推广的依赖时间的局部对流理论

TIME-DEPENDENT CONVECTION THEORY GENERALIZED FOR NONRADIAL OSCILLATIONS OF STARS

本文将依赖时间的对流理论推广到适用于非径向脉动的更为一般的情况。

The time-dependent convection theory is generalized for nonradial oscillations of stars. The statistical theory has some advantages over the phenomenological theory. It can describe the dynamic behaviour of turbulent convection more exactly and it is more easy to generalize for time-dependent or non-local convection theory. The approximations adopted in the statistical theory are very general and acceptable. They can be summarized as follows. 1) The turbulent convection is subsonic, so the relative fluctuations of the density and temperature of fluid are far less than I(Eq. A-1). 2) The Reynold's number of turbulence is very large, hence the size of the eddies l_d, which provide the main contribution to the total viscousity dissipation, is far less than the characteristic length of fluid l (Eq. A-2). 3) The inelastic approximation (Eq. A-3). 4) The local convection approximation (Eq. A-4). 5) The turhulence is nearly local isotropic (Eq. A-5). 6) Referring to the isotropic turbulence, we assume that the dissipation can be expressed as Eq. A-6. Under above approximations we obtain simultaneous dynamics equations of the auto-correlation and cross-correlation functions of the velocity and temperature fluctuations (Eqs. 12—14). After separation of the equilibrium and puisational quantities, we obtain the equilibrium components, (Eq. 21) and the linearized pulsational components (Eqs. 37—41) of turbulent convection. Our equilibrium components are consistent with Vitense's formulae. When we adopt η_e=0.45 and l_(el)=c_1H_p the efficiency of convective energy transport of my theory correspond approximately to l=2C_1H_p in the original Vitense's formulae, The pulsational components have a phaselag depending upon ωτ, where o is the pulsational frequency of the star and τ the time scale of convective motion. That shows the inertia of the convective motion.