Goldreich et al. (1994) used a mixing length model of solar convection to compute the energy input rates for modes with angular degree less than 60. The model energy input rates were very similar to the observed rates. In the Goldreich et al. (1994) model the main source of wave excitation was entropy fluctuations. Numerical simulations of near-surface turbulent convection have also been able to explain the observed frequency dependence of the energy input and damping rates (see, e.g., Stein and Nordlund, 2001). In the Stein and Nordlund (2001) model, the main source of wave excitation is Reynold’s stresses (turbulent pressure) near the boundaries of granules. Samadi et al. (2003a) compared wave excitation in a 3d numerical simulation and 1d mixing length based models. The numerical simulation gave about five times more energy input into the p-modes than did the mixing length model. In the numerical simulations of Samadi et al. (2003a), excitation by entropy fluctuations dominates over excitation by Reynold’s stresses. Samadi et al. (2003b) used a 3d numerical simulation to study the covariance function of the near-surface turbulent velocity and found that the temporal covariance was not Gaussian. As we will discuss in Section 3.4, this covariance is important for computing the power spectrum of solar oscillations.
As both the numerical convection simulations and the analytical convection models become more developed, it seems likely that they will converge and produce a definitive answer as to the source of solar oscillations.
In order to model the driving of solar oscillations by turbulent convection we add a source term to the right hand side of Equation (4), to obtain
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