Time dependent beta-convection in Rapidly Rotating
Spherical Shells
Vincent Morin,
Emmanuel Dormya)
IPGP, 4 place Jussieu, F-75252, Paris, France.
a) Present address: CNRS/UMR8550, Departement de Physique,
Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris Cedex 05, France.
Physics of Fluids, 16, 1603-1609 (2004)
Abstract.
A quasi-geostrophic, or beta, model of non-linear thermal convection in
rapidly rotating spherical fluid shells is investigated. We study time
dependent instabilities for a range of Rayleigh number and Ekman number with a
Prandtl number set to the unity.
Above the onset of convection, increasing the Rayleigh number for a given Ekman
number, we reproduce the sequence of bifurcations described by Busse
[Phys. Fluids 14, No.4, 1301 (2002)]
for the three dimensional case: a first transition results in vacillating flow;
a second transition gives rise to chaotic oscillations in time and localized
convection in space; then a third leads to quasi-periodic relaxation
oscillations. This study shows that the quasigeostrophic model encompasses the
desired bifurcation sequence. It allows the investigation of a range of Ekman
numbers unavailable to three dimensional models with present computing
resources. Decreasing the Ekman number, we unexpectedly found that all three
transitions occur for marginally supercritical Rayleigh number. The range of
Rayleigh number for which the amplitude of convection is steady vanishes in the
asymptotic limit of small Ekman numbers. This effect could significantly alter
the nature of the instability characterizing the onset of convection in
particular whether it is a supercritical or subcritical bifurcation.