Statistical mechanics of two-dimensional vortices and stellar systems
arXiv:cond-mat/0212223
Abstract
The formation of large-scale vortices is an intriguing phenomenon in two-dimensional turbulence. Such organization is observed in large-scale oceanic or atmospheric flows, and can be reproduced in laboratory experiments and numerical simulations. A general explanation of this organization was first proposed by Onsager (1949) by considering the statistical mechanics for a set of point vortices in two-dimensional hydrodynamics. Similarly, the structure and the organization of stellar systems (globular clusters, elliptical galaxies,...) in astrophysics can be understood by developing a statistical mechanics for a system of particles in gravitational interaction as initiated by Chandrasekhar (1942). These statistical mechanics turn out to be relatively similar and present the same difficulties due to the unshielded long-range nature of the interaction. This analogy concerns not only the equilibrium states, i.e. the formation of large-scale structures, but also the relaxation towards equilibrium and the statistics of fluctuations. We will discuss these analogies in detail and also point out the specificities of each system.
arXiv commentChapter of the forthcoming "Lecture Notes in Physics" volume: ``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics Vol. 602, Springer (2002)
References in corpus (13)
- Inequivalence of ensembles in a system with long range interactions
- Thermodynamics of self-gravitating systems
- Phase transitions in self-gravitating systems. Self-gravitating fermions and hard spheres models
- Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions
- Gravitational instability of isothermal and polytropic spheres
- The Formation and Role of Vortices in Protoplanetary Disks
- DID PLANET FORMATION BEGIN INSIDE PERSISTENT GASEOUS VORTICES?
- Statistical mechanics of the shallow water system
- Phase diagram of self-attracting systems
- Quasilinear theory of the 2D Euler equation
- Numerical renormalization group of vortex aggregation in 2D decaying turbulence: the role of three-body interactions
- Thermodynamics of Self-Gravitating Systems with Softened Potentials
- On the effective velocity created by a point vortex in two-dimensional hydrodynamics
Cited by in corpus (15)
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Kinetic theory of two dimensional point vortices from a BBGKY-like hierarchy
- Kinetic theory of Onsager's vortices in two-dimensional hydrodynamics
- Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions
- A statistical mechanics approach to mixing in stratified fluids
- Statistical mechanics of quasi-geostrophic flows on a rotating sphere
- Curious behaviour of the diffusion coefficient and friction force for the strongly inhomogeneous HMF model
- Influence of Reynolds number and forcing type in a turbulent von Kármán flow
- Functional integral derivation of the kinetic equation of two-dimensional point vortices
- Ensemble equivalence for mean field models and plurisubharmonicity
- Field theoretical formulation of the asymptotic relaxation states of two-dimensional ideal fluids
- A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass
- The HMF model for fermions and bosons
- The Turbulent 'Mixing' Layer as a Problem in the Non-equilibrium Statistical Mechanics of a Vortex Gas
- Long-range interacting systems and the Gibbs-Duhem equation