Numerical calculations of fully three-dimensional convection in constant viscosity, compressible spherical shells are interpreted in terms of possible convective motions in the mantles of Venus and Mars. The shells are heated both internally and from below to account for radiogenic heating, secular cooling, and heat flow from the core. The lower boundary of each of the shells is isothermal and shear stress free, as appropriate to the interface between a mantle and a liquid outer core. The upper boundary of each of the shells is rigid and isothermal, as appropriate to the base of a thick immobile lithosphere. Calculations with shear stress-free upper boundaries are also carried out to assess the role of the rigid surface condition. The ratio of the inner radius of each shell to its outer radius is in accordance with possible core sizes in both Venus and Mars. A calculation is also carried out for a Mars model with a small core to simulate mantle convection during early core formation. Different relative proportions of internal and bottom heating are investigated, ranging from nearly complete heating from within to almost all heating from below. The Rayleigh numbers of all the cases are approximately 100 times the critical Rayleigh numbers for the onset of convection. Cylindrical plumes are the prominent form of upwelling in the models independent of the surface boundary condition so long as sufficient heat derives from the core. Thus major volcanic centers on Mars, such as Tharsis and Elysium, and the coronae and some equatorial highlands on Venus may be the surface expressions of cylindrical mantle plumes. The form of the downwelling sheets is significantly affected by the rigid boundary in that the sheets are more irregular in their horizontal structure than when the top boundary is shear stress free.

In the mainly heated-from-within models, the downwelling sheets are also shorter and less temporally durable when the top boundary is rigid than when it is stress free. Thus the free motion of plates on the Earth facilitates extensive durable convective currents that drive the plates, while the stiffening of the lithospheres on Mars and Venus promotes a style of convection that is not particularly effective in breaking the lithosphere into plates. In the rigid top cases, the upper boundary layer surrounding the plumes appears to be interspersed with downwelling currents emanating radially from the plumes' axes; these currents may establish a stress field at the base of hotspot swells that could lead to radial fractures such as those on Tharsis. Models with rigid upper boundaries have higher interior temperatures than do similar models with shear-stress-free upper boundaries.

On this basis, Venus not only has a higher surface temperature than Earth, but it would have a hotter mantle as well. Upwelling plumes are more numerous when theouter boundary is rigid (as compared with shear stress free). Flows dominated by a few strong plumes occur when the proportion of basal heating is large. Thus if the Martian crustal dichotomy were caused by a convective system dominated by spherical harmonic degree l=1, then the convection may have been driven strongly from below by a heating pulse accompanying core formation or from the flow of heat from an early hot core. If a convective mechanism is responsible for the crustal dichotomy, then the dichotomy is likely a very ancient feature. However, the small core models we consider consistently produce a convective pattern with a dominant l=2 signature which does not correlate with the Martian crustal dichotomy; a yet smaller core may be necessary to yield the l=1 pattern. The small core convective pattern does correlate with the geoid and topography signatures of Tharsis, which have strong l=2 components, and the model produces dynamic uplift comparable to the total topography of the Tharsis rise. Models with larger cores (i.e., with the probable inner to outer radius ratio of Mars' present mantle) generated 4 km of uncompensated topography, similar to estimates of the uncompensated Tharsis topography. Thus the Tharsis rise could have achieved its full height early in the evolution of Mars by mantle plume dynamic uplift.

At present, the uncompensated portion of the Tharsis rise topography can be accounted for by dynamic uplift, obviating the need for elastic support. The present compensated portion of the Tharsis topography could be attributed to volcanic or magnetic crustal thickening or depletion of the underlying mantle. Large core models appropriate to the present Mars produce too many plumes to account for just two major volcanic centers (i.e., Tharsis and Elysium). Mantle plume activity could be focussed beneath regions like Tharsis if fracturing or thinning of the lithosphere in these regions has facilitated magma and heat transport across the lithosphere. A similar mechanism could be responsible for clustering of coronae on Venus. There are no deep-seated, active, linear upwellings in the Venus models that could be associated with linear spreading centers in Aphrodite. If linear spreading is actually occurring in Aphrodite, the phenomenon is probably a shallow passive one, similar to mid-ocean ridges on Earth. ¿ American Geophysical Union 1990