Rigorous upper bounds for transport due to passive advection by inhomogeneous turbulence

Journal Article · Sat Aug 01 00:00:00 EDT 1987 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(87)90122-9· OSTI ID:6362908

Krommes, J A; Smith, R A

A variational procedure, due originally to Howard and explored by Busse and others for self-consistent turbulence problems, is employed to determine rigorous upper bounds for the advection of a passive scalar through an inhomogeneous turbulent slab with arbitrary generalized Reynolds number R and Kubo number K. In the basic version of the method, the steady-state energy balance is used as a constraint; the resulting bound, though rigorous, is independent of K. A pedagogical reference model (one dimension, K = infinity) is described in detail; the bound compares favorably with the exact solution. The direct-interaction approximation is also worked out for this model; it is somewhat more accurate than the bound, but requires considerably more labor to solve. For the basic bound, a general formalism is presented for several dimensions, finite correlation length, and reasonably general boundary conditions. Part of the general method, in which a Green's function technique is employed, applies to self-consistent as well as to passive problems and thereby generalizes previous results in the fluid literature. The formalism is extended for the first time to include time-dependent constraints, and a bound is deduced which explicitly depends on K and has the correct physical scalings in all regimes of R and K. Two applications from the theory of turbulent plasmas are described: flux in velocity space, and test particle transport in stochastic magnetic fields. For the velocity space problem, the simplest bound reproduces Dupree's original scaling for the strong turbulence diffusion coefficient.

• Research Organization: Princeton University, Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08544-0451
• OSTI ID: 6362908
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 177:2; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700101 -- Fusion Energy-- Plasma Research-- Confinement
Heating
& Production
700103 -- Fusion Energy-- Plasma Research-- Kinetics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ADVECTION
BOUNDARY CONDITIONS
DATA
EXPERIMENTAL DATA
FUNCTIONS
GREEN FUNCTION
INFORMATION
LIMITING VALUES
MASS TRANSFER
NUMERICAL DATA
PLASMA
TRANSPORT THEORY
TURBULENCE