2D COMPUTER-SIMULATIONS OF STELLAR CONVECTION USING A 3-LAYER MODEL

We performed 2D computations of the time evolution of a model consisti ng of a convectively unstable layer sandwiched between two stable laye rs. The physics and the initial set-up of the model are almost the sam e 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 con stant dynamic viscosity coefficient, which corresponds directly to the ''three-layer'' model, and the second one with a constant value of Pr andtl number in the whole computational domain, which implies a somewh at larger viscosity of stable layers. The computations were performed on two different resolution grids: 40 x 40 and 80 x 80 points. In addi tion, the model relaxed on 40 x 40 grid was projected onto the 80 x 80 grid and evolved further. This solution appeared to have the same mea n stratification and other properties as the model computed on 80 x 80 grid from the beginning, which yielded a check that it is possible to speed up computations by relaxing the initial stratification on a coa rser grid. Our models closely reproduce most of the properties of the model considered by HTM86, including the overall pattern of flows, tem poral dependence of horizontally averaged vertical fluxes and the time averaged values of fluxes. However, rates of working by buoyancy, vis cosity and pressure are smaller in our models by almost 30%, which ind icates small differences between the two models when some local proper ties of the flow and fluctuations of the thermodynamic parameters are considered. The oscillation period of gravity waves generated in stabl e 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 r ange of penetration into both stable zones, calculated as a distance w here the averaged kinetic energy flux stays below 1% of its value at t he 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 s imilar as in HTM86, but in the lower one it is by one third smaller. W e made additional computations to better estimate the extent of penetr ation and mixing. In particular, we marked positions of fluid elements in a fully relaxed model with passive ''corks'' and traced their posi tions during the time evolution. The estimated range of penetration in to stable zones is essentially the same as that obtained with the earl ier criterion. The range of mixing of material reaches almost the whol e upper stable zone whereas in case of the lower stable zone it is two times higher than the range of penetration.