ELSEVIER Physics of the Earth and Planetary Interiors 91 (1995) 77-98 PHYSICS OFTHE EARTH AN D PLANI-!TARY INTERIORS Experimental study of a geostrophic vortex of gallium in a transverse magnetic field Daniel Brito *, Philippe Cardin, Henri-Claude Nataf, Guy Marolleau D~partement Terre Amosph~re Ocean, Ecole Normale Sup~rieure, URA 1316 du CNRS, 24, rue Lhomond, 75231 Paris Cedex 05, France Received 29 November 1994; accepted 27 March 1995 Abstract We have built an experimental set-up to study the interaction between one single vertical vortex of liquid gallium, generated by a disk, and a transverse magnetic field. Magnetic Reynolds number of 0.1 has been reached. This experiment has been conducted on a rotating table. Therefore the dominant forces are Coriolis and Lorentz forces, as in the Earth's core. We measured pressure profiles at the top of the vortex, differences in electrical potentials between some points in the vortex, and the magnetic field induced by the flow. To understand the velocity flow of the vortex, we introduced a simple two-dimensional model which predicts well these three types of measurements. The Elsasser number (ratio of Lorentz to Coriolis forces) is the critical parameter for the dynamical aspect of the vortex. Under the influence of the magnetic field, the vortex is slowed down but remains two-dimensional or geostrophic, up to Elsasser number 0.2. On the other hand, the size of the vortex increases with the strength of the magnetic field. The induced magnetic field forms a horizontal dipole perpendicular to the imposed field, and has a significant vertical component associated with the geometry of electrical currents and insulating boundaries, and not with the helicity. R~sum~ Nous avons EtudiE expErimentalement l'interaction entre un vortex vertical de gallium liquide (gEnErE par un disque) et un champ magnEtique horizontal. Des nombres de Reynolds magnEtique de l'ordre de 0.1 ont pu ~tre atteints. Comme cette experience a EtE realisEe sur une table tournante, les forces de Coriolis et de Lorentz Etaient dominantes dans rEcoulement, comme dans le noyau terrestre. Trois grandeurs ont EtE mesurEes: la pression ~ la surface du vortex, la difference de potentiel entre des points situEs sur la gEnEratrice du vortex, et le champ magnEtique induit par l'Ecoulement. Pour amEliorer notre comprehension du vortex, nous avons introduit un module de vitesse bidimensionnel simple, qui rend tr~s bien compte des trois types de mesures EffectuEes. Le nombre d'Elsasser (rapport entre les forces de Lorentz et les forces de Coriolis) est le param~tre critique contrElant la dynamique du vortex. Sous l'influence du champ magnEtique, le vortex est freinE mais reste bidimensionnel ou gEostrophique, jusqu'~t un hombre d'Elsasser de 0.2. En revanche, la taille du vortex augmente avec l'intensit~ du * Corresponding author. 0031-9201/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0031-9201(95 )03051-4