On the statistical mechanics of the 2D stochastic Euler equation

Freddy Bouchet*, Jason Laurie, Oleg Zaboronski

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


The dynamics of vortices and large scale structures is qualitatively very different in two dimensional flows compared to its three dimensional counterparts, due to the presence of multiple integrals of motion. These are believed to be responsible for a variety of phenomena observed in Euler flow such as the formation of large scale coherent structures, the existence of meta-stable states and random abrupt changes in the topology of the flow. In this paper we study stochastic dynamics of the finite dimensional approximation of the 2D Euler flow based on Lie algebra su(N) which preserves all integrals of motion. In particular, we exploit rich algebraic structure responsible for the existence of Euler's conservation laws to calculate the invariant measures and explore their properties and also study the approach to equilibrium. Unexpectedly, we find deep connections between equilibrium measures of finite dimensional su(N) truncations of the stochastic Euler equations and random matrix models. Our work can be regarded as a preparation for addressing the questions of large scale structures, meta-stability and the dynamics of random transitions between different flow topologies in stochastic 2D Euler flows.

Original languageEnglish
Article number042020
JournalJournal of Physics: Conference Series
Issue numberSECTION 4
Publication statusPublished - 1 Jan 2011
Event13th European Turbulence Conference, ETC13 - Warsaw, Poland
Duration: 12 Sept 201115 Sept 2011


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