| 其他摘要 | In stellar interior, under the effect of ε effect, κ effect or Γ effect, when the Schwarzschild criterion or the Ledoux criterion stands up, then the convection will develop. Since the small viscosity and large convective length-scale in stellar interior, the Reynolds number and Rayleigh number in stellar fluids are so enormous that stellar convection develops into adequately turbulent flows. The observations and researches of the sun are most detailed in all stars. The granulation, meso-granulation, super-granulation on the solar surface is the direct evidence of solar convection in its interior. Between lots of convection theories, the widely used are the mixing length theory and turbulent convection model theories. The hypothesis of the mean convective element in the mixing length theory greatly simplifies the problem of stellar convection, and the equivalent method makes the results got by the mixing length theory to be consistent with the most of observations. However, the mixing length theory don't take into account the effect of convective overshooting, and it's unable to deal with the turbulent diffusion, dissipation and anisotropy. The turbulent convection model theories, however, which include the turbulent diffusion, dissipation and anisotropy, are builded on the found of fluid dynamics, thus solve the convective overshooting and the corresponding element mixing problem very well. Since the turbulent convection model theories don't take the effect of convective rolling cells into account, Li proposes a new stellar convection model. The new convection model evaluates the size of convective cells approximately, and suggests a average shear model of velocity in the fluids of convective cell. Then it specify a macro-length model of turbulence, and obtains the steady state solutions of k-ε model at fully local equilibrium. Furthermore it develops a k-ω model which includes the effect of turbulent diffusion. To apply the k-ω model into common stellar environments, it's necessary to investigate the physical meanings of model paramters to confine their values. The research states that model parameter c’μ can impact the turbulent flows' Péclet Number, kinetic energy, typical time scale and typical length. Besides, model parameter c’μ can accelerate the rate of damping of the turbulent kinetic energy in the overshooting zone below the base of convection zone. Both model parameter c’μ and equivalent mixing length parameter α can enhance the efficiency of convective heat transfer in the convection zone, further inspection shows that their logarithms can satisfy a linear relation. There is also a linear relation between model parameter c’μ and the damping index θ of turbulent kinetic energy in the convective overshooting zone. |
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