A tutorial introduction to the statistical theory of turbulent plasmas, a half-century after Kadomtsev’s Plasma Turbulence and the resonance-broadening theory of Dupree and Weinstock
Abstract
In honour of the 50th anniversary of the influential review/monograph on plasma turbulence by B. B. Kadomtsev as well as the seminal works of T. H. Dupree and J. Weinstock on resonance-broadening theory, an introductory tutorial is given about some highlights of the statistical–dynamical description of turbulent plasmas and fluids, including the ideas of nonlinear incoherent noise, coherent damping, and self-consistent dielectric response. The statistical closure problem is introduced. Incoherent noise and coherent damping are illustrated with a solvable model of passive advection. Self-consistency introduces turbulent polarization effects that are described by the dielectric function$${\mathcal{D}}$$. Dupree’s method of using$${\mathcal{D}}$$to estimate the saturation level of turbulence is described; then it is explained why a more complete theory that includes nonlinear noise is required. The general theory is best formulated in terms of Dyson equations for the covariance$$C$$and an infinitesimal response function$$R$$, which subsumes$${\mathcal{D}}$$. An important example is the direct-interaction approximation (DIA). It is shown how to use Novikov’s theorem to develop an$$\boldsymbol{x}$$-space approach to the DIA that is complementary to the original$$\boldsymbol{k}$$-space approach of Kraichnan. A dielectric function is defined for arbitrary quadratically nonlinear systems, including the Navier–Stokes equation, and an algorithm for determining the form of$${\mathcal{D}}$$in the DIA is sketched. The independent insights of Kadomtsev and Kraichnan about the problem of the DIA with random Galilean invariance are described. The mixing-length formula for drift-wave saturation is discussed in the context of closures that include nonlinear noise (shielded by$${\mathcal{D}}$$). The role of$$R$$in the calculation of the symmetry-breaking (zonostrophic) instability of homogeneous turbulence to the generation of inhomogeneous mean flows is addressed. The second-order cumulant expansion and the stochastic structural stability theory are also discussed in that context. In conclusion, various historical research threads are mentioned and representative entry points to the literature are given. In addition, some outstanding conceptual issues are enumerated.
- Authors:
-
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1256594
- Report Number(s):
- PPPL-5178
Journal ID: ISSN 0022-3778; applab; PII: S0022377815000756
- Grant/Contract Number:
- ACO2-09CH11466
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Plasma Physics
- Additional Journal Information:
- Journal Volume: 81; Journal Issue: 06; Journal ID: ISSN 0022-3778
- Publisher:
- Cambridge University Press
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; direct-interaction approximation; drift-wave turbulence; realizable; markovian closure; linear gyrokinetic equations; non-gaussian; statistics; weakly unstable plasma; magnetic-field; isotropic; turbulence; kinetic-theory; adiabatic modifications
Citation Formats
Krommes, John A. A tutorial introduction to the statistical theory of turbulent plasmas, a half-century after Kadomtsev’s Plasma Turbulence and the resonance-broadening theory of Dupree and Weinstock. United States: N. p., 2015.
Web. doi:10.1017/s0022377815000756.
Krommes, John A. A tutorial introduction to the statistical theory of turbulent plasmas, a half-century after Kadomtsev’s Plasma Turbulence and the resonance-broadening theory of Dupree and Weinstock. United States. https://doi.org/10.1017/s0022377815000756
Krommes, John A. Mon .
"A tutorial introduction to the statistical theory of turbulent plasmas, a half-century after Kadomtsev’s Plasma Turbulence and the resonance-broadening theory of Dupree and Weinstock". United States. https://doi.org/10.1017/s0022377815000756. https://www.osti.gov/servlets/purl/1256594.
@article{osti_1256594,
title = {A tutorial introduction to the statistical theory of turbulent plasmas, a half-century after Kadomtsev’s Plasma Turbulence and the resonance-broadening theory of Dupree and Weinstock},
author = {Krommes, John A.},
abstractNote = {In honour of the 50th anniversary of the influential review/monograph on plasma turbulence by B. B. Kadomtsev as well as the seminal works of T. H. Dupree and J. Weinstock on resonance-broadening theory, an introductory tutorial is given about some highlights of the statistical–dynamical description of turbulent plasmas and fluids, including the ideas of nonlinear incoherent noise, coherent damping, and self-consistent dielectric response. The statistical closure problem is introduced. Incoherent noise and coherent damping are illustrated with a solvable model of passive advection. Self-consistency introduces turbulent polarization effects that are described by the dielectric function${\mathcal{D}}$. Dupree’s method of using${\mathcal{D}}$to estimate the saturation level of turbulence is described; then it is explained why a more complete theory that includes nonlinear noise is required. The general theory is best formulated in terms of Dyson equations for the covariance$C$and an infinitesimal response function$R$, which subsumes${\mathcal{D}}$. An important example is the direct-interaction approximation (DIA). It is shown how to use Novikov’s theorem to develop an$\boldsymbol{x}$-space approach to the DIA that is complementary to the original$\boldsymbol{k}$-space approach of Kraichnan. A dielectric function is defined for arbitrary quadratically nonlinear systems, including the Navier–Stokes equation, and an algorithm for determining the form of${\mathcal{D}}$in the DIA is sketched. The independent insights of Kadomtsev and Kraichnan about the problem of the DIA with random Galilean invariance are described. The mixing-length formula for drift-wave saturation is discussed in the context of closures that include nonlinear noise (shielded by${\mathcal{D}}$). The role of$R$in the calculation of the symmetry-breaking (zonostrophic) instability of homogeneous turbulence to the generation of inhomogeneous mean flows is addressed. The second-order cumulant expansion and the stochastic structural stability theory are also discussed in that context. In conclusion, various historical research threads are mentioned and representative entry points to the literature are given. In addition, some outstanding conceptual issues are enumerated.},
doi = {10.1017/s0022377815000756},
journal = {Journal of Plasma Physics},
number = 06,
volume = 81,
place = {United States},
year = {Mon Sep 21 00:00:00 EDT 2015},
month = {Mon Sep 21 00:00:00 EDT 2015}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 13 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Anomalous scaling of a randomly advected passive scalar
journal, February 1994
- Kraichnan, Robert H.
