Rigorous upper bounds for transport due to passive advection by inhomogeneous turbulence
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 ae 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. For the case of stochastic magnetic fields, the scaling of the bounds is described for the magnetic diffusion coefficient as well as for the particle diffusion coefficient in the so-called collisionless, fluid, and double-streaming regimes.
- Research Organization:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- DOE Contract Number:
- AC02-76CH03073
- OSTI ID:
- 6210639
- Report Number(s):
- PPPL-2422; ON: DE87010632
- Resource Relation:
- Other Information: Portions of this document are illegible in microfiche products. Original copy available until stock is exhausted
- Country of Publication:
- United States
- Language:
- English
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