Computation of rare transitions in the barotropic quasi-geostrophic equations

Jason Laurie (1) , Freddy Bouchet (2)

1 Weizmann Institute of Science [Rehovot, Israël]
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherwise. We adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

Mots clés: rare transitions; bistability; minimum action method; quasi-geostrophic dynamics

Domaines: Mécanique statistique [cond-mat.stat-mech]; Dynamique des Fluides [physics.flu-dyn]

Jason Laurie, Freddy Bouchet. Computation of rare transitions in the barotropic quasi-geostrophic equations. New Journal of Physics, 2015, 17 (015009), pp.25. ⟨10.1088/1367-2630/17/1/015009⟩. ⟨hal-01062701⟩