- Physical Review Letters, Vol. 72, Issue 7
Dielectric Function and Diffusion of a Guiding-Center Plasma
journal, February 1974
- Taylor, J. B.
- Physical Review Letters, Vol. 32, Issue 5
Zonostrophic Instability
journal, May 2012
- Srinivasan, Kaushik; Young, W. R.
- Journal of the Atmospheric Sciences, Vol. 69, Issue 5
Stochasticity and the random phase approximation for three electron drift waves
journal, January 1982
- Terry, Paul
- Physics of Fluids, Vol. 25, Issue 3
Imbalanced Weak Magnetohydrodynamic Turbulence
journal, January 2003
- Lithwick, Yoram; Goldreich, Peter
- The Astrophysical Journal, Vol. 582, Issue 2
Energy transfer in an isotropic turbulent flow
journal, July 1962
- Ogura, Yoshimitsu
- Journal of Geophysical Research, Vol. 67, Issue 8
Non‐Gaussian statistics in isotropic turbulence
journal, November 1989
- Chen, Hudong; Herring, Jackson R.; Kerr, Robert M.
- Physics of Fluids A: Fluid Dynamics, Vol. 1, Issue 11
Non-perturbative models of intermittency in drift-wave turbulence: towards a probabilistic theory of anomalous transport
journal, August 2003
- Kim, Eun-jin; Diamond, P. H.; Malkov, M.
- Nuclear Fusion, Vol. 43, Issue 9
Analytical theories of turbulence
journal, April 1970
- Orszag, Steven A.
- Journal of Fluid Mechanics, Vol. 41, Issue 2
Approximations for Steady-State Isotropic Turbulence
journal, January 1964
- Kraichnan, Robert H.
- Physics of Fluids, Vol. 7, Issue 8
Optimal oscillation-center transformations
journal, August 1985
- Dewar, R. L.
- Physica D: Nonlinear Phenomena, Vol. 17, Issue 1
Saturation of Gyrokinetic Turbulence through Damped Eigenmodes
journal, March 2011
- Hatch, D. R.; Terry, P. W.; Jenko, F.
- Physical Review Letters, Vol. 106, Issue 11
Nonlinear Theory of Macroinstabilities and Enhanced Transport in Plasmas
journal, January 1971
- Weinstock, Jerome
- Physics of Fluids, Vol. 14, Issue 7
Boltzmann's Entropy and Time's Arrow
journal, September 1993
- Lebowitz, Joel L.
- Physics Today, Vol. 46, Issue 9
On the kinetic theory of stable and weakly unstable plasma. Part 1
journal, February 1968
- Rogister, A.; Oberman, C.
- Journal of Plasma Physics, Vol. 2, Issue 1
Gyrokinetic large eddy simulations
journal, July 2011
- Morel, P.; Navarro, A. Bañón; Albrecht-Marc, M.
- Physics of Plasmas, Vol. 18, Issue 7
The clump lifetime revisited: Exact calculation of the second-order structure function for a model of forced, dissipative turbulence
journal, March 1997
- Krommes, John A.
- Physics of Plasmas, Vol. 4, Issue 3
The random walk's guide to anomalous diffusion: a fractional dynamics approach
journal, December 2000
- Metzler, Ralf; Klafter, Joseph
- Physics Reports, Vol. 339, Issue 1
Dynamic procedure for filtered gyrokinetic simulations
journal, January 2012
- Morel, P.; Bañón Navarro, A.; Albrecht-Marc, M.
- Physics of Plasmas, Vol. 19, Issue 1
An almost-Markovian Galilean-invariant turbulence model
journal, June 1971
- Kraichnan, Robert H.
- Journal of Fluid Mechanics, Vol. 47, Issue 3
Electron heat transport from stochastic fields in gyrokinetic simulations
journal, May 2011
- Wang, E.; Nevins, W. M.; Candy, J.
- Physics of Plasmas, Vol. 18, Issue 5
Renormalized dielectric function for collisionless drift wave turbulence
journal, January 1978
- Dupree, Thomas H.; Tetreault, David J.
- Physics of Fluids, Vol. 21, Issue 3
Velocity-space resolution, entropy production, and upwind dissipation in Eulerian gyrokinetic simulations
journal, March 2006
- Candy, J.; Waltz, R. E.
- Physics of Plasmas, Vol. 13, Issue 3
Subcritical Excitation of Plasma Turbulence
journal, September 1996
- Itoh, Kimitaka; -I. Itoh, Sanae; Yagi, Masatoshi
- Journal of the Physical Society of Japan, Vol. 65, Issue 9
Generation and Stability of Zonal Flows in Ion-Temperature-Gradient Mode Turbulence
journal, December 2000
- Rogers, B. N.; Dorland, W.; Kotschenreuther, M.
- Physical Review Letters, Vol. 85, Issue 25
Scaling laws for plasma confinement
journal, October 1977
- Connor, J. W.; Taylor, J. B.
- Nuclear Fusion, Vol. 17, Issue 5
Lagrangian-History Closure Approximation for Turbulence
journal, January 1965
- Kraichnan, Robert H.
