How to deal with the turbulent convection motion in stars is a very important problem in the theory of stellar structure and evolution. A Reynolds stress model based on hydrodynamic moment equations was established and applied to the solar model. The convection model and the free parameters involved in the model are tested and determined in the solar interior. The aim is to test the effects of some physical processes on the structure of the solar convection zone, such as the dissipation, diffusion, and anisotropy of turbulence that have been ignored in the classical mixing-length theory (MLT). Free parameters introduced by the Reynolds stress model are also tested with the aid of helioseismology in order to find appropriate values for astrophysical applications. It is found that, the Reynolds stress models usually give larger convective heat fluxes than the MLT does, and the heat transport efficiency is sensitively related to the dissipation parameters used in the Reynolds stress models. The turbulent diffusion is found to have important effects on the structure of the solar convection zone. It leads to significantly lowered and expanded profiles for the Reynolds correlations, and a larger temperature gradient in the central part of the super-adiabatic convection region but a small one near the boundaries of the convection zone. Solar models with our Reynolds stress model give small but meaningful differences in the global structure such as temperature and sound speed compared with the standard solar model using the MLT. The free parameters involved in the Reynolds stress model are determined in the solar interior with the aid of helioseismology. It is found that, with appropriate choices of the turbulent parameters, solar model with both local and non-local Reynolds stress model can give the calculated p-mode frequencies in better consistent with the observations than the standard solar model does. Decreasing the values of dissipation parameters Ct and Ce or increasing the values of diffusion parameters Ct1 and Ce1 helps to reduce the calculated frequencies, while the parameters Ck and Cs have no obvious effect on the p-mode frequencies. The temperature in the convection zone is changed due to the dissipation and diffusion of the turbulence. It is just this temperature difference that makes the calculated frequencies changed. Combined better values of the free parameters, solar models with our Reynolds stress model can reduce the frequency differences between the model calculations and observation as much as 30 percent for the modes of middle and high l. This result can give a clue to solar modeling, that is, including turbulence in solar models is helpful to reproduce the observed solar p-mode frequencies.
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