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A theoretical study is made to establish the concept of “quasi-stationary (QS)” states in irregular, large-scale atmospheric motions by using a simple model. It is a truncated, two-layer, quasi-geostrophic model in a β-channel with surface topography, external thermal forcing (i.e., meridional differential heating) and dissipative processes. We define a QS state as a period when the magnitude of the time derivative of spectral components, |x˙(t)|, is smaller than a prescribed threshold value. For a wide range of parameter values of the thermal forcing, each QS state is found to occur when the trajectory x(t) passes immediately next to a local minimum point (MP) of |x˙| in phase space; the MP is either a stationary solution or a nonstationary minimum point bifurcating from a limit point of a stationary solution. Moreover, we give the statistical significance to this relation between each QS state and an MP. The relation is almost independent of the threshold value defining the QS states. Therefore...

A Dynamical Model of “Quasi-stationary” States in Large-Scale Atmospheric Motions