Eyink, G. L.
Turbulence Noise
(156K, LaTex)
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.