Large deviation theory and rare events for geophysical turbulent flows and climate dynamics

Many natural and experimental turbulent flows display a bistable behavior: rare and abrupt dynamical transitions between two very different subregions of the phase space. The most prominent natural examples are probably the Earth magnetic field reversals (over geological timescales), the Kuroshio bistability, or the Dansgaard-Oeschger events that have affected the Earth climate during the last glacial period, and are probably due to several attractors of the turbulent ocean dynamics. Recent results show that similar bistability occur also in the turbulent dynamics of atmosphere jets. Those abrupt transitions are extremely rare events that change drastically the nature of the flow and are thus of paramount importance, for instance for climate studies.
Similar bistable phenomena are observed in a wide range of complex dynamical systems, from the dynamics of phase transitions in condensed matter physics, to the dynamics of complex biomolecules and polymers. Common tools, based on non equilibrium statistical mechanics, have been developed recently to study rare events and their dynamics. From a mathematical point of view, the main framework is large deviation theory for stochastic processes. From a computational point of view the key tools are rare event algorithms aimed at sampling efficiently rare by essential dynamical paths.