A new'' approach to the quantitative statistical dynamics of plasma turbulence: The optimum theory of rigorous bounds on steady-state transport

Journal Article · Fri Jun 01 00:00:00 EDT 1990 · Physics of Fluids B; (USA)

DOI:https://doi.org/10.1063/1.859551· OSTI ID:6864402

Krommes, J A ^[1]; Kim, C ^[2]

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1. Plasma Physics Laboratory, Princeton University, P.O. Box 451, Princeton, New Jersey 08543 (USA)
2. Institute for Fusion Studies, University of Texas at Austin, Austin, TX (USA)

The fundamental problem in the theory of turbulent transport is to find the flux {Gamma} of a quantity such as heat. Methods based on statistical closures are mired in conceptual controversies and practical difficulties. However, it is possible to {ital bound} {Gamma} by employing constraints derived rigorously from the equations of motion. Brief reviews of the general theory and its application to passive advection are given. Then, a detailed application is made to anomalous resistivity generated by {ital self}-{ital consistent} turbulence in a reversed-field pinch. A nonlinear variational principle for an upper bound on the turbulent electromotive force for fixed current is formulated from the magnetohydrodynamic equations in cylindrical geometry. Numerical solution of a case constrained solely by energy balance leads to a reasonable bound and nonlinear eigenfunctions that share intriguing features with experimental data: The dominant mode numbers appear to be correct, and field reversal is predicted at reasonable values of the pinch parameter. Although open questions remain, upon considering all bounding calculations to date it can be concluded, remarkably, that global energy balance constrains transport sufficiently so that bounds derived therefrom are not unreasonable and that bounding calculations are feasible even for involved practical problems. The potential of the method has hardly been tapped; it provides a fertile area for future research.

• DOE Contract Number: AC02-76CH03073; FG05-80ET53088
• OSTI ID: 6864402
• Journal Information: Physics of Fluids B; (USA), Journal Name: Physics of Fluids B; (USA) Vol. 2:6; ISSN 0899-8221; ISSN PFBPE
• Country of Publication: United States
• Language: English

Related Subjects

640430* -- Fluid Physics-- Magnetohydrodynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CONFIGURATION
CYLINDRICAL CONFIGURATION
ENERGY
FLUID MECHANICS
HEAT
HYDRODYNAMICS
MAGNETOHYDRODYNAMICS
MECHANICS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
OPTIMIZATION
PLASMA
STATISTICAL MECHANICS
STEADY-STATE CONDITIONS
TURBULENCE
VARIATIONAL METHODS