Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades
Abstract
We formulate a coarse-graining approach to the dynamics of magnetohydrodynamic (MHD) fluids at a continuum of length-scales. In this methodology, effective equations are derived for the observable velocity and magnetic fields spatially-averaged at an arbitrary scale of resolution. The microscopic equations for the bare velocity and magnetic fields are renormalized by coarse-graining to yield macroscopic effective equations that contain both a subscale stress and a subscale electromotive force (EMF) generated by nonlinear interaction of eliminated fields and plasma motions. At large coarse-graining length-scales, the direct dissipation of invariants by microscopic mechanisms (such as molecular viscosity and Spitzer resistivity) is shown to be negligible. The balance at large scales is dominated instead by the subscale nonlinear terms, which can transfer invariants across scales, and are interpreted in terms of work concepts for energy and in terms of topological flux-linkage for the two helicities. An important application of this approach is to MHD turbulence, where the coarse-graining length ℓ lies in the inertial cascade range. We show that in the case of sufficiently rough velocity and/or magnetic fields, the nonlinear inter-scale transfer need not vanish and can persist to arbitrarily small scales. Although closed expressions are not available for subscale stress andmore »
- Authors:
- Publication Date:
- Research Org.:
- Univ. of Rochester, NY (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA), Office of Defense Nuclear Security; USDOE Office of Science (SC), Fusion Energy Sciences (FES); USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1437700
- Alternate Identifier(s):
- OSTI ID: 1356076; OSTI ID: 1358358
- Grant/Contract Number:
- NA0001944; 20150568ER; SC0014318
- Resource Type:
- Published Article
- Journal Name:
- New Journal of Physics
- Additional Journal Information:
- Journal Name: New Journal of Physics Journal Volume: 19 Journal Issue: 2; Journal ID: ISSN 1367-2630
- Publisher:
- IOP Publishing
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 22 GENERAL STUDIES OF NUCLEAR REACTORS; energy-dissipation rate; large-eddy simulation; free magnetic-fields; isotropic turbulence; hydromagnetic turbulence; ideal hydrodynamics; inverse cascade; inertial-range; helicity; flows; magnetohydrodynamics; turbulence; coarse-graining; cascade
Citation Formats
Aluie, Hussein. Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades. United Kingdom: N. p., 2017.
Web. doi:10.1088/1367-2630/aa5d2f.
Aluie, Hussein. Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades. United Kingdom. https://doi.org/10.1088/1367-2630/aa5d2f
Aluie, Hussein. Wed .
"Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades". United Kingdom. https://doi.org/10.1088/1367-2630/aa5d2f.
@article{osti_1437700,
title = {Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades},
author = {Aluie, Hussein},
abstractNote = {We formulate a coarse-graining approach to the dynamics of magnetohydrodynamic (MHD) fluids at a continuum of length-scales. In this methodology, effective equations are derived for the observable velocity and magnetic fields spatially-averaged at an arbitrary scale of resolution. The microscopic equations for the bare velocity and magnetic fields are renormalized by coarse-graining to yield macroscopic effective equations that contain both a subscale stress and a subscale electromotive force (EMF) generated by nonlinear interaction of eliminated fields and plasma motions. At large coarse-graining length-scales, the direct dissipation of invariants by microscopic mechanisms (such as molecular viscosity and Spitzer resistivity) is shown to be negligible. The balance at large scales is dominated instead by the subscale nonlinear terms, which can transfer invariants across scales, and are interpreted in terms of work concepts for energy and in terms of topological flux-linkage for the two helicities. An important application of this approach is to MHD turbulence, where the coarse-graining length ℓ lies in the inertial cascade range. We show that in the case of sufficiently rough velocity and/or magnetic fields, the nonlinear inter-scale transfer need not vanish and can persist to arbitrarily small scales. Although closed expressions are not available for subscale stress and subscale EMF, we derive rigorous upper bounds on the effective dissipation they produce in terms of scaling exponents of the velocity and magnetic fields. These bounds provide exact constraints on phenomenological theories of MHD turbulence in order to allow the nonlinear cascade of energy and cross-helicity. On the other hand, we show that the forward cascade of magnetic helicity to asymptotically small scales is impossible unless 3rd-order moments of either velocity or magnetic field become infinite.},
doi = {10.1088/1367-2630/aa5d2f},
journal = {New Journal of Physics},
number = 2,
volume = 19,
place = {United Kingdom},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}
https://doi.org/10.1088/1367-2630/aa5d2f
Web of Science
Works referenced in this record:
Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining
journal, November 2009
- Eyink, Gregory L.; Aluie, Hussein
- Physics of Fluids, Vol. 21, Issue 11
Sub-Kolmogorov-scale fluctuations in fluid turbulence
journal, October 2007
- Schumacher, J.
