A systematic experimental study of rapidly rotating spherical convection in water and liquid gallium
Résumé
Results of finite-amplitude convection experiments in a rotating spherical shell are presented. Water (Prandtl number P=7) and liquid gallium ( P=0.027) have been used as working fluids. In both liquids, convective velocities could be measured in the equatorial plane using an ultrasonic Doppler velocimetry technique. The parameter space has been systematically explored, for values of the Ekman and Rayleigh numbers E>7×10 -7 and Ra<5×10 9. Both measured convective velocity and zonal circulation are much higher in liquid gallium than in water. A scaling analysis is formulated, which shows that higher convective velocities are an effect of the low Prandtl number in liquid gallium, and that higher zonal flows can be explained through a Reynolds stress mechanism. The Reynolds numbers in gallium ( Re=250-2000) are higher indeed than in water ( Re=25-250). An inertial regime sets up at high Re, in which kinetic energy does not dissipate at the scale of convective eddies and is transferred up to the scale of the container, where it is dissipated through Ekman friction of zonal flow. This upwards energy transfer can be seen as an effect of quasigeostrophic (QG) turbulence. Applying the scaling relations to an hypothetic non-magnetic flow in the Earth's core yields Reynolds numbers of the order of 10 8, in fair agreement with values required for dynamo action, convective velocities of order 10 -3 m/s, zonal flow of similar amplitude, and eddy scales as low as 10 km.