Generation and Propagation of Internal Gravity Waves: Comparison between Two- and Three-Dimensional Models at Low Resolution

Dynamics of a convectively unstable layer sandwiched between two stable layers was investigated using direct hydrodynamical simulations in two and three dimensions. Particular attention was paid to the problem of generation and propagation of internal gravity waves (IGW) in a lower stable zone. The results show that convective motions in a 3-D model are significantly less vigorous than in an equivalent 2-D model, resulting in a lower efficiency of IGW generation and a weaker energy flux carried downwards by the waves. The flux obtained in our 3-D models is of the same order as calculated from a simple parametric model based on MLT. However, the comparison of numerical models with different depths of the convective layer indicates that the efficiency of IGW generation increases with the increasing depth whereas the opposite is true in case of parametric model. Extrapolation of this trend to deeper convective zones, existing in solar type stars, suggests that the parametric formulae may severely underestimate the IGW flux generated in the stellar radiative cores. If it is true, IGW existing in real stars will play an important role in transport of angular momentum and trace elements across their internal radiative zones. Due to existence of a rigid lower boundary, the effect of wave reflection occurs in numerical simulations. A method of suppressing the reflected flux is discussed.