- Europhysics Letters (EPL), Vol. 80, Issue 5
Imprint of Large-Scale Flows on Turbulence
journal, December 2005
- Alexakis, A.; Mininni, P. D.; Pouquet, A.
- Physical Review Letters, Vol. 95, Issue 26
Onset and decay of two-dimensional magnetohydrodynamic turbulence with velocity–magnetic field correlation
journal, January 1986
- Grappin, R.
- Physics of Fluids, Vol. 29, Issue 8
Energy dissipation without viscosity in ideal hydrodynamics I. Fourier analysis and local energy transfer
journal, November 1994
- Eyink, Gregory L.
- Physica D: Nonlinear Phenomena, Vol. 78, Issue 3-4
Field and Charge Measurements in Quantum Electrodynamics
journal, June 1950
- Bohr, N.; Rosenfeld, L.
- Physical Review, Vol. 78, Issue 6
Onsager's conjecture on the energy conservation for solutions of Euler's equation
journal, October 1994
- Constantin, Peter; Weinan, E.; Titi, Edriss S.
- Communications in Mathematical Physics, Vol. 165, Issue 1
Dynamic gradient-diffusion subgrid models for incompressible magnetohydrodynamic turbulence
journal, March 2002
- Müller, Wolf-Christian; Carati, Daniele
- Physics of Plasmas, Vol. 9, Issue 3
A Derivation of the Macroscopic Maxwell Equations
journal, October 1970
- Russakoff, G.
- American Journal of Physics, Vol. 38, Issue 10
Measuring intense rotation and dissipation in turbulent flows
journal, January 2003
- Zeff, Benjamin W.; Lanterman, Daniel D.; McAllister, Ryan
- Nature, Vol. 421, Issue 6919
Scale Locality of Magnetohydrodynamic Turbulence
journal, February 2010
- Aluie, Hussein; Eyink, Gregory L.
- Physical Review Letters, Vol. 104, Issue 8
On the Dynamical Theory of Incompressible Viscous Fluids and the Determination of the Criterion
journal, January 1895
- Reynolds, O.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 186, Issue 0
Measurements of the turbulent energy dissipation rate
journal, March 2002
- Pearson, B. R.; Krogstad, P. -Å.; van de Water, W.
- Physics of Fluids, Vol. 14, Issue 3
Measurements of Photospheric and Chromospheric Magnetic Fields
journal, December 2015
- Lagg, Andreas; Lites, Bruce; Harvey, Jack
- Space Science Reviews, Vol. 210, Issue 1-4
Large-scale flow effects, energy transfer, and self-similarity on turbulence
journal, July 2006
- Mininni, P. D.; Alexakis, A.; Pouquet, A.
- Physical Review E, Vol. 74, Issue 1
Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence
journal, January 1995
- Goldreich, P.; Sridhar, S.
- The Astrophysical Journal, Vol. 438
Atmospheric Diffusion Shown on a Distance-Neighbour Graph
journal, April 1926
- Richardson, L. F.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 110, Issue 756
Onsager and the theory of hydrodynamic turbulence
journal, January 2006
- Eyink, Gregory L.; Sreenivasan, Katepalli R.
- Reviews of Modern Physics, Vol. 78, Issue 1
Flux-freezing breakdown in high-conductivity magnetohydrodynamic turbulence
journal, May 2013
- Eyink, Gregory; Vishniac, Ethan; Lalescu, Cristian
- Nature, Vol. 497, Issue 7450
Scale decomposition in compressible turbulence
journal, March 2013
- Aluie, Hussein
- Physica D: Nonlinear Phenomena, Vol. 247, Issue 1
A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers
journal, April 1970
- Deardorff, James W.
- Journal of Fluid Mechanics, Vol. 41, Issue 2
Remarks on Singularities, Dimension and Energy Dissipation for Ideal Hydrodynamics and MHD
journal, April 1997
- Caflisch, Russel E.; Klapper, Isaac; Steele, Gregory
- Communications in Mathematical Physics, Vol. 184, Issue 2
Small-Scale Structures in Three-Dimensional Magnetohydrodynamic Turbulence
journal, December 2006
- Mininni, P. D.; Pouquet, A. G.; Montgomery, D. C.
