Propagation and trapping of inertial gravity waves in shear flows (ray theory)

The process of propagation and trapping of inertial gravity wave (IGW) packets in oceanic shear flows is studied in the geometric-optics approximation (ray theory). It is shown that wave trapping in strong stable stratification occurs in the region of anticyclonic (horizontal) velocity shear in a narrow frequency range on the left side of the inertial frequency. Beyond this range, the packet (ray) is either reflected from a cyclonic shear layer or propagates freely through the shear layer. The basic equations of ray theory are analyzed qualitatively, and analytical expressions are derived for freely propagating and trapped rays. The influence that vertical shear exerts on the ray behavior is also investigated. It is shown that two-dimensional ray focusing occurs as the velocity profile decreases with depth, so that rays concentrate along a specific latitude.