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On the statistical mechanics of the 2Dstochastic Euler equation
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Bouchet, Freddy, Laurie, Jason and Zaboronski, Oleg V.. (2011) On the statistical mechanics of the 2Dstochastic Euler equation. Journal of Physics: Conference Series, Vol.318 (No.4). 042020. ISSN 1742-6596
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Official URL: http://dx.doi.org/10.1088/1742-6596/318/4/042020
Abstract
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.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QC Physics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Journal of Physics: Conference Series |
| Publisher: | Institute of Physics Publishing Ltd. |
| ISSN: | 1742-6596 |
| Date: | 2011 |
| Volume: | Vol.318 |
| Number: | No.4 |
| Page Range: | 042020 |
| Identification Number: | 10.1088/1742-6596/318/4/042020 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/48220 |
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