Earth rotation prevents exact solid-body rotation of fluids in the laboratory

Jean Boisson (1) , D Cébron (2) , Frederic Moisy (3) , Pierre-Philippe Cortet (3)

1 UME - Unité de Mécanique
2 ISTerre - Institut des Sciences de la Terre
3 FAST - Fluides, automatique, systèmes thermiques

–We report direct evidence of a secondary flow excited by the Earth rotation in a water-filled spherical container spinning at constant rotation rate. This so-called tilt-over flow essentially consists in a rotation around an axis which is slightly tilted with respect to the rotation axis of the sphere. In the astrophysical context, it corresponds to the flow in the liquid cores of planets forced by precession of the planet rotation axis, and it has been proposed to contribute to the generation of planetary magnetic fields. We detect this weak secondary flow using a particle image velocimetry system mounted in the rotating frame. This secondary flow consists in a weak rotation, thousand times smaller than the sphere rotation, around a horizontal axis which is stationary in the laboratory frame. Its amplitude and orientation are in quantitative agreement with the theory of the tilt-over flow excited by precession. These results show that setting a fluid in a perfect solid body rotation in a laboratory experiment is impossible — unless tilting the rotation axis of the experiment parallel to the Earth rotation axis. Introduction. – There are few examples of fluid mechanics experiments at the laboratory scale in which the Earth's Coriolis force has a measurable influence. Such experiments may be considered as fluid analogues to the Foucault pendulum. The most popular instance is certainly the drain of a bathtube vortex [1]. Although this is the subject of common misconception, it is actually possible to detect the influence of the Earth's rotation on the vortex, but only under extremely careful experimental conditions, far from the everyday experience [2]. Thermal convection is another example, in which a slow drift of the large-scale flow due to the Earth rotation has been detected in very controlled systems [3, 4]. In this letter we describe an experiment which may be considered as the most simple fluid Foucault pendulum: it consists in a volume of water enclosed in a spherical container spinning at constant rotation rate Ω 0 (fig. 1). After a transient known as spin-up, the water is expected to rotate as a solid body at the same rate Ω 0 [5]. The (a)

Domaines: Physique [physics]; Mécanique des fluides [physics.class-ph]

Jean Boisson, D Cébron, Frederic Moisy, Pierre-Philippe Cortet. Earth rotation prevents exact solid-body rotation of fluids in the laboratory. EPL - Europhysics Letters, 2012, pp.59002. ⟨10.1209/0295-5075/98/59002⟩. ⟨hal-01152731⟩