The general consensus is that in order to reproduce the observed solar p-mode oscillation frequencies, turbulence should be included in solar models. However, there is no well-tested efficient method to incorporate turbulence into solar modeling. We present two methods to include turbulence in solar modeling within the framework of mixing length theory, using the turbulent velocity obtained from numerical simulations of the highly superadiabatic layer of the sun at three stages of its evolution. The first approach is to include the turbulent pressure alone, and the second is to include both the turbulent pressure and the turbulent kinetic energy. The latter is achieved by introducing two turbulent variables, the turbulent kinetic energy per unit mass and the effective ratio of specific heats due to the turbulent perturbation. These are treated as additions to the standard thermodynamic coordinates (e.g. pressure, temperature). We test these two methods by investigating the effect of different treatments of turbulence on the adiabatic sound speed and the p-mode frequencies. We find that only the second method can reproduce the observed data. This is because the effects of the turbulent pressure are much less than that of turbulent kinetic energy (and turbulent entropy). The evolutionary effect of turbulence in the evolutionary timescale of the sun is negligible.
展开▼
