Compressible convection in a rotating spherical shell. IV - Effects of viscosity, conductivity, boundary conditions, and zone depth

Astronomy and Astrophysics – Astrophysics

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Boundary Conditions, Convective Flow, Hydrodynamics, Solar Rotation, Spherical Shells, Thermal Conductivity, Viscosity, Anelasticity, Astronomical Models, Boundary Value Problems, Boussinesq Approximation, Compressible Flow

Scientific paper

The manner in which variations in given assumptions affect the stability and structure of solutions is demonstrated for the case of a linear, anelastic model of compressible convection in a rotating spherical fluid shell described by Glatzmaier and Gilman (1981). Velocity is shown to be enhanced in the lower part of the zone opposed to the upper part, when the kinematic viscosity is assumed to be inversely proportional to the density rather than constant. The velocity is more uniformly distributed in radius when the kinematic viscosity increases with radius at a rate lower than the inverse density, or when viscous diffusion is small relative to thermal diffusion. When constant temperature boundaries are replaced by constant diffusive heat flux boundaries, the most unstable modes are more unstable and have larger longitudinal dimensions; this is in agreement with previous studies of plane-parallel, Boussinesq convection.

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