恒星对流超射区内的湍流混合-JamesENeff.PPT

A k-? model for turbulently thermal convection in solar like and RGB stars Li Yan Yunnan Astronomical Observatory, CAS 1. Turbulently thermal convection in stars Thermal convection：In a gravitationally stratified fluid, the temperature gradient results in buoyancy to drive hot fluid moving upward and cold fluid moving downward. The structure of thermal convection is characterized by rolling cells, acting as thermal engines to transform heat into kinetic energy. * 1. Turbulently thermal convection in stars 2. Basic equations and the mixing length theory 3. k-? model for stellar turbulent convection 4. Local solution of the k-? model 5. Applications to the solar model 6. Applications to RGB stars 1. Turbulently thermal convection in stars Effects of turbulently thermal convection in stars： transfer of heat mixing of materials Equation of mass continuity： Navier-Stokes equations： Equation of energy conservation： 2. Basic equations and the mixing length theory Mixing length theory：Convection cells move in average a mixing length l. Equation of momentum： Equation of energy conservation： Equation of heat flux： 2. Basic equations and the mixing length theory Equation of mixing length theory： Defining a heat transfer efficiency of convection： we obtain the famous cubic equation of the MLT： where Question: What is the effect of rolling cell’s structure How to determine the mixing length l Solution is unavailable in stably stratified region 2. Basic equations and the mixing length theory Equation of turbulent kinetic energy： Equation of dissipation rate of turbulent kinetic energy： where , Shear production rate： Buoyancy production rate： 3. k-? model for stellar turbulent convection Stellar structure: Shear of convective rolling cells: Temperature difference of convective rolling cells: 3. k-? model for stell