 95254 Eyink, G. L.
 Turbulence Noise
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Jun 6, 95

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Abstract. We show that the largeeddy motions in turbulent fluid flow obey a modified hydrodynamic equation with a stochastic
turbulent stress whose distribution is a causal functional of the largescale velocity field itself. We do so
by means of an exact procedure of ``statistical filtering'' of the NavierStokes 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 fieldtheoretic pathintegral methods within the
MartinSiggiaRose formalism for classical statistical dynamics. We also establish within the MSR formalism a
``leasteffectiveaction 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 fieldtheorywhich characterizes the static effective action
as the minimum expected value of the quantum Hamiltonian over all state vectors with prescribed expectations of
fieldsis extended to MSR theory with nonHermitian Hamiltonian. This allows stationary mean velocity profiles and
other turbulence statistics to be calculated variationally by a RayleighRitz procedure. Finally, we develop
approximations of the exact Langevin equations for large eddies, e.g. a randomcoupling 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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