The onset of convection in fluids with strongly temperature-dependent viscosity cooled from above with implications for planetary lithospheres

Abstract

The convective instability of a viscous fluid with strongly temperature-dependent viscosity cooled from above provides a basis for better understanding the thermal evolution of the Earth and other planets. The role of temperature-dependent viscosity in the initiation of thermal convection is important since thermally activated creep is strongly temperature dependent. This study introduces a criterion for convective instability based on the ratio of the Rayleigh–Taylor (R-T) growth rate of the thermal density stratification due to conductive cooling and the rate of conductive smoothing of convectively generated temperature variations. This definition of a critical boundary layer Rayleigh number that must be reached for the onset of convection is consistent with numerical experiments reported here as well as earlier theoretical and experimental studies. The length and temperature scales appearing in this Rayleigh number provide valuable physical insight into the behavior of the fluid at the onset of convection. A consistently defined viscosity ratio across the convecting thermal boundary layer leads to a characteristic temperature difference (Δ T c) across this layer. The viscosity ratio inferred from the onset times in numerical experiments reported here (≈10) is similar to that seen in laboratory experiments [Geophys. Res. 99 (1994) 19853] and is consistent with the linearized R-T analysis. Calculation of the onset time of convection and the conductive lid thickness at onset, based on laboratory-derived rheological parameters, provides a better basis to assess the convective instability of the oceanic upper mantle and the possible formation of a thick cratonic lithosphere by the cooling of continental mantle.