  The general consensus is that in order to reproduce the observed solar p-mode
oscillation frequencies, turbulence should be included in solar models.
However, until now there has not been any well-tested efficient method to
incorporate turbulence into solar modeling. We present here two methods to
include turbulence in solar modeling within the framework of the 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 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 and temperature). We investigate the effects of both
treatments of turbulence on the structure variables, the adiabatic sound speed,
the structure of the highly superadiabatic layer, and the p-mode frequencies.
We find that the second method reproduces the SAL structure obtained in 3D
simulations, and produces a p-mode frequency correction an order of magnitude
better than the first method.
