Estimated Instability of Internal Waves due to Time-Dependent Shear

The ocean and atmosphere are characterized mainly by stable stratification which sustains propagation of particular ocurrances called internal gravity waves. These internal waves are generated as long as a perturbation to the stratification occurs at a frequency lower than the buoyancy (natural) frequency of the medium. These waves, once generated, propagate with wavelengths which can vary from a few meters to hundreds of meters in the vertical and thousands of meters in the horizontal. These waves propagate through the ocean and atmosphere interacting with other flow phenomena and eventually overturn and break, dissipating their energy. This energy dissipation affects circulation, heat transport, nutrient distribution and biological activity in the oceans and the atmosphere. The scales at which this energy transfer occurs are relatively small for overall oceanic models, hence the interest in finding the connection between the energy these waves dissipate and where the overall oceanic and atmospheric systems. We have focused our attention to interactions of an internal gravity wave with a time dependent shear flow in the form of a near-inertial wave, which is common in the ocean. These interactions are studied using ray theory, which is a linear analysis and fully non-linear numerical simulations. The aim of this analysis is to compare the instability estimates found from both methods and to define the accuracy of ray tracing in approximating these wave-wave interactions