Properties Of The K-ω Model For Stellar Convection

In stellar interior, under the efect of efect, κ efect or Γ efect, when theSchwarzschild criterion or the Ledoux criterion stands up, then the convectionwill develop. Since the small viscosity and large convective length-scale in stel-lar interior, the Reynolds number and Rayleigh number in stellar fluids are soenormous that stellar convection develops into adequately turbulent flows. Theobservations and researches of the sun are most detailed in all stars. The gran-ulation, meso-granulation, super-granulation on the solar surface is the directevidence of solar convection in its interior.Among lots of convection theories, the widely used are the mixing lengththeory and turbulent convection model theories. The hypothesis of the meanconvective element in the mixing length theory greatly simplifies the problemof stellar convection, and the equivalent method makes the results got by themixing length theory to be consistent with the most of observations. However,the mixing length theory don’t take into account the efect of convective over-shooting, and it’s unable to deal with the turbulent difusion, dissipation andanisotropy. The turbulent convection model theories, however, which include theturbulent difusion, dissipation and anisotropy, are builded on the found of fluiddynamics, thus solve the convective overshooting and the corresponding elementmixing problem very well. Since the turbulent convection model theories don’ttake the efect of convective rolling cells into account, Li proposes a new stel-lar convection model. The new convection model evaluates the size of convectivecells approximately, and suggests a average shear model of velocity in the fluids ofconvective cell. Then it specify a macro-length model of turbulence, and obtainsthe steady state solutions of k ε model at fully local equilibrium. Furthermoreit develops a k ω model which includes the efect of turbulent difusion.To apply the k ω model into common stellar environments, it’s necessaryto investigate the physical meanings of model paramters to confine their values.The research states that model parameter cμcan impact the turbulent flows’ P′eclet Number, kinetic energy, typical time scale and typical length. Besides,model parameter cμcan accelerate the rate of damping of the turbulent kineticenergy in the overshooting zone below the base of convection zone. Both modelparameter cμand equivalent mixing length parameter α can enhance the efciencyof convective heat transfer in the convection zone, further inspection shows thattheir logarithms can satisfy a linear relation. There is also a linear relationbetween model parameter cμand the damping index θ of turbulent kinetic energyin the convective overshooting zone.