Convection experiments in fluids with highly temperature-dependent viscosity and the thermal evolution of the planets

Abstract

Convection experiments in fluids whose viscosity depends on temperature were carried out. Ratios of the top viscosity over the bottom viscosity up to 10 5 have been studied. Horizontally-averaged temperature versus depth profiles are presented, as well as accurate Nusselt number measurements and temperature isogradient cell pattern for Rayleigh numbers ( R) in the moderate range. The difference between the actual interior temperature and the mean of the top and bottom temperatures increases with the viscosity ratio. This difference reaches 25% of the overall temperature drop for a viscosity ratio of 10 5. As previously reported, the Nusselt number ( Nu) first decreases when the viscosity ratio increases, as compared to the constant viscosity case, provided the Rayleigh number is defined using the viscosity at the mean of the top and bottom temperatures. However, the trend is reversed for viscosity ratios larger than ∼5000. This is consistent with an Nu- R relationship based on the critical Rayleigh number. All planetary thermal evolution models using the parameterized convection approach divide the convective planet into a conductive lid and a convective region of constant viscosity underneath. Due to the lack of knowledge about convection in a temperature-dependent viscosity fluid, assumptions have to be made in order to define the cut-off between the two regions. The most commonly made assumptions are not supported by our experiments. Our experimental results can be used for extrapolating to situations of geophysical interest and for answering basic questions such as: what is the interior temperature of the convective system as a function of the rheological law and heat flux, and, what is the thickness of the lid?