Atmospheric gravity wave ray tracing: Ordinary and extraordinary waves

In the absence of wind, gravity waves are restricted to a fan of propagation directions centered about horizontal propagation, but asymptotic gravity waves (in the Bousinesq approximation) have a fixed propagation direction for a given frequency. In the presence of a horizontal wind, however, the wave-normal direction is restricted to a fan of directions in the upwind direction, but not in the downwind direction. The ray direction for upwind propagation has no restrictions. A short review of gravity wave theory and the gravity wave dispersion relation is included.