Turbulence noise

We show that the large-eddy motions in turbulent fluid flow obey a modified hydrodynamic equation with a stochastic turbulent stress whose distribution is a causal functional of the large-scale velocity field itself. We do so my means of an exact procedure of open-quotes statistical filteringclose quotes of the Navier-Stokes equations, which formally solves the closure problem, and we discuss the relation of our analysis with the open-quotes decimation theoryclose quotes of Kraichnan. We show that the statistical filtering procedure can be formulated using field-theoretic path-integral methods within the Martin-Siggia-Rose (MSR) formalism for classical statistical dynamics. We also establish within the MSR formalism a open-quotes least-effective-action principleclose quotes for mean turbulent velocity profiles, which generalizes Onsager's principle of least dissipation.This minimum principle is a consequence of a simple realizability inequality and therefore holds also in any realizable closure. Symanzik's theorem in field theory - which characterizes the static effective action as the minimum expected value of the quantum Hamiltonian over all state vectors with prescribed expectations of fields - is extended to MSR theory with non-Hermitian Hamiltonian. This allows stationary mean velocity profiles and other turbulence statistics to be calculated variationally by a Rayleigh-Ritz procedure. Finally, we develop approximations of the exact Langevin equations for large eddies, e.g., a random-coupling DIA model, which yield new stochastic LES models. These are compared with stochastic subgrid modeling schemes proposed by Rose, Chasnov, Leith, and others, and various applications are discussed