- Physical Review Letters, Vol. 97, Issue 24
Large eddy simulation of decaying magnetohydrodynamic turbulence with dynamic subgrid-modeling
journal, July 2001
- Agullo, O.; Müller, W. -C.; Knaepen, B.
- Physics of Plasmas, Vol. 8, Issue 7
Locality of turbulent cascades
journal, July 2005
- Eyink, Gregory L.
- Physica D: Nonlinear Phenomena, Vol. 207, Issue 1-2
Recent progress in astrophysical MHD
journal, July 2007
- Stone, James M.; Gardiner, Thomas A.
- Computer Physics Communications, Vol. 177, Issue 1-2
Kinematic α-effect in isotropic turbulence simulations
journal, March 2008
- Sur, Sharanya; Brandenburg, Axel; Subramanian, Kandaswamy
- Monthly Notices of the Royal Astronomical Society: Letters, Vol. 385, Issue 1
Forced turbulence in large-eddy simulation of compressible magnetohydrodynamic turbulence
journal, October 2010
- Chernyshov, A. A.; Karelsky, K. V.; Petrosyan, A. S.
- Physics of Plasmas, Vol. 17, Issue 10
Energy transfers in forced MHD turbulence
journal, January 2006
- Carati, Daniele; Debliquy, Olivier; Knaepen, Bernard
- Journal of Turbulence, Vol. 7
Turbulent cascades, transfer, and scale interactions in magnetohydrodynamics
journal, August 2007
- Alexakis, A.; Mininni, P. D.; Pouquet, A.
- New Journal of Physics, Vol. 9, Issue 8
The topological properties of magnetic helicity
journal, October 1984
- Berger, Mitchell A.; Field, George B.
- Journal of Fluid Mechanics, Vol. 147, Issue -1
Solar magnetic fields as revealed by Stokes polarimetry
journal, September 2013
- Stenflo, J. O.
- The Astronomy and Astrophysics Review, Vol. 21, Issue 1
Turbulence noise
journal, June 1996
- Eyink, Gregory L.
- Journal of Statistical Physics, Vol. 83, Issue 5-6
Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence
journal, March 1990
- Domaradzki, J. Andrzej; Rogallo, Robert S.
- Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 3
MHD simulations and astrophysical applications
journal, January 2005
- Gómez, Daniel O.; Mininni, Pablo D.; Dmitruk, Pablo
- Advances in Space Research, Vol. 35, Issue 5
On Hydromagnetic Equilibrium
journal, September 1958
- Woltjer, L.
- Proceedings of the National Academy of Sciences, Vol. 44, Issue 9
Grid-Based Hydrodynamics in Astrophysical Fluid Flows
journal, August 2015
- Teyssier, Romain
- Annual Review of Astronomy and Astrophysics, Vol. 53, Issue 1
Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics
journal, July 2015
- Miesch, Mark; Matthaeus, William; Brandenburg, Axel
- Space Science Reviews, Vol. 194, Issue 1-4
Bihelical magnetic relaxation and large scale magnetic field growth
journal, January 2005
- Blackman, Eric G.
- Physics of Plasmas, Vol. 12, Issue 1
General Relativistic Hydrodynamic Simulation of Accretion flow from a Stellar Tidal Disruption
journal, May 2015
- Shiokawa, Hotaka; Krolik, Julian H.; Cheng, Roseanne M.
- The Astrophysical Journal, Vol. 804, Issue 2
Turbulence, Magnetism, and Shear in Stellar Interiors
journal, January 2009
- Miesch, Mark S.; Toomre, Juri
- Annual Review of Fluid Mechanics, Vol. 41, Issue 1
Dynamics of decaying two‐dimensional magnetohydrodynamic turbulence
journal, October 1989
- Biskamp, D.; Welter, H.
- Physics of Fluids B: Plasma Physics, Vol. 1, Issue 10
Locality properties of the energy flux in turbulence
journal, February 2009
- Domaradzki, J. Andrzej; Teaca, Bogdan; Carati, Daniele
- Physics of Fluids, Vol. 21, Issue 2
A substantial amount of hidden magnetic energy in the quiet Sun
journal, July 2004
- Bueno, J. Trujillo; Shchukina, N.; Ramos, A. Asensio
- Nature, Vol. 430, Issue 6997
On the Spectrum of Magnetohydrodynamic Turbulence
journal, May 2005
- Boldyrev, Stanislav
- The Astrophysical Journal, Vol. 626, Issue 1
Problems with kinematic mean field electrodynamics at high magnetic Reynolds numbers
journal, May 2009
- Cattaneo, F.; Hughes, D. W.
