Turbulence noise

Journal Article · Sat Jun 01 04:00:00 EDT 1996 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/BF02179551· OSTI ID:471796

Eyink, G L ^[1]

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1. Univ. of Arizona, Tucson, AZ (United States)

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 filtering{close_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 theory{close_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 principle{close_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.

• Sponsoring Organization: USDOE
• OSTI ID: 471796
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 5-6 Vol. 83; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
66 PHYSICS
ANALYTICAL SOLUTION
EDDY CURRENTS
HYDRODYNAMICS
LANGEVIN EQUATION
NAVIER-STOKES EQUATIONS
NOISE
TURBULENT FLOW
VARIATIONAL METHODS