Connection of periodic orbits and variability patterns of circulation for the barotropic model of atmospheric dynamics

Abstract

We have investigated the relationship between periodic trajectories of barotropic atmospheric model and the modes of the model variability. In particular, we have studied the nature of “25 day” mode of variability (Branstator, 1987; Kushnir 1987). This mode arises as a first complex empirical orthogonal function (or “Hilbert EOF” according to (H. von Storch, Zwiers)) for a given system and is a dominant rotational component of the system dynamics. It was shown that the mode structure coincides with several least unstable periodic orbits of the system. The phase portrait of the system in the plane of the first complex EOF has regular shape with maximum of the probability density function in the vicinity of these weakly unstable periodic orbits.