The nonlinear turbulent interactions between acoustic gravity waves are investigated using two‐dimensional nonlinear fluid simulations. The acoustic gravity waves consist of velocity and density perturbations and propagate across the density gradients in the vertical direction in the Earth's atmosphere. We find that the coupled two component model exhibits generation of large‐scale velocity potential flows along the vertical direction, while the density perturbations relax toward an isotropic random distribution. The characteristic turbulent spectrum associated with the system has a Kolmogorov‐like feature and tends to relax toward a k−5/3 spectrum, where k is a typical wave number. The cross field diffusion associated with the velocity potential grows linearly and saturates in the nonlinear phase.