- Physics of Fluids, Vol. 8, Issue 4
Renormalized turbulence theory for the ion acoustic problem
journal, January 1979
- Horton, Wendell; Choi, Duk-In
- Physics Reports, Vol. 49, Issue 3
Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen
journal, January 1905
- Einstein, A.
- Annalen der Physik, Vol. 322, Issue 8
On the relation between ‘‘mixing length’’ and ‘‘direct interaction approximation’’ theories of turbulence
journal, January 1985
- Sudan, R. N.; Pfirsch, D.
- Physics of Fluids, Vol. 28, Issue 6
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
book, January 1983
- Guckenheimer, John; Holmes, Philip
- Applied Mathematical Sciences
Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria
journal, January 1982
- Frieman, E. A.
- Physics of Fluids, Vol. 25, Issue 3
Two-Dimensional Turbulence
journal, January 2012
- Boffetta, Guido; Ecke, Robert E.
- Annual Review of Fluid Mechanics, Vol. 44, Issue 1
Turbulent Plasmas in a Magnetic Field—A Statistical Theory
journal, January 1970
- Weinstock, Jerome
- Physics of Fluids, Vol. 13, Issue 9
Renormalized kinetic theory of nonequilibrium many-particle classical systems
journal, April 1979
- Rose, Harvey A.
- Journal of Statistical Physics, Vol. 20, Issue 4
On Variational Methods In the Physics of Plasma Waves
journal, January 2014
- Dodin, I. Y.
- Fusion Science and Technology, Vol. 65, Issue 1
Amplitude Limitation of a Collisional Drift Wave Instability
journal, January 1971
- Hinton, F. L.
- Physics of Fluids, Vol. 14, Issue 1
Direct-Interaction Approximation for Shear and Thermally Driven Turbulence
journal, January 1964
- Kraichnan, Robert H.
- Physics of Fluids, Vol. 7, Issue 7
XXVII. A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies
journal, September 1828
- Brown, Robert
- The Philosophical Magazine, Vol. 4, Issue 21
Closure theories with non‐Gaussian restarts for truncated two‐dimensional turbulence
journal, September 1994
- Frederiksen, J. S.; Davies, A. G.; Bell, R. C.
- Physics of Fluids, Vol. 6, Issue 9
Paul Langevin’s 1908 paper “On the Theory of Brownian Motion” [“Sur la théorie du mouvement brownien,” C. R. Acad. Sci. (Paris) 146 , 530–533 (1908)]
journal, November 1997
- Lemons, Don S.; Gythiel, Anthony
- American Journal of Physics, Vol. 65, Issue 11
Transition to Collisionless Ion-Temperature-Gradient-Driven Plasma Turbulence: A Dynamical Systems Approach
journal, June 2005
- Kolesnikov, R. A.; Krommes, J. A.
- Physical Review Letters, Vol. 94, Issue 23
Reformulation of quasi-linear theory
journal, August 1972
- Kaufman, Allan N.
- Journal of Plasma Physics, Vol. 8, Issue 1
Eulerian and Lagrangian renormalization in turbulence theory
journal, November 1977
- Kraichnan, Robert H.
- Journal of Fluid Mechanics, Vol. 83, Issue 2
Direct interaction approximation for Vlasov turbulence from the Kadomtsev weak coupling approximation
journal, January 1985
- DuBois, D. F.; Pesme, D.
- Physics of Fluids, Vol. 28, Issue 5
Up-down symmetry of the turbulent transport of toroidal angular momentum in tokamaks
journal, June 2011
- Parra, Felix I.; Barnes, Michael; Peeters, Arthur G.
- Physics of Plasmas, Vol. 18, Issue 6
Turbulence spectra from a tidal channel
journal, February 1962
- Grant, H. L.; Stewart, R. W.; Moilliet, A.
- Journal of Fluid Mechanics, Vol. 12, Issue 02
Intrinsic momentum transport in up–down asymmetric tokamaks
journal, July 2014
- Ball, Justin; Parra, Felix I.; Barnes, Michael
- Plasma Physics and Controlled Fusion, Vol. 56, Issue 9
Resistive drift-wave plasma turbulence and the realizable Markovian closure
journal, June 1995
- Hu, Genze; Krommes, John A.; Bowman, John C.
- Physics Letters A, Vol. 202, Issue 1
The fluctuation-dissipation theorem
journal, January 1966
- Kubo, R.
- Reports on Progress in Physics, Vol. 29, Issue 1
Beyond Brownian Motion
journal, February 1996
- Klafter, Joseph; Shlesinger, Michael F.; Zumofen, Gert
- Physics Today, Vol. 49, Issue 2
Fluid moment models for Landau damping with application to the ion-temperature-gradient instability
journal, June 1990
- Hammett, Gregory W.; Perkins, Francis W.
- Physical Review Letters, Vol. 64, Issue 25
Discrete particle noise in particle-in-cell simulations of plasma microturbulence
journal, December 2005
- Nevins, W. M.; Hammett, G. W.; Dimits, A. M.
- Physics of Plasmas, Vol. 12, Issue 12
Aspects of a renormalized weak plasma turbulence theory
journal, January 1979
- Krommes, John A.; Kleva, Robert G.
- Physics of Fluids, Vol. 22, Issue 11
Memory Effects in Irreversible Thermodynamics
journal, November 1961
- Zwanzig, Robert
- Physical Review, Vol. 124, Issue 4
S3T Stability of the Homogeneous State of Barotropic Beta-Plane Turbulence
journal, May 2015
- Bakas, Nikolaos A.; Constantinou, Navid C.; Ioannou, Petros J.
