95-254 Eyink, G. L.

Turbulence Noise (156K, LaTex) Jun 6, 95

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Abstract. 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 by means of an exact procedure of ``statistical filtering'' of the Navier-Stokes equations, which formally solves the closure problem, and we discuss relations of our analysis with the ``decimation theory'' of Kraichnan. We show that the statistical filtering procedure can be formulated using field-theoretic path-integral methods within the Martin-Siggia-Rose formalism for classical statistical dynamics. We also establish within the MSR formalism a ``least-effective-action principle'' 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 modelling schemes proposed by Rose, Chasnov, Leith, and others, and various applications are discussed.

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