 
Summary: Physics of the Earth and Planetary Interiors 128 (2001) 5174
A systematic experimental study of rapidly rotating spherical
convection in water and liquid gallium
Julien Aubert, Daniel Brito, HenriClaude Nataf, Philippe Cardin, JeanPaul Masson
Laboratoire de Géophysique Interne et Tectonophysique, Observatoire des Sciences de l'Univers de Grenoble,
BP 53X, 38041 Grenoble Cedex 9, France
Received 31 December 2000; accepted 14 August 2001
Abstract
Results of finiteamplitude 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 × 107 and Ra < 5 × 109. 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 = 2502000) are higher indeed than in water
(Re = 25250). 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 nonmagnetic flow in the Earth's core yields Reynolds numbers of the order of 108, in fair agreement with values
required for dynamo action, convective velocities of order 103 m/s, zonal flow of similar amplitude, and eddy scales as low