- Journal of the Atmospheric Sciences, Vol. 72, Issue 5
Gyrofluid turbulence models with kinetic effects
journal, March 1993
- Dorland, W.; Hammett, G. W.
- Physics of Fluids B: Plasma Physics, Vol. 5, Issue 3
Dielectric response in guiding center plasma
journal, January 1980
- Krommes, John A.; Similon, Philippe
- Physics of Fluids, Vol. 23, Issue 8
A dynamic subgrid‐scale eddy viscosity model
journal, July 1991
- Germano, Massimo; Piomelli, Ugo; Moin, Parviz
- Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 7
Critically Balanced Ion Temperature Gradient Turbulence in Fusion Plasmas
journal, September 2011
- Barnes, M.; Parra, F. I.; Schekochihin, A. A.
- Physical Review Letters, Vol. 107, Issue 11
Nonequilibrium gyrokinetic fluctuation theory and sampling noise in gyrokinetic particle-in-cell simulations
journal, September 2007
- Krommes, John A.
- Physics of Plasmas, Vol. 14, Issue 9
A Perturbation Theory for Strong Plasma Turbulence
journal, January 1966
- Dupree, T. H.
- Physics of Fluids, Vol. 9, Issue 9
Critical balance in magnetohydrodynamic, rotating and stratified turbulence: towards a universal scaling conjecture
journal, March 2011
- Nazarenko, Sergei V.; Schekochihin, Alexander A.
- Journal of Fluid Mechanics, Vol. 677
Diffusion of Plasma Across a Magnetic Field
journal, March 1961
- Taylor, J. B.
- Physical Review Letters, Vol. 6, Issue 6
On a self-sustaining process in shear flows
journal, April 1997
- Waleffe, Fabian
- Physics of Fluids, Vol. 9, Issue 4
Magnetohydrodynamic turbulence in a strongly magnetised plasma
journal, January 2010
- Sridhar, S.
- Astronomische Nachrichten, Vol. 331, Issue 1
Foundations of nonlinear gyrokinetic theory
journal, April 2007
- Brizard, A. J.; Hahm, T. S.
- Reviews of Modern Physics, Vol. 79, Issue 2
Theory of Phase Space Density Granulation in Plasma
journal, January 1972
- Dupree, Thomas H.
- Physics of Fluids, Vol. 15, Issue 2
The realizable Markovian closure and realizable test-field model. II. Application to anisotropic drift-wave dynamics
journal, November 1997
- Bowman, John C.; Krommes, John A.
- Physics of Plasmas, Vol. 4, Issue 11
Statistical properties of an ensemble of vortices interacting with a turbulent field
journal, November 2005
- Spineanu, F.; Vlad, M.
- Physics of Plasmas, Vol. 12, Issue 11
Rigorous upper bounds for transport due to passive advection by inhomogeneous turbulence
journal, August 1987
- Krommes, John A.; Smith, Ralph A.
- Annals of Physics, Vol. 177, Issue 2
An efficient non-Markovian theory of non-equilibrium dynamics
journal, January 1985
- Rose, Harvey A.
- Physica D: Nonlinear Phenomena, Vol. 14, Issue 2
A Theory of Baroclinic Turbulence
journal, August 2009
- Farrell, Brian F.; Ioannou, Petros J.
- Journal of the Atmospheric Sciences, Vol. 66, Issue 8
Statistical theory of resistive drift-wave turbulence and transport
journal, June 1997
- Hu, Genze; Krommes, John A.; Bowman, John C.
- Physics of Plasmas, Vol. 4, Issue 6
A Theory for the Forcing and Dissipation in Stochastic Turbulence Models
journal, December 2001
- DelSole, Timothy
- Journal of the Atmospheric Sciences, Vol. 58, Issue 24
Theory of two-point correlation function in a Vlasov plasma
journal, January 1981
- Boutros-Ghali, Teymour
- Physics of Fluids, Vol. 24, Issue 10
Onsager and the theory of hydrodynamic turbulence
journal, January 2006
- Eyink, Gregory L.; Sreenivasan, Katepalli R.
- Reviews of Modern Physics, Vol. 78, Issue 1
Role of subdominant stable modes in plasma microturbulence
journal, May 2011
- Hatch, D. R.; Terry, P. W.; Jenko, F.
- Physics of Plasmas, Vol. 18, Issue 5
Kolmogorov's Hypotheses and Eulerian Turbulence Theory
journal, January 1964
- Kraichnan, Robert H.
- Physics of Fluids, Vol. 7, Issue 11
Gyrokinetic turbulence: a nonlinear route to dissipation through phase space
journal, November 2008
- Schekochihin, A. A.; Cowley, S. C.; Dorland, W.
- Plasma Physics and Controlled Fusion, Vol. 50, Issue 12
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
book, January 2010
- Holmes, Philip; Lumley, John L.; Berkooz, Gal
Direct interaction approximation and plasma turbulence theory
journal, December 1978
- DuBois, D. F.; Espedal, M.
- Plasma Physics, Vol. 20, Issue 12
On the relationship between mixing length and strong turbulence estimates for transport due to drift turbulence
journal, January 2001
- Connor, J. W.; Pogutse, O. P.
- Plasma Physics and Controlled Fusion, Vol. 43, Issue 2
A proposed modification of the Germano subgrid‐scale closure method
journal, March 1992
- Lilly, D. K.
- Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 3
Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows
journal, October 2013
- Abel, I. G.; Plunk, G. G.; Wang, E.
- Reports on Progress in Physics, Vol. 76, Issue 11
The direct-interaction approximation and statistically steady states of three nonlinearly coupled modes
journal, January 1982
- Krommes, John A.
