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The anelastic modal equations presented in Paper I are considered in their simplest version: only one mode is retained in the representation of the fluctuating dynamic and thermodynamic variables of convection theory. These single-mode equations are used to examine the structure of the second convection zone of an A-type star. Two- and three-dimensional numerical solutions are obtained for a range of parameters in the theory, and a simple analysis is provided for their interpretation. The principal results are for three-dimensional motions, since these are most likely to be relevant to stellar convection. Such motions produce a convective heat flux several orders of magnitude greater than predicted by standard mixing-length theory for the same situation; we find that convection carries up to 6 percent of the total flux. The most significant astrophysical implication of our results is that they suggest strong overshooting into the adjacent radiative zones. We anticipate that mixing will extend to the overlying hydrogen convection zone. This would rule out some interpretations of metallic-line stars which invoke diffusive element separation between the two convection zones. Subject headings: convection - stars: interiors - stars: metallic-line
Toomre et al. (Thu,) studied this question.