Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978azh....55..501k&link_type=abstract
Astronomicheskii Zhurnal, vol. 55, May-June 1978, p. 501-515. In Russian.
Astronomy and Astrophysics
Astrophysics
1
Astrophysics, Convective Heat Transfer, Free Convection, Stellar Atmospheres, Atmospheric Stratification, Boussinesq Approximation, Inhomogeneity, Partial Differential Equations
Scientific paper
A justification is given for simplifications of the free-convection equations in deep, highly stratified, and evolving convection regions. Simplifications are obtained in three cases, where the spatial and time scales are of the same order as, appreciably less than, or much less than the pressure and temperature time scales and depth of the convection region. In the first and third cases the simplified equations are found to correspond to the anelastic and Boussinesq approximations; the second case is designated the 'mesoscale convection' approximation. The simplifications are justified by conducting a scaling analysis of the equations with the use of depth- and time-dependent local scales specified for free convection. It is noted that all three approximations are based on the assumption of small relative horizontal temperature inhomogeneities.
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