Variations in Wave Energy and Amplitudes along the Energy Dispersion Paths of Nonstationary Barotropic Rossby Waves

The variations in the wave energy and the amplitude along the energy dispersion paths of the barotropic Rossby waves in zonally symmetric basic flow are studied by solving the wave energy equation, which expresses that the wave energy variability is determined by the divergence of the group velocity and the energy budget from the basic flow. The results suggest that both the wave energy and the amplitude of a leading wave increase significantly in the propagating region that is located south of the jet axis and enclosed by a southern critical line and a northern turning latitude. The leading wave gains the barotropic energy from the basic flow by eddy activities. The amplitude continuously climbs up a peak at the turning latitude due to increasing wave energy and enlarging horizontal scale (shrinking total wavenumber). Both the wave energy and the amplitude eventually decrease when the trailing wave continuously approaches southward to the critical line. The trailing wave decays and its energy is continuously absorbed by the basic flow. Furthermore, both the wave energy and the amplitude oscillate with a limited range in the propagating region that is located near the jet axis and enclosed by two turning latitudes. Both the leading and trailing waves neither develop nor decay significantly. The jet works as a waveguide to allow the waves to propagate a long distance.