EFFECTS OF STRONGLY VARIABLE VISCOSITY ON 3-DIMENSIONAL COMPRESSIBLE CONVECTION IN PLANETARY MANTLES

A systematic investigation into the effects of temperature dependent v iscosity on three-dimensional compressible mantle convection has been performed by means of numerical simulations in Cartesian geometry usin g a finite volume multigrid code, with a factor of 1000-2500 viscosity variation, Rayleigh numbers ranging from 10(5)-10(7), and stress-free upper and lower boundaries. Considerable differences in model behavio r are found depending on the details of rheology, heating mode, compre ssibility, and boundary conditions. Parameter choices were guided by r ealistic Earth models. In Boussinesq, basally heated cases with viscos ity solely dependent on temperature and stress-free, isothermal bounda ries, very long wavelength flows (similar to 25,000 km, assuming the d epth corresponds to mantle thickness) with cold plumes and hot upwelli ng sheets result, in contrast to the upwelling plumes and downwelling sheets found in small domains, illustrating the importance of simulati ng wide domains. The addition of depth dependence results in small cel ls and reverses the planform, causing hot plumes and cold sheets. The planform of temperature dependent viscosity convection is due predomin antly to vertical variations in viscosity resulting from the temperatu re dependence. Compressibility, with associated depth-dependent proper ties, results in a tendency for broad upwelling plumes and narrow down welling sheets, with large aspect ratio cells. Perhaps the greatest mo dulation effect occurs in internally heated compressible cases, in whi ch the short-wavelength pattern of time-dependent cold plumes commonly observed in constant-viscosity calculations completely changes into a very long wavelength pattern of downwelling sheets (spaced up to 24,0 00 km apart) with time-dependent plumelike instabilities. These result s are particularly interesting, since the basal heat flow in the Earth 's mantle is usually thought to be very low, e.g., 5-20% of total. The effects of viscous dissipation and adiabatic heating play only a mino r role in the overall heat budget for constant-viscosity cases, an obs ervation which is not much affected by the Rayleigh number. However, v iscous dissipation becomes important in the stiff upper boundary layer when viscosity is temperature dependent. This effect is caused by the very high stresses occurring in this stiff lid, typically 2 orders of magnitude higher than the stresses in the interior of the domain for the viscosity contrast modeled here. The temperature in the interior o f convective cells is highly sensitive to the material properties, wit h temperature dependent viscosity and depth-dependent thermal conducti vity strongly increasing the internal temperature, and depth-dependent viscosity strongly decreasing it. The sensitivity of the observed flo w pattern to these various complexities clearly illustrates the import ance of performing compressible, variable-viscosity mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.