- Physics of Fluids, Vol. 25, Issue 8
Interactions of disparate scales in drift-wave turbulence
journal, December 2000
- Krommes, John A.; Kim, Chang-Bae
- Physical Review E, Vol. 62, Issue 6
The realizable Markovian closure. I. General theory, with application to three‐wave dynamics
journal, October 1993
- Bowman, John C.; Krommes, John A.; Ottaviani, Maurizio
- Physics of Fluids B: Plasma Physics, Vol. 5, Issue 10
Size Scaling of Turbulent Transport in Magnetically Confined Plasmas
journal, April 2002
- Lin, Z.; Ethier, S.; Hahm, T. S.
- Physical Review Letters, Vol. 88, Issue 19
The 1976 Oppenheimer lectures: Critical problems in plasma astrophysics. I. Turbulence and nonlinear waves
journal, January 1979
- Sagdeev, Roald Z.
- Reviews of Modern Physics, Vol. 51, Issue 1
Dielectric response and thermal fluctuations in gyrokinetic plasma
journal, April 1993
- Krommes, John A.
- Physics of Fluids B: Plasma Physics, Vol. 5, Issue 4
Transport, Collective Motion, and Brownian Motion
journal, March 1965
- Mori, Hazime
- Progress of Theoretical Physics, Vol. 33, Issue 3
Comment on ‘‘Adiabatic modifications to plasma turbulence theories’’
journal, January 1981
- Weinstock, J.
- Physics of Fluids, Vol. 24, Issue 9
Statistical Continuum Theories
journal, October 1968
- Beran, Mark J.; Pytte, Agnar
- American Journal of Physics, Vol. 36, Issue 10
Comparisons and physics basis of tokamak transport models and turbulence simulations
journal, March 2000
- Dimits, A. M.; Bateman, G.; Beer, M. A.
- Physics of Plasmas, Vol. 7, Issue 3
Convergents to turbulence functions
journal, March 1970
- Kraichnan, Robert H.
- Journal of Fluid Mechanics, Vol. 41, Issue 1
Self-Consistency Effects in Quasilinear Theory: A Model for Turbulent Trapping
journal, July 1984
- Laval, G.; Pesme, D.
- Physical Review Letters, Vol. 53, Issue 3
Particles and fields in fluid turbulence
journal, November 2001
- Falkovich, G.; Gawȩdzki, K.; Vergassola, M.
- Reviews of Modern Physics, Vol. 73, Issue 4
Suppression of turbulence and transport by sheared flow
journal, January 2000
- Terry, P. W.
- Reviews of Modern Physics, Vol. 72, Issue 1
Spherical model for turbulence
journal, February 1993
- Mou, Chung-yu; Weichman, Peter B.
- Physical Review Letters, Vol. 70, Issue 8
Generation of zonal flows through symmetry breaking of statistical homogeneity
journal, March 2014
- Parker, Jeffrey B.; Krommes, John A.
- New Journal of Physics, Vol. 16, Issue 3
Nonlinear gyrokinetic equations
journal, January 1983
- Dubin, Daniel H. E.
- Physics of Fluids, Vol. 26, Issue 12
On the nature of turbulence
journal, September 1971
- Ruelle, David; Takens, Floris
- Communications in Mathematical Physics, Vol. 20, Issue 3
General Circulation Experiments with the Primitive Equations: i. the Basic Experiment*
journal, March 1963
- Smagorinsky, J.
- Monthly Weather Review, Vol. 91, Issue 3
Mapping closure for probability distribution function in low frequency magnetized plasma turbulence
journal, May 1995
- Das, Amita; Kaw, Predhiman
- Physics of Plasmas, Vol. 2, Issue 5
Nonlinear Theory of Drift-Wave Turbulence and Enhanced Diffusion
journal, January 1967
- Dupree, T. H.
- Physics of Fluids, Vol. 10, Issue 5
Statistical Dynamics of Classical Systems
journal, July 1973
- Martin, P. C.; Siggia, E. D.; Rose, H. A.
- Physical Review A, Vol. 8, Issue 1
Stochastic differential equations
journal, March 1976
- Van Kampen, N. G.
- Physics Reports, Vol. 24, Issue 3
Gyrokinetic approach in particle simulation
journal, January 1983
- Lee, W. W.
- Physics of Fluids, Vol. 26, Issue 2
The role of dissipation in the theory and simulations of homogeneous plasma turbulence, and resolution of the entropy paradox
journal, October 1994
- Krommes, John A.; Hu, Genze
- Physics of Plasmas, Vol. 1, Issue 10
Kinetic simulation of steady states of ion temperature gradient driven turbulence with weak collisionality
journal, April 2004
- Watanabe, T. -H.; Sugama, H.
- Physics of Plasmas, Vol. 11, Issue 4
In memory of Boris Borisovich Kadomtsev
journal, November 1998
- Velikhov, E. P.; Ginzburg, Vitalii L.; Gaponov-Grekhov, Andrei V.
- Physics-Uspekhi, Vol. 41, Issue 11
Deterministic Nonperiodic Flow
journal, March 1963
- Lorenz, Edward N.
- Journal of the Atmospheric Sciences, Vol. 20, Issue 2
On the kinetic theory of stable and weakly unstable plasma. Part 2
journal, February 1969
- Rogister, A.; Oberman, C.
- Journal of Plasma Physics, Vol. 3, Issue 1
Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades in Magnetized Weakly Collisional Plasmas
journal, May 2009
- Schekochihin, A. A.; Cowley, S. C.; Dorland, W.
