TURBULENCE NOISE

We show that the large-eddy motions in turbulent fluid flow obey a mod ified hydrodynamic equation with a stochastic turbulent stress whose d istribution is a causal Functional of the large-scale velocity field i tself We do so by means of an exact procedure of ''statistical filteri ng'' of the Navier-Stokes equations, which formally solves the closure problem, and we discuss the relation of our analysis with the ''decim ation theory'' of Kraichnan. We show that the statistical filtering pr ocedure can be formulated using field-theoretic path-integral methods within the Martin-Siggia-Rose (MSR) formalism for classical statistica l dynamics. We also establish within the MSR formalism a ''least-effec tive-action principle'' for mean turbulent velocity profiles, which ge neralizes Onsager's principle of least dissipation. This minimum princ iple is a consequence of a simple realizability inequality and therefo re holds also in any realizable closure. Symanzik's theorem in field t heory-which characterizes the static effective action as the minimum e xpected value of the quantum Hamiltonian over all state vectors with p rescribed expectations of fields-is extended to MSR theory with non-He rmitian Hamiltonian, This allows stationary mean velocity profiles and other turbulence statistics to be calculated variationally by a Rayle igh-Ritz procedure. Finally, we develop approximations of the exact La ngevin equations for large eddies, e.g., a random-coupling DIA model, which yield new stochastic LES models. These are compared with stochas tic subgrid modeling schemes proposed by Rose, Chasnov, Leith, and oth ers; and various applications are discussed.