Derivation of maximum entropy principles in two-dimensional turbulence vialarge deviations

The continuum limit of lattice models arising in tale-dimensional turbulenc e is analyzed by means of the theory of large deviations. In particular. th e 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 f ramework, and the maximum entropy principles that govern these models are r igorously derived by a new method. In this method, a doubly indexed, measur e-valued random process is introduced to represent the coarse-grained vorti city field. The natural large deviation principle for this process is estab lished and is then used to derive the equilibrium conditions satisfied by t he most probable macrostates in the continuum models. The physical implicat ions of these results are discussed, and some modeling issues of importance to the theory of long-lived, large-scale coherent vortices in turbulent fl ows are clarified.