Philippe Cardin

MHD FLOW IN A SLIGHTLY DIFFERENTIALLY ROTATING SPHERICAL SHELL, WITH CONDUCTING INNER CORE, IN A DIPOLAR MAGNETIC FIELD

Motion is generated in a rotating spherical shell, by a slight differential rotation of the inner core. We show how the numerical solution tends, with decreasing Ekman number, to the asymptotic limit of Proudman [J. Fluid Mech. 1 (1956) 505‐516]. Starting from geophysically large values, we show that the main qualitative features of the asymptotic solution show up only when the Ekman number is decreased below 10 6 . Then, we impose a dipolar and force-free magnetic field with internal sources. Both the inner core and the liquid shell are electrically conducting. The first effect of the Lorentz force is to smooth out the change in angular velocity at the tangent cylinder. As the Elsasser number is further increased, the Proudman‐Taylor constraint is violated, Ekman layers are changed into Hartmann type layers, shear at the inner sphere boundary vanishes, and the flow tends to a bulk rotation together with the inner sphere. Unexpectedly, for increasing strength of the field, there is a super-rotation (the angular velocity does not reach a maximum at the inner core boundary but in the interior of the fluid) localized in an equatorial torus. At a given field strength, the amplitude of this phenomenon depends on the Ekman number and tends to vanish in the magnetostrophic limit.

The onset of thermal convection in rotating spherical shells

The correct asymptotic theory for the linear onset of instability of a Boussinesq fluid rotating rapidly in a self-gravitating sphere containing a uniform distribution of heat sources was given recently by Jones et al. (2000). Their analysis confirmed the established picture that instability at small Ekman number

A systematic experimental study of rapidly rotating spherical convection in water and liquid gallium

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Quasigeostrophic model of the instabilities of the Stewartson layer in flat and depth-varying containers

is characterized by quasi-geostrophic thermal Rossby waves, which vary slowly in the axial direction on the scale of the sphere radius

Numerical study of the motions within a slowly precessing sphere at low Ekman number

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Experimental study of super-rotation in a magnetostrophic spherical Couette flow

and have short azimuthal length scale

Rotating spherical Couette flow in a dipolar magnetic field : experimental study of magneto-inertial waves

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Viscomagnetic torque at the core mantle boundary

. They also confirmed the localization of the convection about some cylinder radius

Experimental evidence of inertial waves in a precessing spheroidal cavity

s\,{=}\,s_M

Thermal convection in Earth's inner core with phase change at its boundary

roughly