Astronomy and Astrophysics – Astrophysics
Scientific paper
Jul 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979apj...231..176m&link_type=abstract
Astrophysical Journal, Part 1, vol. 231, July 1, 1979, p. 176-192.
Astronomy and Astrophysics
Astrophysics
13
Convective Heat Transfer, Spheres, Spherical Shells, Stellar Envelopes, Stellar Models, Stellar Rotation, Angular Momentum, Boussinesq Approximation, Fluid Boundaries, Scalars, Turbulent Diffusion, Velocity Distribution
Scientific paper
In the present paper, a set of nonlinear modal equations is derived to describe convection in self-gravitating spheres and spherical shells of Boussinesq fluids with internal heat sources that are functions of radius. (In a Boussinesq fluid, the depth is much less than its pressure scale-height and viscous dissipation of kinetic energy is absent.) The velocity field is written as a sum of two parts - the toroidal field generated from a pseudo-scalar and the poloidal field generated from a scalar. The nonlinear terms on the modal equations are written in terms of the scalar and pseudo-scalar. The nonlinear three-eddy interactions are parametrized with a set of dimensionless B-numbers and C-numbers. These numbers are calculated for several sets of planforms.
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