Derivation of maximum entropy principles in two-dimensional turbulence via large deviations
Publication Date
2000
Journal or Book Title
JOURNAL OF STATISTICAL PHYSICS
Abstract
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.
Pages
1235-1278
Volume
98
Issue
5-6
Recommended Citation
Boucher, C; Ellis, RS; and Turkington, B, "Derivation of maximum entropy principles in two-dimensional turbulence via large deviations" (2000). JOURNAL OF STATISTICAL PHYSICS. 336.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/336
Comments
The published version is located at http://www.springerlink.com/content/u278467w73113713/