Steady, three-dimensional thermal convection in a basally heated
spherical shell with isothermal and stress-free boundaries is
systematically examined for an infinite Prandtl number, Boussinesq
fluid with temperature-dependent viscosity. Convective flows
exhibiting cubic () and tetrahedral (
) symmetry are generated with a finite-volume numerical model for
various combinations of Rayleigh number Ra (defined with viscosity
based on the average of the boundary temperatures) and viscosity
contrast
(ratio of maximum to minimum viscosities). The
range of Ra for which these symmetric flows in spherical geometry can
be maintained in steady-state is sharply reduced by even mild viscosity
variations (
), in contrast with analogous calculations
in cartesian geometry where relatively simple, three-dimensional
convective planforms remain steady for
. The
mild viscosity contrasts employed place some solutions marginally in
the sluggish-lid transition regime in Ra-
parameter space.
Global heat transfer, given by the Nusselt number Nu, is found to
obey a single power-law relation with Ra when Ra is scaled by its
critical value. A power law of the form Nu
(
is the minimum critical value of Ra
for the onset of convection) is obtained, in agreement with previous
results for isoviscous spherical-shell convection with cubic and
tetrahedral symmetry. The calculations of this paper demonstrate that
temperature-dependent viscosity exerts a strong control on the nature
of three-dimensional convection in spherical geometry, an effect that
is likely to be even more important at Rayleigh numbers and viscosity
contrasts more representative of the mantles of terrestrial planets.
The robustness of the Nu-Ra relation, when scaled by
,
is important for studies of planetary thermal history that rely on
parameterizations of convective heat transport and account for temperature
dependence of mantle viscosity.
AGU Index Terms: 3230 Numerical solutions; Mineralogy, Petrology, and Rock Chemistry; 8120 Dynamics of lithosphere and mantle-general; 8121 Dynamics, convection currents and mantle plumes; 8162 Rheology-mantle
Keywords/Free Terms: 3D numerical models, Mantle convection, Temperature-dependent rheology.
JGR-Solid Earth 96JB02097
Vol. 101
, No. B11
, p. 25,473