Physics
Scientific paper
Jan 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006geoji.164..160b&link_type=abstract
Geophysical Journal International, Volume 164, Issue 1, pp. 160-167.
Physics
12
Scientific paper
Motivated by recent numerical results on convection in the Earth's mantle in the presence of a low-viscosity zone, an analytical model is derived for 2-D steady convection with symmetric low-viscosity layers at the upper and lower boundaries. The asymptotic limits of high Rayleigh and high Prandtl number are assumed. The low- viscosity layers carry with minimal dissipation most of the horizontal component of the convection flow and thereby increase the efficiency of the convective heat transport. A Nusselt number (Nu)-Rayleigh number (R) relationship of the form Nu~R1/3 (l/δ)2/3 is obtained for an aspect ratio 2l of the convection cell of order unity or less. Here δ denotes the fraction of the layer depth occupied by each of the low-viscosity channels. For large l and τ~l6δ-3, where τ denotes the ratio between the viscosity of the interior and that of the thin low-viscosity layers, Nu reaches a maximum value of the order (Rτ2/3)1/3 at l= (τδ3/9)1/6π/2. This result suggests that the aspect ratio of convection increases with viscosity contrast.
Busse Friedrich H.
Lenardic Adrian
Richards Anita M.
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