The propagation of energy on the sphere as described by the linear barotropic vorticity equation is studied. For simple flows, the concept of group velocity is examined. Planetary-scale vorticity anomalies exhibit a surprising lack of dispersion in a hemispheric domain. On the sphere, there is more dispersion and a significant cross-equatorial propagation of energy. Planetary-scale vorticity sources tend to produce an orderly downstream train of waves which exhibit a strong tilt (NE-SW for sources in the northern hemisphere) and cross the equator. Zonally elongated sources produce an almost north-south train of waves. For realistic zonal flows with equatorial easterlies, large-scale transients cross the equator, but the long-term forced response in the opposite hemisphere is small.

Comparison of the results with observations of atmospheric wave behaviour is made, and some possible implications are presented.