Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems

By Pierre-Henri Chavanis. 2002

202 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/68788a74bc5efedbb99c20aa3f2b72113562661f

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Citations in the corpus

Gravitational instability of finite isothermal spheres (2001, background): “The beautiful analogy between two-dimensional vortices and stellar systems has been described extensively by Chavanis (see [8, 17, 10, 12] and references therein).”
Thermodynamics and dynamics of systems with long-range interactions (2010, methodology): “, self-gravitating systems such as globular clusters, [5]) where the temperature could be sufficiently high to make the entropic term TS compete with the energy E, resulting in a non-trivial thermodynamics.”
Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model (2003, background): “Indeed, in the context of two-dimensional fluid-dynamics [23,24] and plasma physics [24], the existence of an infinity of stationary states is known since a long time .”
Statistical Mechanics of Violent Relaxation in Stellar Systems (2002, background): “The computation of isothermal Fermi-Dirac spheres has been performed only recently by Chavanis & Sommeria [25].”
Onsager and the theory of hydrodynamic turbulence (2006, background): “Lundgren and Pointin (1977) have performed numerical simulations of the point-vortex model with initial conditions corresponding to several local clusters of vortices at some distance from each other.”
Statistical mechanics of two-dimensional and geophysical flows (2011, methodology): “For these we refer the reader to [ 180, 186], [113, 9, 74, 3] and [66, 43] respectively.”