Physics
Scientific paper
Jun 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979pepi...19..149b&link_type=abstract
(Lunar and Planetary Institute and NASA, Workshop on Solid Convection in the Terrestrial Planets, Moffett Field, Calif., Dec. 12
Physics
3
Flat Layers, Free Convection, Spherical Shells, Boussinesq Approximation, Convective Heat Transfer, Equations Of Motion, Linear Systems, Nonlinear Systems, Prandtl Number, Rayleigh Number, Temperature Dependence, Thermal Conductivity, Thermodynamics
Scientific paper
The theory of buoyancy-driven convection in a layer heated from below is reviewed, emphasizing the case of an infinite Prandtl number. An analysis of neutral convection modes is conducted for the special, linear case of small-amplitude convection and for the general, nonlinear case, in which solutions in the forms of rolls and two types of hexagonal cells are derived. The stability of these rolls is considered in the limit of an infinite Prandtl number and effects of an infinite Prandtl number on the development of convective turbulence are discussed. Convection in a spherical shell is compared to the solutions for a plane, noting that the preferred patterns on a sphere correspond to an octahedron and a dodecahedron. It is also pointed out that axisymmetric forms of convection occur on a spherical shell only in a small region of the parameter space.
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