Axisymmetric convection in a rotating sphere. I - Stress-free surface

Details Axisymmetric convection in a rotating sphere. I - Stress-free surface Axisymmetric convection in a rotating sphere. I - Stress-free surface

May 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976jfm....75...49w&link_type=abstract

Journal of Fluid Mechanics, vol. 75, May 13, 1976, p. 49-79.

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27

Axisymmetric Flow, Convective Flow, Rotating Spheres, Stellar Models, Stellar Rotation, Angular Momentum, Angular Velocity, Boussinesq Approximation, Equations Of Motion, Finite Difference Theory, Laminar Flow, Stress Distribution, Temperature Effects

Scientific paper

This paper examines large-scale nonlinear thermal convection in a rotating self-gravitating sphere of Boussinesq fluid containing a uniform distribution of heat sources. Conservative finite-difference forms of the equations of axisymmetric laminar motion are marched forward in time. The surface is assumed to be stress-free and at constant temperature. Numerical solutions are obtained for Taylor numbers in the range from zero to 10,000 and Rayleigh numbers ranging from the critical value to about 10 times that value. For high Prandtl numbers (greater than 5), the solutions are steady and most of them resemble the solutions of the linear stability equations, though other steady solutions are also found. For Prandtl numbers not exceeding unity, the steady solutions have a horizontal wavenumber equal to unity and nearly uniform angular momentum per unit mass, rather than nearly uniform angular velocity. This rotation law seems to be independent of many details of the model and may hold in the convective core of a rotating star.

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