- The Astrophysical Journal Supplement Series, Vol. 182, Issue 1
On the Theory of the Brownian Motion II
journal, April 1945
- Wang, Ming Chen; Uhlenbeck, G. E.
- Reviews of Modern Physics, Vol. 17, Issue 2-3
Renormalised canonical perturbation theory for stochastic propagators
journal, December 1976
- Dewar, R. L.
- Journal of Physics A: Mathematical and General, Vol. 9, Issue 12
Nonlinear instabilities driven by coherent phase-space structures
journal, March 2013
- Lesur, M.; Diamond, P. H.
- Physical Review E, Vol. 87, Issue 3
Planetary Atmospheres as Nonequilibrium Condensed Matter
journal, March 2012
- Marston, J. B.
- Annual Review of Condensed Matter Physics, Vol. 3, Issue 1
Formulation of a Statistical Theory of Strong Plasma Turbulence
journal, January 1969
- Weinstock, Jerome
- Physics of Fluids, Vol. 12, Issue 5
Application of the Novikov-Furutsu theorem to the random acceleration problem
journal, April 1978
- Cook, I.
- Plasma Physics, Vol. 20, Issue 4
Nondimensional transport scaling in the Tokamak Fusion Test Reactor: Is tokamak transport Bohm or gyro‐Bohm?
journal, February 1993
- Perkins, F. W.; Barnes, Cris W.; Johnson, D. W.
- Physics of Fluids B: Plasma Physics, Vol. 5, Issue 2
Statistical Simulation of the Magnetorotational Dynamo
journal, February 2015
- Squire, J.; Bhattacharjee, A.
- Physical Review Letters, Vol. 114, Issue 8
7. Bericht über Untersuchungen zur ausgebildeten Turbulenz
journal, January 1925
- Prandtl, L.
- ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 5, Issue 2
Bob Dewar and turbulence theory: lessons in creativity and courage
journal, December 2011
- Krommes, John A.
- Plasma Physics and Controlled Fusion, Vol. 54, Issue 1
Analytical Descriptions of Plasma Turbulence
book, November 2006
- Krommes, John A.
- Lecture Notes on Turbulence and Coherent Structures in Fluids, Plasmas and Nonlinear Media
Equilibrium fluctuation energy of gyrokinetic plasma
journal, January 1986
- Krommes, John A.; Lee, W. W.; Oberman, C.
- Physics of Fluids, Vol. 29, Issue 8
Geometric view on noneikonal waves
journal, April 2014
- Dodin, I. Y.
- Physics Letters A, Vol. 378, Issue 22-23
Bifurcation theory of the transition to collisionless ion-temperature-gradient-driven plasma turbulence
journal, December 2005
- Kolesnikov, R. A.; Krommes, J. A.
- Physics of Plasmas, Vol. 12, Issue 12
Turbulence theories and modelling of fluids and plasmas
journal, February 2001
- Yoshizawa, Akira; Itoh, Sanae-I; Itoh, Kimitaka
- Plasma Physics and Controlled Fusion, Vol. 43, Issue 3
Astrophysical Fluid Dynamics via Direct Statistical Simulation
journal, January 2011
- Tobias, S. M.; Dagon, K.; Marston, J. B.
- The Astrophysical Journal, Vol. 727, Issue 2
The Gyrokinetic Description of Microturbulence in Magnetized Plasmas
journal, January 2012
- Krommes, John A.
- Annual Review of Fluid Mechanics, Vol. 44, Issue 1
Field theoretical techniques in statistical fluid dynamics: With application to nonlinear wave dynamics
journal, April 1982
- Carnevale, George F.; Martin, Paul C.
- Geophysical & Astrophysical Fluid Dynamics, Vol. 20, Issue 1-2
Energy Transfer in a Normally Distributed and Isotropic Turbulent Velocity Field in Two Dimensions
journal, January 1962
- Ogura, Yoshimitsu
- Physics of Fluids, Vol. 5, Issue 4
Turbulent Diffusion, Particle Orbits, and Field Fluctuations in a Plasma in a Magnetic Field
journal, January 1968
- Weinstock, Jerome
- Physics of Fluids, Vol. 11, Issue 9
Magnetic fluctuations can contribute to plasma transport, ‘‘self-consistency constraints’’ notwithstanding
journal, January 1988
- Krommes, John A.; Kim, Chang-Bae
- Physics of Fluids, Vol. 31, Issue 4
Transition in shear flows. Nonlinear normality versus non‐normal linearity
journal, December 1995
- Waleffe, Fabian
- Physics of Fluids, Vol. 7, Issue 12
Fractional diffusion in plasma turbulence
journal, August 2004
- del-Castillo-Negrete, D.; Carreras, B. A.; Lynch, V. E.
- Physics of Plasmas, Vol. 11, Issue 8
Direct Statistical Simulation of Out-of-Equilibrium Jets
journal, March 2013
- Tobias, S. M.; Marston, J. B.
- Physical Review Letters, Vol. 110, Issue 10
The mechanism of self‐sustainment in collisional drift wave turbulence
journal, August 1992
- Scott, Bruce D.
- Physics of Fluids B: Plasma Physics, Vol. 4, Issue 8
Numerical study of drift wave turbulence with simple models for wave–wave nonlinear coupling
journal, January 1983
- Waltz, R. E.
- Physics of Fluids, Vol. 26, Issue 1
Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence
journal, January 1995
- Goldreich, P.; Sridhar, S.
- The Astrophysical Journal, Vol. 438
Fundamental statistical descriptions of plasma turbulence in magnetic fields
journal, April 2002
- Krommes, John A.
- Physics Reports, Vol. 360, Issue 1-4
Dynamics of Nonlinear Stochastic Systems
journal, January 1961
- Kraichnan, Robert H.
