Title:

Onset and stability of the Torsional flows of convection in rotating
fluid spheres.

By  Joan Sanchez Umbria and Marta Net

Abstract:

The onset of convection in rotating fluid spheres and shells usually
gives rise to rotating waves, which can travel in the prograde or
retrograde direction relative to the frame of reference rotating with
the bulk of the fluid. It was discovered recently that axisymmetric
periodic regimes can also be preferred at low Prandtl, Pr, and Ekman,
Ek, numbers. These flows are known as torsional.

In order to determine the parameter space region where the torsional
flows are the first bifurcated solutions, the curves of double Hopf
points corresponding to simultaneous transitions to azimuthal wave
numbers $(m_1,m_2)$=(0,1), (1,1), (0,2), etc. were computed. These
curves form the skeleton of the bifurcation diagram, separating the
regions of different preferred azimuthal wave numbers. Their
intersections are triple Hopf points, several of which were found. It
turned out that the region of interest was limited by the curves
$(m_1,m_2)$=(0,1) and (0,2).

The torsional solutions emerging form the conduction state were
computed for several pairs (Pr,Ek) inside the above mentioned region,
and their stability to azimuthal dependence was studied using Floquet
multipliers.