An anisotropic nonlocal convection theory

We present in this paper an anisotropic nonlocal theory of stellar convection. Following the idea of Rotta, we propose that the correlation of turbulent pressure and velocity gradient tends to make the turbulent velocity isotropic, and we further introduce a convection parameter c(3) to measure the strength of such isotropization. By using such a theory, the structure of the solar convection zone is calculated. Our calculation shows that the radial component dominates in the convectively unstable zone, in which the ratio between the radial component and the horizontal component is w(r)(2)/w(h)(2) = ( 3 + c(3))/2c(3). In the upper overshooting zone, turbulent velocity is almost isotropic ( w(r)(2)/w(h)(2) similar to 0.5) and is independent of c(3), while in the lower overshooting zone, w(r)(2)/w(h)(2) similar to 0.5, and it tends to decrease as c(3) decreases. We also studied the effects of anisotropic convection on the structure and evolution of stars. It is shown that the anisotropy hardly affects the temperature and pressure structure of stars. However, the anisotropy increases with the decrease of c(3); therefore, the effect of overshooting decreases. Thus, the effects of anisotropy of turbulent convection on stellar evolution cannot be neglected.