Stability and bifurcation diagram of Boussinesq thermal convection in a moderately rotating spherical shell

2011 ◽  
Vol 23 (7) ◽  
pp. 074101 ◽  
Author(s):  
Keiji Kimura ◽  
Shin-ichi Takehiro ◽  
Michio Yamada
Keyword(s):  
Spherical Shell ◽  
Bifurcation Diagram ◽  
Thermal Convection ◽  
Stability And Bifurcation

scholarly journals Density Stratification Effects on the Thermal Convection in a Rotating Spherical Shell

2001 ◽  
Vol 203 ◽  
pp. 195-197
Author(s):  
N. Nishikawa ◽  
K. Kusano
Keyword(s):  
Spherical Shell ◽  
Thermal Convection ◽  
Structural Transition ◽  
Rotation Axis ◽  
Three Dimensional ◽  
Density Stratification ◽  
Nonlinear Convection ◽  
Solar Convection Zone ◽  
Solar Convection ◽  
The Stability

The density stratification effects on the thermal convection in a rotating spherical shell, which is the representative of the solar convection zone, are investigated by three dimensional numerical simulations. It is found that, the convection structure in the strongly stratified system is switched from parallel cells aligned to the rotation axis to zonal rolles dominated by the longitudinally averaged mode, as the Rayleigh number increases much larger than the stability threshold. Corresponding to this structural transition, the averaged kinetic helicity reverses the sign in each hemisphere (from negative to positive in the northern hemisphere). The results indicate that the density stratification is much important for the nonlinear convection process in the rotating spherical shell.

On the retrograde propagation of critical thermal convection in a slowly rotating spherical shell

2010 ◽  
Vol 659 ◽  
pp. 505-515 ◽  
Author(s):  
SHIN-ICHI TAKEHIRO
Keyword(s):  
Spherical Shell ◽  
Thermal Convection ◽  
Rotation Speed ◽  
Spherical Geometry ◽  
Radial Component ◽  
Equatorial Region ◽  
Propagation Mechanism ◽  
Budget Analysis ◽  
Axis Of Rotation ◽  
Vorticity Budget

The retrograde propagation mechanism of critical thermal convection with a sectorial pattern emerging in a slowly rotating spherical shell is investigated through vorticity budget analysis. In the equatorial region, stretching and shrinking of the fluid columns in the direction of the axis of rotation due to the radial component of velocity causes retrograde propagation, whereas in the mid-latitudes, tilting of the radial component of planetary vorticity by the radial shear of the latitudinal component of velocity is dominant. The switching of the propagating direction from retrograde to prograde according to the increase in the rotation speed of the shell originates from the transition of the morphology of vortices from the ‘banana-shaped’ type due to the constraint of the spherical geometry to the columnar type due to the Taylor–Proudman constraint. The variation of the morphology of vortices reverses the tendency of stretching/shrinking of fluid columns accompanied by their cylindrically radial displacement.

Spherical shell rotating convection in the presence of a toroidal magnetic field

1995 ◽  
Vol 448 (1933) ◽  
pp. 245-268 ◽  
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Spherical Shell ◽  
Lorentz Force ◽  
Thermal Convection ◽  
Toroidal Magnetic Field ◽  
Wave Number ◽  
Convective Motions ◽  
Magnetic Convection ◽  
Convection Rolls

Convective instabilities of a self-gravitating, rapidly rotating fluid spherical shell are investigated in the presence of an imposed azimuthal axisymmetric magnetic field in the form of the toroidal decay mode that satisfies electrically insulating boundary conditions and has dipole symmetry. Concentration is on two major questions: how purely thermal convection of the different forms (Zhang 1992, 1994) is affected by the Lorentz force, the strength of which is measured by the Elsasser number ∧, and in what manner purely magnetic instabilities in a spherical shell (Zhang & Fearn 1993, 1994) are associated with magnetic convection. It is found that the two-dimensionality of purely thermal convection (Busse 1970) survives under the influence of a strong Lorentz force. Convective motions always attempt to satisfy the Proudman–Taylor constraint and remain predominantly two-dimensional in the whole range of ∧, 0 ≤ ∧ ≤ ∧ c , where ∧ c ═ O (10) is the critical Elsasser number for purely magnetic instabilities. Though the optimum azimuthal wave number m of convection rolls decreases drastically, from m ~ O ( T 1/6 ) at ∧ ═ 0 to m ═ O (5) at ∧ ═ O (1). We show that there exist no optimum values of ∧ that can give rise to an overall minimum of the (modified) Rayleigh number R *; the optimum value of R * is a monotonically, smoothly decreasing function of ∧, from R * ═ O ( T 1/6 ) at ∧ < O ( T -1/6 ) to R * ═ O (–10) at ∧ ═ 20. We also show that the influence of the magnetic field on thermal convection is crucially dependent on the size of the Prandtl number. At sufficiently small Prandtl number, the Poincaré convection mode (Zhang 1994) is preferred in the region 0 ≤ ∧ < ∧ c , and is only slightly affected by the presence of the toroidal magnetic field. Analytical solutions of the magnetic convection problem are then obtained based on a perturbation analysis, showing a good agreement with the numerical solution.

Sign in / Sign up

Export Citation Format

Share Document