Numerical studies of convective penetration in plane parallel layers and the integral constraint

Details Numerical studies of convective penetration in plane parallel layers and the integral constraint Numerical studies of convective penetration in plane parallel layers and the integral constraint

Sep 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...277...93r&link_type=abstract

Astronomy and Astrophysics, Vol. 277, p. 93 (1993)

Astronomy and Astrophysics

Astrophysics

27

Convection - Stars: Interiors - Stars: Evolution

Scientific paper

We report the results of numerical studies of 2- dimensional fully compressible convection of a fluid in which the dependence of radiative conductivity on temperature T is taken as K0(T3 + T-5) so that central regions of the layer are unstable to convection whereas the surrounding layers are stable. Calculations have been undertaken for Rayleigh numbers at the centre of the unstable layer Ra =4.78 106-9.56 1O7 and Prandtl numbers σ = 0.05-1. The main result of these studies is that in a (statistically) stationary state the viscous dissipation decreases with decreasing Prandtl number, and that the equilibrium of the whole layer is governed by a substantial penetrative region in which the convective flux is negative. The radiative flux is found to be well approximated by the value obtained using the mean temperature and mean temperature gradient. The numerical simulations are compared with the traditional astrophysical solution where convectively unstable layers are adiabatically stratified and stable layers are in radiative equilibrium; the simulations show that convective penetration establishes a weakly stable penetrative region below the base of the unstable zone. The results suggest that, at least in the parameter range studied here, the simple criterion obtained by neglecting viscous dissipation and quadratic fluctuations in the intergral constant proposed by Roxburgh (1976, 1978, 1989) gives a reasonable estimate of convective penetration at small Prandtl numbers.

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