Rossby wave ray tracing in a barotropic divergent atmosphere

The effects of divergence on low-frequency Rossby wave propagation are examined by using the twodimensional Wentzel-Kramers-Brillouin (WKB) method and ray tracing in the framework of a linear barotropic dynamic system. The WKB analysis shows that the divergent wind decreases Rossby wave frequency (for wave propagation northward in the Northern Hemisphere). Ray tracing shows that the divergent wind increases the zonal group velocity and thus accelerates the zonal propagation of Rossby waves. It also appears that divergence tends to feed energy into relatively high wavenumber waves, so that these waves can propagate farther downstream. The present theory also provides an estimate of a phase angle between the vorticity and divergence centers. In a fully developed Rossby wave, vorticity and divergence display a pi/2 phase difference, which is consistent with the observed upper-level structure of a mature extratropical cyclone. It is shown that these theoretical results compare well with observations.