- Journal of Mathematical Physics, Vol. 2, Issue 1
Contributions to Non-Equilibrium Thermodynamics. I. Theory of Hydrodynamical Fluctuations
journal, January 1970
- Fox, Ronald Forrest
- Physics of Fluids, Vol. 13, Issue 8
Random shearing by zonal flows and transport reduction
journal, December 2004
- Kim, Eun-jin; Diamond, P. H.
- Physics of Plasmas, Vol. 11, Issue 12
Plasma Edge Turbulence
journal, February 1983
- Hasegawa, Akira; Wakatani, Masahiro
- Physical Review Letters, Vol. 50, Issue 9
A review of zonal flow experiments
journal, December 2008
- Fujisawa, Akihide
- Nuclear Fusion, Vol. 49, Issue 1
Adiabatic modifications to plasma turbulence theories
journal, January 1978
- Catto, P. J.
- Physics of Fluids, Vol. 21, Issue 1
On the Stability of Internal Baroclinic Jets in a Rotating Atmosphere
journal, March 1962
- Charney, J. G.; Stern, M. E.
- Journal of the Atmospheric Sciences, Vol. 19, Issue 2
Pseudo-three-dimensional turbulence in magnetized nonuniform plasma
journal, January 1978
- Hasegawa, Akira; Mima, Kunioki
- Physics of Fluids, Vol. 21, Issue 1
Gyrokinetic simulations of turbulent transport
journal, March 2010
- Garbet, X.; Idomura, Y.; Villard, L.
- Nuclear Fusion, Vol. 50, Issue 4
Zonal flow as pattern formation
journal, October 2013
- Parker, Jeffrey B.; Krommes, John A.
- Physics of Plasmas, Vol. 20, Issue 10
Modulational instability of Rossby and drift waves and generation of zonal jets
journal, May 2010
- Connaughton, Colm P.; Nadiga, Balasubramanya T.; Nazarenko, Sergey V.
- Journal of Fluid Mechanics, Vol. 654
Suppression of an instability by the introduction of external turbulence
journal, January 1979
- Hershcovitch, Ady; Politzer, Peter A.
- Physics of Fluids, Vol. 22, Issue 2
Fluid models of phase mixing, Landau damping, and nonlinear gyrokinetic dynamics
journal, March 1992
- Hammett, G. W.; Dorland, W.; Perkins, F. W.
- Physics of Fluids B: Plasma Physics, Vol. 4, Issue 7
Signature of a universal statistical description for drift-wave plasma turbulence
journal, November 2010
- Anderson, Johan; Xanthopoulos, Pavlos
- Physics of Plasmas, Vol. 17, Issue 11
Model Equations for Strong Turbulence in a Vlasov Plasma
journal, January 1967
- Orszag, Steven A.
- Physics of Fluids, Vol. 10, Issue 8
Nonlinear Self-Sustained Drift-Wave Turbulence
journal, December 1995
- Drake, J. F.; Zeiler, A.; Biskamp, D.
- Physical Review Letters, Vol. 75, Issue 23
Zonal flows in plasma—a review
journal, April 2005
- Diamond, P. H.; Itoh, S-I; Itoh, K.
- Plasma Physics and Controlled Fusion, Vol. 47, Issue 5
Oscillation center quasilinear theory
journal, January 1973
- Dewar, R. L.
- Physics of Fluids, Vol. 16, Issue 7
Verification of Gyrokinetic Particle Simulation of Device Size Scaling of Turbulent Transport
journal, December 2012
- Ethier, S.; Hahm, T. S.; Tang, W. M.
- Plasma Science and Technology, Vol. 14, Issue 12
Parastochastics
journal, February 1970
- Frisch, U.; Bourret, R.
- Journal of Mathematical Physics, Vol. 11, Issue 2
Developments in the gyrofluid approach to Tokamak turbulence simulations
journal, August 1993
- Hammett, G. W.; Beer, M. A.; Dorland, W.
- Plasma Physics and Controlled Fusion, Vol. 35, Issue 8
Invariance principles and plasma confinement
journal, June 1988
- Connor, J. W.
- Plasma Physics and Controlled Fusion, Vol. 30, Issue 6
Comments on ‘‘Adiabatic modifications to plasma turbulence theory’’
journal, January 1981
- Krommes, John A.
- Physics of Fluids, Vol. 24, Issue 9
Generalized Cumulant Expansion Method
journal, July 1962
- Kubo, Ryogo
- Journal of the Physical Society of Japan, Vol. 17, Issue 7
A consequence of the zero-fourth-cumulant approximation in the decay of isotropic turbulence
journal, May 1963
- Ogura, Yoshimitsu
- Journal of Fluid Mechanics, Vol. 16, Issue 01
The structure of isotropic turbulence at very high Reynolds numbers
journal, May 1959
- Kraichnan, Robert H.
- Journal of Fluid Mechanics, Vol. 5, Issue 04
The generalized Balescu-Lenard collision Operator
journal, April 1988
- Mynick, Harry E.
- Journal of Plasma Physics, Vol. 39, Issue 2
On the nature of turbulence
journal, December 1971
- Ruelle, D.; Takens, F.
