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Testing the limits of quasi-geostrophic theory: application to observed laboratory flows outside the quasi-geostrophic regime

Published online by Cambridge University Press:  13 April 2010

PAUL D. WILLIAMS ,
PETER L. READ  and
THOMAS W. N. HAINE
PAUL D. WILLIAMS*
Affiliation:
Department of Meteorology, University of Reading, Earley Gate, Reading RG6 6BB, UK
PETER L. READ
Affiliation:
Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
THOMAS W. N. HAINE
Affiliation:
Department of Earth and Planetary Sciences, 329 Olin Hall, 34th and North Charles Streets, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: [email protected]
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Abstract

We compare laboratory observations of equilibrated baroclinic waves in the rotating two-layer annulus, with numerical simulations from a quasi-geostrophic model. The laboratory experiments lie well outside the quasi-geostrophic regime: the Rossby number reaches unity; the depth-to-width aspect ratio is large; and the fluid contains ageostrophic inertia–gravity waves. Despite being formally inapplicable, the quasi-geostrophic model captures the laboratory flows reasonably well. The model displays several systematic biases, which are consequences of its treatment of boundary layers and neglect of interfacial surface tension and which may be explained without invoking the dynamical effects of the moderate Rossby number, large aspect ratio or inertia–gravity waves. We conclude that quasi-geostrophic theory appears to continue to apply well outside its formal bounds.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 649 , 25 April 2010 , pp. 187 - 203
Copyright
Copyright © Cambridge University Press 2010

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