VARIABLE VISCOSITY CONVECTION EXPERIMENTS WITH A STRESS-FREE UPPER BOUNDARY AND IMPLICATIONS FOR THE HEAT-TRANSPORT IN THE EARTHS MANTLE

We carried out laboratory convection experiments in a large aspect rat io tank to study the effect of a stress-free upper boundary on the hea t transfer and the size of convection cells. We used a concentrated su crose solution to achieve both a high Prandtl number and a strongly te mperature-dependent viscosity. We find that for a stress-free upper bo undary the Nusselt number is proportional to the cubic root of the Ray leigh number, if the latter is defined with the viscosity at the mean of surface and bottom temperature and if the viscosity contrast is kep t constant. For a parametrization with constant surface temperature an d a Rayleigh number defined with the viscosity at the average temperat ure we obtain Nu is-proportional-to Ra0.2. The Nusselt number drops by some 20% for viscosity contrasts between 50 and 5000. At large viscos ity contrast, a stagnant lid forms on top of an actively convecting re gion, and the Nusselt number and the size of the convection cells are nearly identical for both no-slip and free-slip experiments. For visco sity 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, whi ch hampers the movement of the upper boundary layer and reduces the Nu sselt number. For viscosity contrasts less than 250 the heat transfer data agree well with results from three-dimensional numerical calculat ions. At higher viscosity contrasts the numerical data are 10% lower t han the experimental values both for a stress-free and rigid upper bou ndary.