Heat transport by variable viscosity convection II: pressure influence, non-Newtonian rheology and decaying heat sources

Abstract

This study is an extension of previous work on the heat transport properties of convection with Newtonian temperature-dependent viscosity. There it has been found that the Nusselt number ( Nu) only weakly depends on the Rayleigh number defined with the viscosity at the mean internal temperature ( Ra T ) when the temperature at the top boundary is fixed. Here the cases are considered where the viscosity depends not only on temperature, but additionally on pressure, or on stress according to a third-power law. Numerical solutions for bottom-heated steady state cells with free boundaries are calculated. The weak dependence of Nu on Ra T is also found with pressure influence on the viscosity, provided only that the temperature dependence is stronger. On the other hand, the pressure dependence can reduce the internal temperature of the cell below the mean of the top and bottom temperature, even when the temperature effect is much stronger. With power-law rheology and strong temperature influence a sharp transition between convective regimes with active and stagnant lid is found. In the region of the NuRa-space where present-day whole mantle convection may be located, the heat transport becomes insensitive to the internal Rayleigh number also with power-law creep. Finally, two numerical experiments of time-dependent convection with a decaying rate of bottom or internal heating and variable Newtonian viscosity were performed. The bottom heated cases is found in good agreement with the parameterization derived from steady state results. For internal heating the exponent in the Nu Ra T -relationship is ∼0.10, thus slightly larger than with bottom heating but still much lower than the value for constant viscosity convection. These results strengthen the view that the parameterized models for the thermal evolution of a cooling planet, based on results of constant viscosity convection, need a revision.