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REVIEW ARTICLES: Geophysical Flows

Sidewall Instability and Eddy Generation in a Rotating Fluid Subject to Periodic Forcing

[+] Author and Article Information
John E. Hart

Department of Astrophysical, Planetary and Atmospheric Sciences, University of Colorado, Boulder CO 80309

Appl. Mech. Rev 47(6S), S118-S122 (Jun 01, 1994) doi:10.1115/1.3124385 History: Online April 29, 2009

Abstract

Laboratory experiments concerned with the generation of waves and vortices by sidewall instability in a rotating cylinder containing a homogeneous liquid are described. Motions are driven by modulating the basic rotation rate Ω of the cylinder sinusoidally in time at amplitude δ and frequency γ. In addition, a rotating lid, revolving differentially at rate ω provides a steady bias to the motion. The basic state consists of an axisymmetric flow composed of solid body rotation, sloshing periodically in time, with a Stokes-Stewartson boundary layer at the cylinder’s vertical wall. This oscillatory boundary layer is subject to a number of quasi-geostrophic (depth independent) and ageostrophic (depth varying) instabilities. At low values of the rotation modulation δ, the dominant instabilities are ageostrophic small scale propagating-horizontal and stationary-spiral roll vortices that are imbedded in the vertical boundary layer adjacent to the wall, along with propagating vertically-oriented waves that are also trapped in the boundary layer. These instabilities are found only when ω > 0. As the modulation amplitude is increased from zero, columnar vortices form by barotropic instability of the Stokes-Stewartson layer, and for sufficiently supercritical conditions these eddies may penetrate deep into the interior. At low modulation frequency (long period forcing), the interaction of the instabilities with the fluctuating horizontal shear results in a predominance of anticyclonic vortices. On the other hand, at moderate to high frequency modulation dipoles are favored. The formation of both ageostrophic and columnar instabilities is enhanced when the gyre is biased by a cyclonic steady surface stress (ω > 0). Gyres with anticyclonic bias (tending to generate a cyclonic boundary layer) are more stable.

Copyright © 1994 by American Society of Mechanical Engineers
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