Stratospheric multiple equilibria and seasonal variations

Using a vertical one-dimensional model, we discuss the equilibrium of the stratospheric mean zonal flow and planetary wave forced by the surface corrugation. Their stabilities are also examined. It is shown that in late autumn and early spring, there exist two stable equilibrium solutions and one unstable equilibrium solution, while one stable equilibrium solution in mid-winter. It is noted that we have no vacillating solution as obtained by Holton and Mass (1976) and Chao (1985). Solving the time-dependent problems with changing the vertical shear of the basic zonal wind with one year period as an indicator of seasonal variation, we can obtain the growth of planetary wave twice in winter and the intensification of westerly wind between these two amplitude peaks. In addition, it is shown that a drastic transition of the mean zonal winds from westerlies to easterlies resembling the final warming occurs in later winter or early spring. These are very similar to the results of data analysis by Smith (1983) and those of the numerical simulation by Holton and Wehrbein (1980). Thus, the stratospheric seasonal variation can be interpreted as a hysteresis phenomenon caused by the change in the solar differential heating in the presence of multiple equilibria. The breakdown of polar, night vortex with the final warming is a kind of nonlinear instability. That is, if the winter westerly wind in the upper stratosphere is close to the Charney-Drazin’s critical velocity and if it is perturbed by a planetary wave, then the refractive index is changed and this change causes the amplification of the wave. The amplified wave, in turn, changes the refractive index is changed and this change causes the amplification of the wave. The amplified wave, in turn, changes the refractive index by accelerating easterlies. This process provides a feedback, and the polar night vortex breaks down in the end. The present instability is not the resonance breakdown as in Plumb (1981). Finally, we make some comments on Chao’s (1985) results.