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A geophysical-scale model of vertical natural convection boundary layers

Published online by Cambridge University Press:  31 July 2008

ANDREW J. WELLS  and
M. GRAE WORSTER
ANDREW J. WELLS
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK
M. GRAE WORSTER
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK
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Abstract

A model is developed for turbulent natural convection in boundary layers formed next to isothermal vertical surfaces. A scaling analysis shows that the flow can be described by plume equations for an outer turbulent region coupled to a resolved near-wall laminar flow. On the laboratory scale, the inner layer is dominated by its own buoyancy and the Nusselt number scales as the one-third power of the Rayleigh number (Nu ∝ ). This gives a constant heat flux, consistent with previous experimental and theoretical studies. On larger geophysical scales the buoyancy is strongest in the outer layer and the laminar layer is driven by the shear imposed on it. The predicted heat transfer correlation then has the Nusselt number proportional to the one-half power of Rayleigh number (Nu ∝ ) so that a larger heat flux is predicted than might be expected from an extrapolation of laboratory-scale results. The criteria for transitions between flow regimes are consistent with a hierarchy of instabilities of the near-wall laminar flow, with a buoyancy-driven instability operating on the laboratory scale and a shear-driven instability operating on geophysical scales.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 609 , 25 August 2008 , pp. 111 - 137
Copyright
Copyright © Cambridge University Press 2008

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