Propagation of topographically generated internal waves in the atmosphere

The propagation of small-scale internal gravity wave packets through large-scale inertial frequency waves is investigated through ray theory and numerically solving the fully non-linear Navier-Stokes equations in two dimensions. Small-scale internal waves generated by flow over topography interact with both time-independent background shear profiles and time-dependent shears present in the atmosphere in the form of large-scale waves of inertial frequency propagating upward. Interaction with a time-independent shear may lead to a critical layer interaction and eventual short wave absorption or breaking. When the shear is time-dependent and the energy of both the small- and large-scale waves are propagating in the same direction, a critical layer may be approached, but because of the time-dependent nature of the background it may disappear before the small-scale wave is absorbed or breaks. Although both numerical and observational studies have been performed to address this issue, the details of this type interaction are not fully understood, and seem to be highly sensitive to initial wave parameters and location. Through ray theory many small-scale waves can be traced, and data collected on the evolution of their energy and propensity to break. An investigation of many small-scale waves with a range of realistic initial wave parameters and vertical locations propagating upward through an upward propagating inertial wave give insight into the propagation of terrain generated internal waves through a time-dependent background flow, and result in a classification of probable types of short wave interactions.