Computation of rare transitions in the barotropic quasi-geostrophic equations

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...

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Bibliographic Details
Published in:New journal of physics 2015-01, Vol.17 (1), p.15009-25
Main Authors: Laurie, Jason, Bouchet, Freddy
Format: Article
Language:English
Subjects:
47.10.ad
47.20.Ky
Algorithms
Bistability
Computation
Computational fluid dynamics
Computer simulation
Condensed Matter
Deviation
Economic models
Fluid Dynamics
Geophysical methods
Geophysics
Instantons
Mathematical analysis
Mathematical models
minimum action method
Navier-Stokes equations
Numerical analysis
Optimization
Physics
quasi-geostrophic dynamics
rare transitions
Statistical Mechanics
Transition probabilities
Turbulence
Two dimensional models
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Summary: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.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/17/1/015009