Influence of lattice thermal conductivity on thermal convection with strongly temperature-dependent viscosity

To examine the effects of temperature-dependent lattice thermal conductivity (lattice-k) on the thermal convection with a temperature-dependent viscous fluid, particularly on the upper thermal boundary layer, we have studied numerically 2-D thermal convective flows with both constant thermal conductivity (constant-k) and lattice-k models. Numerical experiments with large viscosity contrasts, greater than a million, produce a cooler and thinner upper thermal boundary layer for the lattice-k compared with those for the constant-k, implying that thermal convection with lattice-k produces a much sharper boundary between the lithosphere and asthenosphere. The differences between the constant-k and lattice-k can be reasonably explained by the following two causes: (i) the decreasing lattice-k with depth increases an effective Rayleigh number around the bottom of the thermal boundary layer, and (ii) the distribution of lattice-k and uniform vertical heat flux within the thermal boundary layer determine the temperature distribution. The predicted sharper boundary, i.e. sharper vertical viscosity gradient near the bottom of the lithosphere, may play an important role on controlling the amount of lithospheric deformation associated with the downwelling.