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Instantons in atmospheric dynamics

I was browsing through the AGU conference program and noticed a poster applying path integrals and instanton physics to atmospheric turbulence, specifically to deriving the probabilities of large, rare deviations. I thought some readers here might find it interesting.

TITLE: EXPLICIT COMPUTATIONS OF INSTANTONS AND LARGE DEVIATIONS IN BETA-PLANE TURBULENCE

AUTHORS: Jason Laurie1, Freddy Bouchet1, Oleg Zaboronski2

INSTITUTIONS: 1. Laboratoire de Physique, Ecole Normale Supérieure de Lyon, Lyon, France. 2. Mathematics Institute, University of Warwick, Coventry, United Kingdom.

ABSTRACT BODY: We use a path integral formalism and instanton theory in order to make explicit analytical predictions about large deviations and rare events in beta-plane turbulence.

The path integral formalism is a concise way to get large deviation results in dynamical systems forced by random noise. In the most simple cases, it leads to the same results as the Freidlin-Wentzell theory, but it has a wider range of applicability. This approach is however usually extremely limited, due to the complexity of the theoretical problems. As a consequence it provides explicit results in a fairly limited number of models, often extremely simple ones with only a few degrees of freedom. Few exception exist outside the realm of equilibrium statistical physics.

We will show that the barotropic model of beta-plane turbulence is one of these non-equilibrium exceptions. We describe sets of explicit solutions to the instanton equation, and precise derivations of the action functional (or large deviation rate function). The reason why such exact computations are possible is related to the existence of hidden symmetries and conservation laws for the instanton dynamics.

We outline several applications of this apporach. For instance, we compute explicitly the very low probability to observe flows with an energy much larger or smaller than the typical one. Moreover, we consider regimes for which the system has multiple attractors (corresponding to different numbers of alternating jets), and discuss the computation of transition probabilities between two such attractors. These extremely rare events are of the utmost importance as the dynamics undergo qualitative macroscopic changes during such transitions.

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