MGAT10 - Chaos in rotating systems |
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Speaker |
Bouchet, Freddy |
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Co-autors |
Eric Simonnet and Hidetoshi Morita |
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Talk Title |
Phase transitions for the large scales of 2D and planetary atmosphere turbulence |
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Abstract |
One of the most important problem in turbulence is the prediction of large-scale structures of flows with very high Reynolds number. The class of two dimensionnal and geostrophic flows is relevant for applications for geophysical applications (for instance the atmosphere of Jovian planets). We consider the two-dimensional Navier-Stokes equation with weak stochastic forcing and dissipation in the inertial limit. This is an example of dynamical system, where an out of equilibrium stationary state is reached, without detailed balance. We discuss theses examples from a statistical mechanics point of view: for instance we discuss the existence of out of equilibrium phase transitions, or consider kinetic theory approaches. The most striking result is the existence of out of equilibrium phase transitions. One observe transitions from one type of flow (unidirectional) to an other one (dipole), at random time. This is similar to the classical two wheel potential with noise. By contrast, in our case, no such potential exists and the turbulent nature of the flow (infinite number of degrees of freedom) renders the phenomena much richer. Analogies with the Earth magnetic field reversal, and with similar phenomena in experiment of two dimensionnal and geophysical flows will be discussed. The approach of these phenomena using kinetic theory will be discussed. This is the most natural way for a theory for the self organized jets of geophysical turbulence, for instance in Jovian atmospheres. We prove new results for the linearized Euler and Navier-Stokes equations with random forces, and their relations to turbulent fluctuations. Analogies with kinetic theories for other systems with long range interactions, like self gravitating masses or plasma will be discussed. |
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