Theoretical studies on the interaction between the general circulation and small-scale phenomena.

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In the so-called parameterization, we evaluate the effects of smaller scale phenomena on the large-scale motion considered, usually with use of the latter variables. However, if we treat the interaction correctly, the equations will become non-linear, including the feed-back effects of the large-scale motion modified by the smaller ones, and will lead us to somewhat difficult situation, because it is generally impossible to omit the feed-back, except the case where its time-scale is sufficiently longer. The non-linearity of equation may cause the bifurcation of solutions. The idea of parameterization does not necessarily involve such a consideration. Then, in this wotk, as the first step toward founding a reasonable idea of parameterization, we have a vertical one dimensional model of the stratosphere as a non-linear system in which the mean zonal flow and planetary waves are mutually affecting, and examined the bifurcation of the solutions and also the response to external forcing.As the result, we have succeeded to answer reasonably or soundly the problems such as why the planetary waves can amplify in late winter, why the sudden warmings prefer late winter or early spring to other seasons and so on. These phenomena can be interpreted as the transitions among stable equilibrium states, occuring in the stratosphere responding to the seasonal change in solar differential heating.We anticipate that similar situations may appear in the prblem of interaction between gravity wave and the mean circulation, which is being intensively studied in recent years with respect to the gravity wave parameterization.