P. Cardin $^{a}$, D. Brito $^{a}$ and J. Aurnou $^{b}$
$^{a}$ LGIT, Observatoire de Grenoble, France. $^{b}$ Department of terrestrial magnetism, Carnegie Institution of Washington, USA.
philippe.cardin@ujf-grenoble.fr
The effective viscosity of the Earth's liquid outer core has long been a topic of debate among geophysicists. Here we present preliminary results from a suite of laboratory experiments which demonstrate that the concept of turbulent viscosity does apply to planetary core fluids. In these experiments, we measure the spin-up time in a spherical shell of water using an ultrasonic Doppler velocimetry method with and without the presence of strong thermal convection. In the laminar spin-up regime, the spin-up time (i.e., the characteristic time of synchronization between the fluid and the boundary after a sudden change of the boundary rotation rate) is proportional to the square root of the molecular kinematic viscosity. An apparent or turbulent viscosity must be introduced that is 50% greater than the molecular kinematic viscosity in order to explain the spin-up measurements made with turbulent thermal convection occurring in the sphere ($Ra \sim 30Ra_C$). >From these experimental measurements, we deduce a phenomenological law for turbulent fluid viscosity and apply it to planetary cores. This result has many consequences for geophysical studies of the variations of the length of day, nutations and precession of the Earth and other planets. In addition, our findings give support to numerical geodynamo studies, which use large fluid viscosities.