Turbulence is ubiquitous in astrophysics, ranging from cosmology, interstellar medium to stars, accretion disks, etc. Stars exist rely on turbulence convection to transport heat when radiate process is insufficient. But common usage of phenomenological turbulence expressions in stellar convection, just like mixing-length theory makes turbulent convection models perennially unpredictive. At the same time, Reynolds stress models (RSM) are deduced by many researchers, but it is hard to apply them in the stellar structure and evolution, mainly because the calculation of the differential turbulence convection equations is the main obstacle on the way to the better theories. Our study is focused on the semi-empirical theory, especially in different turbulence processes. We apply the theory into two kinds of stars during their Main Sequence, which are 1Msun star and 1.85Msun star. In Chapter I, the importance of turbulence is recalled with the development process. The historical and characters of turbulence are introduced. Then we showed our understanding to turbulence in one section since the turbulence is an unknown and controversial question up to now. In Chapter II, the numerical method of turbulent convection theory is carefully constructed. We analyzed the convection stability in the turbulence modeling and finally constructed an effective numerical method to solve the equations. In Chapter III and Chapter IV, we focus on how much our convection theory can describe turbulence in two kinds of stars. We firstly deduced the medial and local theory from the non-local formula, and then mainly compared the non-local with the local theories. In solar-like star, all the description of turbulence in the models, namely diffusion, dissipation, isotropic and buoyancy, were agreed well with the characters of turbulence. In the delta Scuti type stars, the present conclusion were reconfirmed and we found the turbulent value in the non-local models are greatly lager than those in the local models. Furthermore, we made models of one of the delta Scuti type stars, named FG Vir. Generally speaking, all of this work showed the semi-empirical convection theory is better than the mixing-length theory.
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