Anisotropy and dissipation of turbulence and their effects on solar models

Based on a dynamic model for turbulent convection, we investigate the effects of dissipation and anisotropy of the turbulence on the convective energy transport. We introduce two time scales to describe the dissipation of the turbulence, and approximate the anisotropy of the turbulence by Rotta's proposal of "return to isotropy". The improved turbulence model results in an equation to determine the temperature gradient in the convection zone, which is of similar form as that of the MIT. We apply the improved MIT to solar models, and find that the increases of the anisotropy and decreases of the dissipation of the turbulence reduce the value of the convection parameter a, because these processes enhance the convective energy transfer rate. Compared with the observed solar p-mode frequencies, it is plausible that the dissipation of the turbulence in the solar convection zone should be fairly strong, while the degree of anisotropy of the turbulence plays a less significant role on the structure of the solar convection zone.