Three‐dimensional variable viscosity convection of an infinite Prandtl Number Boussinesq fluid in a spherical shell

Abstract

We investigate a three‐dimensional, spherical‐shell model of mantle convection with strongly temperature‐dependent viscosity. Numerical calculations of convection in an infinite Prandtl number, Boussinesq fluid heated from below at a Rayleigh number of Ra = 105 are carried out for the isoviscous case and for a viscosity contrast across the shell of 1,000. In the isoviscous case, convection is time dependent with quasi‐cylindrical upflow plumes and sheet‐like downflows. When viscosity varies strongly across the shell, convection is also time dependent, but major quasi‐cylindrical downflows with spider‐like extensions occur at both poles and interconnected upflow plumes occur all around the equator. The surface expression of mantle convection in the Earth (downwelling sheets at trenches, upwelling plumes at hot spots, and upwelling sheets at midocean ridges) resembles structures seen in both the isoviscous and variable viscosity models. The dominance of spherical harmonic degree ℓ = 2 in the variable viscosity model agrees with the ℓ = 2 dominance in the Earth's geoid, topography, and seismic tomography. The overall pattern of convection in the variable viscosity case is similar to the distribution of major highlands and volcanic rises on Venus.