- Communications in Mathematical Physics, Vol. 23, Issue 4
Renormalized turbulence theory for the ion acoustic problem
journal, January 1979
- Horton, Wendell; Choi, Duk-In
- Physics Reports, Vol. 49, Issue 3
Turbulent Diffusion, Particle Orbits, and Field Fluctuations in a Plasma in a Magnetic Field
journal, January 1968
- Weinstock, Jerome
- Physics of Fluids, Vol. 11, Issue 9
Turbulent Plasmas in a Magnetic Field—A Statistical Theory
journal, January 1970
- Weinstock, Jerome
- Physics of Fluids, Vol. 13, Issue 9
Pseudo-three-dimensional turbulence in magnetized nonuniform plasma
journal, January 1978
- Hasegawa, Akira; Mima, Kunioki
- Physics of Fluids, Vol. 21, Issue 1
Renormalized dielectric function for collisionless drift wave turbulence
journal, January 1978
- Dupree, Thomas H.; Tetreault, David J.
- Physics of Fluids, Vol. 21, Issue 3
Aspects of a renormalized weak plasma turbulence theory
journal, January 1979
- Krommes, John A.; Kleva, Robert G.
- Physics of Fluids, Vol. 22, Issue 11
Suppression of an instability by the introduction of external turbulence
journal, January 1979
- Hershcovitch, Ady; Politzer, Peter A.
- Physics of Fluids, Vol. 22, Issue 2
Theory of two-point correlation function in a Vlasov plasma
journal, January 1981
- Boutros-Ghali, Teymour
- Physics of Fluids, Vol. 24, Issue 10
Direct interaction approximation for Vlasov turbulence from the Kadomtsev weak coupling approximation
journal, January 1985
- DuBois, D. F.; Pesme, D.
- Physics of Fluids, Vol. 28, Issue 5
Equilibrium fluctuation energy of gyrokinetic plasma
journal, January 1986
- Krommes, John A.; Lee, W. W.; Oberman, C.
- Physics of Fluids, Vol. 29, Issue 8
Transition in shear flows. Nonlinear normality versus non‐normal linearity
journal, December 1995
- Waleffe, Fabian
- Physics of Fluids, Vol. 7, Issue 12
On a self-sustaining process in shear flows
journal, April 1997
- Waleffe, Fabian
- Physics of Fluids, Vol. 9, Issue 4
Mapping closure for probability distribution function in low frequency magnetized plasma turbulence
journal, May 1995
- Das, Amita; Kaw, Predhiman
- Physics of Plasmas, Vol. 2, Issue 5
Statistical theory of resistive drift-wave turbulence and transport
journal, June 1997
- Hu, Genze; Krommes, John A.; Bowman, John C.
- Physics of Plasmas, Vol. 4, Issue 6
Field theoretical techniques in statistical fluid dynamics: With application to nonlinear wave dynamics
journal, April 1982
- Carnevale, George F.; Martin, Paul C.
- Geophysical & Astrophysical Fluid Dynamics, Vol. 20, Issue 1-2
Imbalanced Weak Magnetohydrodynamic Turbulence
journal, January 2003
- Lithwick, Yoram; Goldreich, Peter
- The Astrophysical Journal, Vol. 582, Issue 2
Gyrokinetic simulations of turbulent transport
journal, March 2010
- Garbet, X.; Idomura, Y.; Villard, L.
- Nuclear Fusion, Vol. 50, Issue 4
Direct interaction approximation and plasma turbulence theory
journal, December 1978
- DuBois, D. F.; Espedal, M.
- Plasma Physics, Vol. 20, Issue 12
Gyrokinetic turbulence: a nonlinear route to dissipation through phase space
journal, November 2008
- Schekochihin, A. A.; Cowley, S. C.; Dorland, W.
- Plasma Physics and Controlled Fusion, Vol. 50, Issue 12
Generation of zonal flows through symmetry breaking of statistical homogeneity
journal, March 2014
- Parker, Jeffrey B.; Krommes, John A.
- New Journal of Physics, Vol. 16, Issue 3
Non-Gaussian statistics, classical field theory, and realizable Langevin models
journal, May 1996
- Krommes, John A.
- Physical Review E, Vol. 53, Issue 5
Experimental Signatures of Critically Balanced Turbulence in MAST
journal, April 2013
- Ghim, Y. -c.; Schekochihin, A. A.; Field, A. R.
- Physical Review Letters, Vol. 110, Issue 14
Two-Dimensional Turbulence
journal, January 2012
- Boffetta, Guido; Ecke, Robert E.
- Annual Review of Fluid Mechanics, Vol. 44, Issue 1
Non-diffusive transport in plasma turbulence: a fractional diffusion approach
text, January 2004
- del-Castillo-Negrete, D.; Carreras, B. A.; Lynch, V. E.
- arXiv
Statistical properties of an ensemble of vortices interacting with a turbulent field
text, January 2005
- Spineanu, F.; Vlad, M.
- arXiv
Zonal flow generation by modulational instability
text, January 2006
- Dewar, R. L.; Abdullatif, R. F.
- arXiv
Works referencing / citing this record:
Projection-operator methods for classical transport in magnetized plasmas. Part 2. Nonlinear response and the Burnett equations
journal, November 2018
- Krommes, John A.
- Journal of Plasma Physics, Vol. 84, Issue 6
Extensions of the Novikov–Furutsu theorem, obtained by using Volterra functional calculus
journal, August 2019
- Athanassoulis, Gerassimos A.; Mamis, Konstantinos I.
- Physica Scripta, Vol. 94, Issue 11
S3T stability of the homogeneous state of barotropic beta-plane turbulence
text, January 2014
- Bakas, Nikolaos A.; Constantinou, Navid C.; Ioannou, Petros J.
- arXiv
Statistical State Dynamics: a new perspective on turbulence in shear flow
text, January 2014
- Farrell, Brian F.; Ioannou, Petros J.
- arXiv
Emergence of non-zonal coherent structures
preprint, January 2015
- Bakas, Nikolaos A.; Ioannou, Petros J.
- arXiv