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A theoretical model for horizontal convection at high Rayleigh number

Published online by Cambridge University Press:  22 May 2007

G. O. HUGHES ,
R. W. GRIFFITHS ,
J. C. MULLARNEY  and
W. H. PETERSON
G. O. HUGHES
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia
R. W. GRIFFITHS
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia
J. C. MULLARNEY
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia Department of Oceanography, Dalhousie University, Halifax, NS, B3H 4J1, Canada
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Abstract

We present a simple flow model and solution to describe ‘horizontal convection’ driven by a gradient of temperature or heat flux along one horizontal boundary of a rectangular box. Following laboratory observations of the steady-state convection, the model is based on a localized vertical turbulent plume from a line or point source that is located anywhere within the area of the box and that maintains a stably stratified interior. In contrast to the ‘filling box’ process, the convective circulation involves vertical diffusion in the interior and a stabilizing buoyancy flux distributed over the horizontal boundary. The stabilizing flux forces the density distribution to reach a steady state. The model predictions compare well with previous laboratory data and numerical solutions. In the case of a point source for the plume (the case which best mimics the localized sinking in the large-scale ocean overturning) the thermal boundary layer is much thicker than that given by the two-dimensional boundary layer scaling of H. T. Rossby (Tellus, vol. 50, 1965, p. 242).

Type
Papers
Information
Journal of Fluid Mechanics , Volume 581 , 25 June 2007 , pp. 251 - 276
Copyright
Copyright © Cambridge University Press 2007

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