Dynamics of thin rotating flows subject to electric and magnetic fields -

Abstract

We investigate the properties of thin rotating flows subject to a Lorentz force. The height of the fluid in motion is ten times smaller than its diameter allowing two-dimensional theory to be applied. This study is motivated by fundamental problems in nature related to geophysical flows, namely polar vortices and to accretion disks around black holes. In all of these areas, the main topic is the interplay between turbulence and average rotation. Using the Navier-Stokes equations with external Lorentz force, along with the appropriate boundary conditions, the base flow is found. Stability analysis using perturbation theory in slab geometry allows us to predict the unstable region of the flow. Experimentally, the fluid is a thin layer of Galinstan (liquid metal) placed in a cylindrical container. At its edge eight electrodes are biased with respect to a middle one in order to draw a current among them. A strong axial magnetic field is applied by permanent magnets. Using laser diagnostic technique, velocity fluctuations are measured versus several controlling parameters. It is shown that the fluid becomes unstable in absence of magnetic field fluctuations. This instability occurs in the (r,θ)-plane and this is observed for the first time.