Nonlinear convective motion in shallow convective envelopes

Abstract

Finite-difference techniques are used to obtain numerical solutions to the conservation equations in two spatial dimensions and time for large-amplitude convective motion in two shallow convective envelopes slightly interior to the photosphere of a model main-sequence star. The calculations are carried to the point where shear motions break up the largest convection cells. The essentially linear problem of the formation of cells of a preferred width is examined, and it is shown that such cells will form and will have growth rates larger than those for cells of other widths. It is found that nonlinear terms alter the velocity distribution by shifting the maximum of the vertical velocity amplitude to deeper parts of the convective region and by introducing a significant asymmetry between upward and downward moving elements. Decomposition of the largest cells is discussed. The results indicate that matter flows from the top of the convective zone to the bottom, even when the depth of the convective zone is several pressure scale heights.