Emmanuel Dormy

A numerical dynamo benchmark

We present the results of a benchmark study for a convection-driven magnetohydrodynamic dynamo problem in a rotating spherical shell. The solutions are stationary aside from azimuthal drift. One case of non-magnetic convection and two dynamos that differ in the assumptions concerning the inner core are studied. Six groups contributed numerical solutions which show good agreement. This provides an accurate reference standard with high confidence.

On the ill-posedness of the Prandtl equation

The concern of this paper is the Cauchy problem for the Prandtl equation. This problem is known to be well-posed for analytic data or for data with monotonicity properties. We prove here that it is linearly ill-posed in Sobolev type spaces. The key of the analysis is the construction, at high tangential frequencies, of unstable quasimodes for the linearization around solutions with non-degenerate critical points. Interestingly, the strong instability is due to vicosity, which is coherent with well-posedness results obtained for the inviscid version of the equation. A numerical study of this instability is also provided.

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

Mathematical aspects of natural dynamos

E

Simple Mechanism for Reversals of Earth's Magnetic Field

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

Weak‐ and strong‐field dynamos: from the Earth to the stars

r_o

Stability of mixed Ekman-Hartmann boundary layers

and have short azimuthal length scale

Effect of magnetic boundary conditions on the dynamo threshold of von Kármán swirling flows

O(E^{1/3}r_o)

A super-rotating shear layer in magnetohydrodynamic spherical Couette flow

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

THE DYNAMO BIFURCATION IN ROTATING SPHERICAL SHELLS

s\,{=}\,s_M