An Introduction to Large Deviations and Equilibrium Statistical Mechanics for Turbulent Flows
arXiv:1703.06779 · doi:10.1007/978-3-319-18206-3_3
Abstract
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large scales. In this short course, we show how the principles of equilibrium statistical mechanics apply to this problem and predict the condensation of energy at large scales and allow for computing the resulting coherent structures. We focus on the structure of the theory using the language of large deviation theory.
Lecture notes from the "Stochastic Equations for Complex Systems: Theory and Applications" summer school organized at the University of Wyoming in June 2014
References in corpus (29)
- The large deviation approach to statistical mechanics
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot
- Inverse energy cascade in three-dimensional isotropic turbulence
- Growing condensate in two-dimensional turbulence
- Random changes of flow topology in two dimensional and geophysical turbulence
- An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
- Mathematical and Physical Ideas for Climate Science
- Geophysical turbulence and the duality of the energy flow across scales
- Statistical mechanics of the shallow water system
- Simpler Variational Problem for Statistical Equilibria of the 2D Euler Equation and Other Systems with Long Range Interactions
- Dynamics and thermodynamics of axisymmetric flows: I. Theory
- Statistical mechanics of Beltrami flows in axisymmetric geometry: Theory reexamined
- Bottom-trapped currents as statistical equilibrium states above topographic anomalies
- On the mean-field spherical model
- Hyperviscosity and statistical equilibria of Euler turbulence on the torus and the sphere
- Restricted Equilibrium and the Energy Cascade in Rotating and Stratified Flows
- Statistical mechanics of the 3D axi-symmetric Euler equations in a Taylor-Couette geometry
- The catalytic role of beta effect in barotropization processes
- Invariant measures of the 2D Euler and Vlasov equations
- Oceanic rings and jets as statistical equilibrium states
- Additional Invariants and Statistical Equilibria for the 2D Euler Equations on a spherical domain
- Statistical mechanics of quasi-geostrophic flows on a rotating sphere
- Statistical mechanics of Fofonoff flows in an oceanic basin
- Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere
- Restricted Partition Functions and Inverse Energy Cascades in Parity Symmetry Breaking flows
- Sampling microcanonical measures of the 2D Euler equations through Creutz's algorithm: a phase transition from disorder to order when energy is increased
- Nonlinear energy transfers and phase diagrams for geostrophically balanced rotating--stratified flows
- Statistical mechanics of the shallow-water system with a prior potential vorticity distribution