Derivation of maximum entropy principles in two-dimensional turbulence via large deviations
The continuum limit of lattice models arising in two-dimensional turbulence is analyzed by means of the theory of large deviations. In particular, the Miller-Robert continuum model of equilibrium states in an ideal fluid and a modification of that model due to Turkington are examined in a unified framework, and the maximum entropy principles that govern these models are rigorously derived by a new method. In this method, a doubly indexed, measure-valued random process is introduced to represent the coarse-grained vorticity field. The natural large deviation principle for this process is established and is then used to derive the equilibrium conditions satisfied by the most probable macrostates in the continuum models. The physical implications of these results are discussed, and some modeling issues of importance to the theory of long-lived, large-scale coherent vortices in turbulent flows are clarified.
- Research Organization:
- Illinois Wesleyan Univ., Bloomington, IL (US)
- Sponsoring Organization:
- USDOE; National Science Foundation (NSF)
- DOE Contract Number:
- FG02-99ER25376
- OSTI ID:
- 20030422
- Journal Information:
- Journal of Statistical Physics, Vol. 98, Issue 5-6; Other Information: PBD: Mar 2000; ISSN 0022-4715
- Country of Publication:
- United States
- Language:
- English
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