A Numerical Investigation of Thermal Convection in Highly Viscous Spherical Shells with Applications to Mantle Dynamics in the Earth and Other Terrestrial Planets
Abstract
Numerical models of thermal convection in highly viscous spherical shells are used to investigate mantle convection in the Earth, Mars and Venus. Three-dimensional Boussinesq and compressible convection in basally heated shells are examined for different convective patterns. The influences of heating mode and mechanical boundary conditions are investigated. Three-dimensional models of Boussinesq convection for basal heating show that two polyhedral convective patterns predicted by perturbation theory are stable up to Rayleigh numbers Ra (a measure of convective vigor) on the order 100Racr (Racr is the critical Ra for the onset of convection). The stability of these patterns to flow reversal is tested for several Ra. Compressibility has its greatest effect when the superadiabatic temperature drop Delta T_ {sa} is small (relative to the characteristic adiabatic temperature). When Delta T_ {sa} is small, convection at Ra ~ 10Ra_ {cr} becomes penetrative and time dependent. At large Delta Tsa, solutions with polyhedral planforms are stable up to Ra ~ 100Ra_ {cr} and the wave numbers of spherical harmonic modes that grow fastest with increasing Ra are odd integer multiples of the dominant mode's wave numbers. Solutions with irregular patterns at Ra = 100Racr are time dependent and compressibility affects their pattern evolution. An analysis of axisymmetric convection with either basal or internal heating (for Ra <=q 27Racr) indicates that dynamic topography and convection cell wavelength increase across bifurcations with increasing Ra . Topography and geoid with basal heating are approximately five times larger than with internal heating. For a wide range of heating modes, three-dimensional convection (at Ra ~ 100Racr) displays downwelling in planar sheets, and (with some component of basal heating) upwelling in cylindrical plumes. This agrees with geophysical and geological evidence of convection in the Earth's mantle. The imposition of a rigid upper boundary on three -dimensional models of convection (with applications to the mantles of Mars and Venus) makes downwelling regions irregularly structured and short-lived and causes the upper boundary layer around upwelling plumes to be interspersed with narrow downwelling regions emanating radially from the plumes' axes (which may correlate with radial fractures on the Tharsis bulge). The dependence of convection cell wavelength on heating mode and core size implies that large scale geologic features may have originated during core formation. Dynamic topography for the Mars models is comparable to Tharsis topography.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1989
- Bibcode:
- 1989PhDT........30B
- Keywords:
-
- MARS;
- VENUS;
- Geophysics, Physics: Astronomy and Astrophysics;
- Convective Heat Transfer;
- Free Convection;
- Heating;
- Mars (Planet);
- Mathematical Models;
- Spherical Shells;
- Structural Properties (Geology);
- Three Dimensional Models;
- Topography;
- Venus (Planet);
- Boundary Layers;
- Compressibility;
- Convection Cells;
- Mars Surface;
- Perturbation Theory;
- Plumes;
- Rayleigh Number;
- Stability;
- Upwelling Water;
- Geophysics