Computation of rare transitions in the barotropic quasi-geostrophic equations

@article{Laurie2014ComputationOR,
  title={Computation of rare transitions in the barotropic quasi-geostrophic equations},
  author={Jason Laurie and Freddy Bouchet},
  journal={arXiv: Statistical Mechanics},
  year={2014}
}
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… 
Multistability and rare spontaneous transitions in barotropic β-plane turbulence
We demonstrate that turbulent zonal jets, analogous to Jovian ones, which are quasi-stationary, are actually metastable. After extremely long times, they randomly switch to new configurations with a
Multistability and rare spontaneous transitions between climate and jet configurations in a barotropic model of the Jovian mid-latitude troposphere
We demonstrate that turbulent zonal jets, analogous to Jupiter ones, which are quasi-stationary are actually metastable. After extremely long times they randomly switch to new configurations with a
The instanton method and its numerical implementation in fluid mechanics
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent
Kinetic theory and large deviations for the dynamics of geophysical flows
This thesis deals with the dynamics of geophysical turbulent flows at large scales, more particularly their organization into east-west parallel flows (zonal jets). These structures have the
Efficient Computation of Instantons for Multi-Dimensional Turbulent Flows with Large Scale Forcing
TLDR
This work outlines a novel method for finding the minimizing trajectory in a wide class of problems that typically occurs in turbulence setups, where the underlying dynamical system is a non-gradient, non-linear partial differential equation, and the forcing is restricted to a limited length scale.
A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence
TLDR
A robust reduced-order modeling approach for near real-time prediction of mesoscale flows that combines physics-based projection methods with neural network closures to account for truncated modes and introduces a weighting parameter between the Galerkin projection and extreme learning machine models.
Geometric microcanonical theory of two-dimensional truncated Euler flows
This paper presents a geometric microcanonical ensemble perspective on two-dimensional truncated Euler flows, which contain a finite number of (Fourier) modes and conserve energy and enstrophy. We
Extremely rare collapse and build-up of turbulence in stochastic models of transitional wall flows.
TLDR
This analytical analysis shows that the physical effects controlling collapse and build-up trajectories and corresponding passage times with an emphasis on the saddle points between laminar and turbulent states lead to the asymmetric probability density function of kinetic energy of turbulence.
Instantons for the Destabilization of the Inner Solar System.
TLDR
In a simple deterministic model of Mercury dynamics, it is shown that the first exit time of such a resonance can be computed and it is demonstrated that path probabilities actually concentrate close to this instanton, for events which occur within a few hundred million years.
Edge States in the Climate System: Exploring Global Instabilities and Critical Transitions
Multistability is a ubiquitous feature in systems of geophysical relevance and provides key challenges for our ability to predict a system's response to perturbations. Near critical transitions small
...
...

References

SHOWING 1-10 OF 74 REFERENCES
Langevin Dynamics, Large Deviations and Instantons for the Quasi-Geostrophic Model and Two-Dimensional Euler Equations
We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path
The equilibrium statistical mechanics of simple quasi-geostrophic models
We have applied the methods of classical statistical mechanics to derive the inviscid equilibrium states for one- and two-layer nonlinear quasi-geostrophic flows, with and without bottom topography
A complete theory of low-energy phase diagrams for two-dimensional turbulence steady states and equilibria
For the 2D Euler equations and related models of geophysical flows, minima of energy--Casimir variational problems are stable steady states of the equations (Arnol'd theorems). The same variational
Bimodal Behavior in the Zonal Mean Flow of a Baroclinic β-Channel Model
Abstract The dynamical origin of midlatitude zonal-jet variability is examined in a thermally forced, quasigeostrophic, two-layer channel model on a β plane. The model’s behavior is studied as a
Minimum action method for the study of rare events
The least action principle from the Wentzell‐Freidlin theory of large deviations is exploited as a numerical tool for finding the optimal dynamical paths in spatially extended systems driven by a
Emergence and equilibration of jets in beta-plane turbulence
AbstractStochastic structural stability theory (S3T) provides analytical methods for understanding the emergence and equilibration of jets from the turbulence in planetary atmospheres based on the
Generalized thermodynamics and Fokker-Planck equations: applications to stellar dynamics and two-dimensional turbulence.
  • P. Chavanis
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
TLDR
A class of generalized Fokker-Planck equations that conserve energy and mass and increase a generalized entropy functional until a maximum entropy state is reached are introduced and the idea of a classification of generalized entropies in "classes of equivalence" is proposed.
Random changes of flow topology in two-dimensional and geophysical turbulence.
TLDR
It is proved that bifurcations in the flow topology occur either by changing the domain shape, the nonlinearity of the vorticity-stream-function relation, or the energy for inertial flows.
Large fluctution for a non linear heat equation with noise
Studies a nonlinear heat equation in a finite interval of space subject to a white noise forcing term. The equation without the forcing term exhibits several equilibrium configurations, two of which
...
...