Variations in Amplitudes and Wave Energy along the Energy Dispersion Paths for Rossby Waves in the Quasigeostrophic Barotropic Model

Variations in wave energy and amplitude for Rossby waves are investigated by solving the wave energy equation for the quasigeostrophic barotropic potential vorticity model. The results suggest that compared with rays in the nondivergent barotropic model, rays in the divergent model can have enhanced meridional and zonal propagation, accompanied by a more dramatic variability in both wave energy and amplitude, which is caused by introducing the divergence effect of the free surface in the quasigeostrophic model. For rays propagating in a region enclosed by a turning latitude and a critical latitude, the wave energy approaches the maximum value inside the region, while the amplitude approaches the maximum at the turning latitude. Waves can develop when both the wave energy and amplitude increase. For rays propagating in a region enclosed by two turning latitudes, the wave energy approaches the minimum value at one turning latitude and the maximum value at the other latitude, while the total wavenumber approaches the maximum value inside the region. The resulting amplitude increases if the total wavenumber decreases or the wave energy increases more significantly and decreases if the total wavenumber increases or the wave energy decreases more significantly. The matched roles of the energy from the basic flow and the divergence of the group velocity contribute to the slightly oscillating wave energy, which causes a slightly oscillating amplitude as well as the slightly oscillating total wavenumber.