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A remark on the vertical transport of large-scale temperature fluctuations by smaller-scale convection

Published online by Cambridge University Press:  19 December 2013

D.O. Gough
D.O. Gough*
Affiliation:
Institute of Astronomy & Department of Applied Mathematics and Theoretical Physics, Madingley Road, Cambridge, CB3 0HA, UK
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Abstract

A simple mixing-length discussion of vertical diffusive transport of a scalar by small-scale turbulent convection is presented, likening it to the microscopic transport in a classical gas. If the scalar is passive, the transport is governed by the well known telegraph equation. Temperature, on the other hand, influences the dynamics of the small-scale motion by modifying the buoyancy that drives the turbulent eddies; it leads to a rather more complicated equation, which, for relatively rapid variation reduces to the same wave equation as for a passive scalar, with maximal propagation speed comparable with the rms vertical eddy velocity; but in the slow diffusive limit it reduces, for good reason, to the classical diffusion equation with a diffusivity enhanced by a factor 3/2 over that pertaining to a passive scalar.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 63: New Advances in Stellar Physics: From Microscopic to Macroscopic Processes , 2013 , pp. 255 - 262
Copyright
© EAS, EDP Sciences, 2013

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