Transitions in thermal convection with strongly variable viscosity

One of the most important material properties influencing the style of convection in the mantles of terrestrial planets is the extreme temperature-dependence of viscosity. Three-dimensional numerical convection calculations in a wide (8 x 8 x 1) cartesian box and in a spherical shell (ratio of inner to outer radius of 0.55, characteristic of terrestrial planets) both display two fundamental transitions as the viscosity contrast is progressively increased from unity to a factor of 10(5). These transitions not only mark changes in the style of deformation in the upper boundary layer from mobile-lid to sluggish-lid to stagnant-lid but also have dramatic effects on the style, planform, and horizontal length scales of convection in the entire domain. Vertical variations of viscosity are the most important for determining the horizontal length scales of the convective patterns while lateral viscosity variations play a role in shaping the relative structures of the upwelling and downwelling flows, Convection in Venus appears to be represented most closely by the sluggish-lid regime of convection, whereas the Earth, with plate tectonics, more closely resembles the mobile-lid style of convection. Forcing plate-like characteristics onto the convective flows in the form of imposed weak zones and prescribed surface velocities results in flow patterns dominated entirely by the form used to enforce the plate-like behavior and tells us little about why the mantle exhibits long-wavelength heterogeneity. (C) 1997 Elsevier Science B.V.