Compressible Convection in a Rotating Spherical Shell - Part Two - a Linear Anelastic Model

Details Compressible Convection in a Rotating Spherical Shell - Part Two - a Linear Anelastic Model Compressible Convection in a Rotating Spherical Shell - Part Two - a Linear Anelastic Model

Feb 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981apjs...45..351g&link_type=abstract

Astrophysical Journal Supplement, Vol. 45, P. 351, 1981

Astronomy and Astrophysics

Astrophysics

69

Scientific paper

We study the onset of convection for a compressible fluid in a rotating spherical shell via linear anelastic fluid equations for a depth of 40% of the radius, constant kinematic viscosity and thermometric diffusivity, Taylor numbers up to l05, and density stratifications up to seven e-folds across the zone. The perturbations are expanded in spherical harmonics, and the radially dependent equations are solved with a Newton-Raphson relaxation method.
The most unstable modes are single cells extending from the bottom to the top of the convection zone. As the density stratification and rotation rate increase, the horizontal dimension of these cells decreases, while their prograde longitudinal phase velocity and the enhancement of the velocity near the top of the zone increase. Cylindrical cells arranged symmetrically about the equator develop parallel to the rotation axis as the rotation rate increases, but for large stratifications, their axes bend toward the pole at midlatitude instead of intersecting the outer surface, as they do for small stratifications. The buoyancy force does negative work near the top of the zone, while the pressure force does a net positive amount of work for large stratifications. Helicity profiles and convective heat flux profiles for the most unstable modes do not change significantly as the density stratification increases, although distinct differences develop for modes that are not the most unstable. The radial momentum flux for the most unstable modes at high rotation rates is inward for large stratifications instead of outward as it is for small stratifications; this may have a significant effect on differential rotation and magnetic field generation in nonlinear, compressible models.

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