Journal of Fluid Mechanics

Table of Contents - Volume 649 - 2010  

Papers

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

PAUL D. WILLIAMSa1 c1, PETER L. READa2 and THOMAS W. N. HAINEa3

a1 Department of Meteorology, University of Reading, Earley Gate, Reading RG6 6BB, UK

a2 Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK

a3 Department of Earth and Planetary Sciences, 329 Olin Hall, 34th and North Charles Streets, Johns Hopkins University, Baltimore, MD 21218, USA

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.

(Received February 03 2009)

(Revised November 09 2009)

(Accepted November 09 2009)

Correspondence:

c1 Email address for correspondence: p.d.williams@reading.ac.uk

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