Baroclinic instability of a midlatitude zonal mean state changing with time

A characteristic frequency equation is formulated for atmospheric Rossby waves embedded in a basic zonal mean state changing periodically with time, based on the two-layer model in the midlatitude β-plane. The characteristic frequencies are calculated for a truncated set of waves including up to the third higher harmonics of geopotential and temperature, and the results are compared with the classical baroclinic instability theory. The zonal mean thermal wind oscillating around the stationary state is found to be more unstable against small perturbations than the instability predicted by classical theory. The oscillating thermal wind influences the Rossby waves in two ways, firstly by enhancing the growth rate and secondly by modulating the propagation phase speed around the central phase velocity. The relative magnitudes of these two effects depend on the frequency and the amplitude of the changing thermal wind. On the other hand, the changing zonal mean wind mainly affects the phase speed of the Rossby waves with little influence on the growth rate. Using a highly truncated model it is shown that a resonant-type interaction is possible between the geopotential and the temperature wave modes in the perturbation when the zonal mean thermal wind changes periodically with time. It is suggested that the discrepancy often observed between the phase speed of developing Rossby waves on weather maps and classic baroclinic instability theory might be partly due to the changing zonal mean state with time.