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Dissipative heating in convective flows

Published online by Cambridge University Press:  29 March 2006

J. M. Hewitt
Department of Geodesy and Geophysics, University of Cambridge
D. P. Mckenzie
Department of Geodesy and Geophysics, University of Cambridge
N. O. Weiss
Department of Applied Mathematics and Theoretical Physics, University of Cambridge


Dissipative heating is produced by irreversible processes, such as viscous or ohmic heating, in a convecting fluid; its importance depends on the ratio d/HT of the depth of the convecting region to the temperature scale height. Integrating the entropy equation for steady flow yields an upper bound to the total rate of dissipative heating in a convecting layer. For liquids there is a regime in which the ratio of dissipative heating to the convected heat flux is approximately equal to c(d/HT), where the constant c is independent of the Rayleigh number. This result is confirmed by numerical experiments using the Boussinesq approximation, which is valid only if d/HT is small. For deep layers the dissipative heating rate may be much greater than the convected heat flux. If the earth's magnetic field is maintained by a convectively driven dynamo, ohmic losses are limited to 5% of the convected flux emerging from the core. In the earth's mantle viscous heating may be important locally beneath ridges and behind island arcs.

Research Article
© 1975 Cambridge University Press

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