A simple model of high Prandtl and high Rayleigh number convection bounded by thin low-viscosity layers

Abstract

SUMMARY 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 ∼R 1/3 (�/δ ) 2/3 is obtained for an aspect ratio 2� of the convection cell of order unity or less. Here δ denotes the fraction of the layer depth occupied by each of the low