Study on Properties of the k − ω Model for Stellar Convection

For applying the k − ω model proposed by Li to the general stellar environment, it is necessary to study the physical meanings of the parameters in this model, in order to set a limit for the range of their values. It is indicated by the study that the variation of the parameter clμ impacts all the Péclet number, kinetic energy, characteristic timescale and characteristic length of turbulent flows. Besides, as the model parameter clμ increases, the damping rate of turbulent kinetic energy in the bottom convective overshoot region can be accelerated evidently. Both the model parameter clμ and the equivalent mixing length parameter α are proportional to the effciency of convective heat transfer in the convection zone, and their logarithms have a linear relation. There is also a linear relation between the logarithms of the model parameter clμ and the damping index θ of turbulent kinetic energy in the convective overshoot region. For the Sun, a group of appropriate model parameters are obtained to be: clμ = 0.004, and α = 1.7.