1964 The unsteady flow within a spinning cylinder. J. Fluid Mech. 20, 383–399.Google Scholar