Nonlinear interactions among internal gravity waves are investigated by direct numerical experiments. Cases which solve the full Navier-Stokes equations (three dimensional, 3D) are compared to cases in which variability is suppressed in one direction (two dimensional, 2D). It is found that the 3D and 2D simulations exhibit certain similarities. This result may seem surprising, remains in part unexplained, and also is encouraging with respect to the utility of application of 2D simulations. We find both in 3D and in 2D that the transfer of kinetic energy (KE) from large to small scales is less efficient than the transfer of potential energy (PE). The imbalance between these transfers leads to a characteristic buoyancy flux spectrum which is negative (KE to PE) at large scales and positive (PE to KE) at small scales. Integrated over all scales, the buoyancy flux is very small for a wide range of flow regimes. However, results concerning buoyancy flux are sensitive to assumptions about the manner of energetic forcing. ¿ American Geophysical Union 1992