Variable viscosity convection experiments with a stress-free upper boundary and implications for the heat transport in the Earth's mantle

Abstract

We carried out laboratory convection experiments in a large aspect ratio tank to study the effect of a stress-free upper boundary on the heat transfer and the size of convection cells. We used a concentrated sucrose solution to achieve both a high Prandtl number and a strongly temperature-dependent viscosity. We find that for a stress-free upper boundary the Nusselt number is proportional to the cubic root of the Rayleigh number, if the latter is defined with the viscosity at the mean of surface and bottom temperature and if the viscosity contrast is kept constant. For a parametrization with constant surface temperature and a Rayleigh number defined with the viscosity at the average temperature we obtain Nu ∝ Ra 0.2. The Nusselt number drops by some 20% for viscosity contrasts between 50 and 5000. At large viscosity contrast, a stagnant lid forms on top of an actively convecting region, and the Nusselt number and the size of the convection cells are nearly identical for both no-slip and free-slip experiments. For viscosity contrasts up to 1000 the surface layer is mobile, and we observe convection cells with aspect ratios ranging from 1.5 to 3.5. Our heat transfer data are reliable only for Rayleigh numbers up to 10 5. For higher Rayleigh numbers an evaporation skin forms on the surface, which hampers the movement of the upper boundary layer and reduces the Nusselt number. For viscosity contrasts less than 250 the heat transfer data agree well with results from three-dimensional numerical calculations. At higher viscosity contrasts the numerical data are 10% lower than the experimental values both for a stress-free and rigid upper boundary.