Journal of Fluid Mechanics

Dissipative heating in convective flows

J. M.  Hewitt a1, D. P.  Mckenzie a1 and N. O.  Weiss a2
a1 Department of Geodesy and Geophysics, University of Cambridge
a2 Department of Applied Mathematics and Theoretical Physics, University of Cambridge

Article author query
hewitt jm   [Google Scholar] 
mckenzie dp   [Google Scholar] 
weiss no   [Google Scholar] 


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.

(Published Online March 29 2006)
(Received June 10 1974)