Atmospheric gravity wave ray tracing: Ordinary and extraordinary waves

Abstract

Calculation of internal gravity-wave ray paths in the atmosphere using a general three-dimensional ray tracing computer program is discussed. To initialize a ray-path calculation, it is necessary to specify the initial values for the components of the wave vector at the source so that the dispersion relation is satisfied. For acoustic waves, or for gravity waves in the absence of wind, there is no ambiguity in determining the magnitude of the wave vector once the frequency and direction of propagation (wave-normal direction) have been specified. For gravity waves with wind, however, it is necessary to solve a quartic equation to specify the magnitude of the wavenumber. Two of the roots of the quartic reduce to the usual solutions in the absence of wind, and we designate these roots as ‘ordinary waves.’ The two new roots (whose values approach infinity as the wind speed approaches zero), we designate as ‘extraordinary waves.’ A section contrasts the properties of the different gravity wave types.Comparison with some previously published examples of ray-path calculations of gravity waves shows that those previous examples were actually extraordinary waves, but their significance was not recognized at that time.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.