2D Computer Simulations of Stellar Convection Using a Three-Layer Model

Details 2D Computer Simulations of Stellar Convection Using a Three-Layer Model 2D Computer Simulations of Stellar Convection Using a Three-Layer Model

Oct 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995aca....45..685k&link_type=abstract

Acta Astronomica, v.45, pp.685-704, (1995).

Statistics

Computation

8

Convection, Hydrodynamics

Scientific paper

We performed 2D computations of the time evolution of a model consisting of a convectively unstable layer sandwiched between two stable layers. The physics and the initial set-up of the model are almost the same as in the "three-layer" model considered by Hurlburt et al. (1986) (HTM86) in a study of convective penetration into a stably stratified medium. Here we discuss two types of models: the first one with a constant dynamic viscosity coefficient, which corresponds directly to the "three-layer" model, and the second one with a constant value of Prandtl number in the whole computational domain, which implies a somewhat larger viscosity of stable layers. The computations were performed on two different resolution grids: 40 times 40 and 80 times 80 points. In addition, the model relaxed on 40 times 40 grid was projected onto the 80 times 80 grid and evolved further. This solution appeared to have the same mean stratification and other properties as the model computed on 80 times 80 grid from the beginning, which yielded a check that it is possible to speed up computations by relaxing the initial stratification on a coarser grid. Our models closely reproduce most of the properties of the model considered by HTM86, including the overall pattern of flows, temporal dependence of horizontally averaged vertical fluxes and the time averaged values of fluxes. However, rates of working by buoyancy, viscosity and pressure are smaller in our models by almost 30%, which indicates small differences between the two models when some local properties of the flow and fluctuations of the thermodynamic parameters are considered. The oscillation period of gravity waves generated in stable zones is similar in the both compared papers, and it is about seven times longer that the sound travel time across the whole domain. The range of penetration into both stable zones, calculated as a distance where the averaged kinetic energy flux stays below 1% of its value at the border of the unstable zone, is in our models equal to about 40% of the thickness of the unstable zone. In the upper zone this range is similar as in HTM86, but in the lower one it is by one third smaller. We made additional computations to better estimate the extent of penetration and mixing. In particular, we marked positions of fluid elements in a fully relaxed model with passive "corks" and traced their positions during the time evolution. The estimated range of penetration into stable zones is essentially the same as that obtained with the earlier criterion. The range of mixing of material reaches almost the whole upper stable zone whereas in case of the lower stable zone it is two times higher than the range of penetration.

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