3 research outputs found
Statistical mechanics of two-dimensional vortices and stellar systems
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.Comment: Chapter 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