- Monthly Notices of the Royal Astronomical Society: Letters, Vol. 395, Issue 1
Resolution of magnetic flux tubes on the Sun
journal, September 1992
- Keller, C. U.
- Nature, Vol. 359, Issue 6393
The breakdown of Alfvén’s theorem in ideal plasma flows: Necessary conditions and physical conjectures
journal, November 2006
- Eyink, Gregory L.; Aluie, Hussein
- Physica D: Nonlinear Phenomena, Vol. 223, Issue 1
Local energy flux and the refined similarity hypothesis
journal, January 1995
- Eyink, Gregory L.
- Journal of Statistical Physics, Vol. 78, Issue 1-2
Hydromagnetic Dynamo Theory
journal, April 1956
- Elsasser, Walter M.
- Reviews of Modern Physics, Vol. 28, Issue 2
The response of isotropic turbulence to isotropic and anisotropic forcing at the large scales
journal, May 1991
- Yeung, P. K.; Brasseur, James G.
- Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5
A Theorem on Force-Free Magnetic Fields
journal, June 1958
- Woltjer, L.
- Proceedings of the National Academy of Sciences, Vol. 44, Issue 6
Extreme events in computational turbulence
journal, September 2015
- Yeung, P. K.; Zhai, X. M.; Sreenivasan, Katepalli R.
- Proceedings of the National Academy of Sciences, Vol. 112, Issue 41
Cascade of circulations in fluid turbulence
journal, December 2006
- Eyink, Gregory L.
- Physical Review E, Vol. 74, Issue 6
Inertial ranges and resistive instabilities in two‐dimensional magnetohydrodynamic turbulence
journal, December 1989
- Politano, H.; Pouquet, A.; Sulem, P. L.
- Physics of Fluids B: Plasma Physics, Vol. 1, Issue 12
The degree of knottedness of tangled vortex lines
journal, January 1969
- Moffatt, H. K.
- Journal of Fluid Mechanics, Vol. 35, Issue 1
Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box
journal, February 2003
- Kaneda, Yukio; Ishihara, Takashi; Yokokawa, Mitsuo
- Physics of Fluids, Vol. 15, Issue 2
Statistical Theory of Turbulence
journal, September 1935
- Taylor, G. I.
- Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, Vol. 151, Issue 873
Spectrum of Magnetohydrodynamic Turbulence
journal, March 2006
- Boldyrev, Stanislav
- Physical Review Letters, Vol. 96, Issue 11
The renormalization group: Critical phenomena and the Kondo problem
journal, October 1975
- Wilson, Kenneth G.
- Reviews of Modern Physics, Vol. 47, Issue 4
Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows
book, January 1975
- Leonard, A.
- Turbulent Diffusion in Environmental Pollution, Proceedings of a Symposium held at Charlottesville
Finite dissipation and intermittency in magnetohydrodynamics
journal, August 2009
- Mininni, P. D.; Pouquet, A.
- Physical Review E, Vol. 80, Issue 2
Colloquium: Magnetohydrodynamic turbulence and time scales in astrophysical and space plasmas
journal, December 2004
- Zhou, Ye; Matthaeus, W.; Dmitruk, P.
- Reviews of Modern Physics, Vol. 76, Issue 4
Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence
journal, April 1975
- Frisch, U.; Pouquet, A.; LÉOrat, J.
- Journal of Fluid Mechanics, Vol. 68, Issue 4
The Signature of Initial Conditions on Magnetohydrodynamic Turbulence
journal, June 2014
- Dallas, V.; Alexakis, A.
- The Astrophysical Journal, Vol. 788, Issue 2
Compressible Turbulence: The Cascade and its Locality
journal, April 2011
- Aluie, Hussein
- Physical Review Letters, Vol. 106, Issue 17
Decay of homogeneous, nearly isotropic turbulence behind active fractal grids
journal, February 2014
- Thormann, Adrien; Meneveau, Charles
- Physics of Fluids, Vol. 26, Issue 2
Fully Developed Anisotropic Hydromagnetic Turbulence in Interplanetary Space
journal, July 1980
- Dobrowolny, M.; Mangeney, A.; Veltri, P.
- Physical Review Letters, Vol. 45, Issue 2
Development of large eddy simulation for modeling of decaying compressible magnetohydrodynamic turbulence
journal, May 2007
- Chernyshov, A. A.; Karelsky, K. V.; Petrosyan, A. S.
- Physics of Fluids, Vol. 19, Issue 5
Dissipative anomalies in singular Euler flows
journal, August 2008
- Eyink, Gregory L.
- Physica D: Nonlinear Phenomena, Vol. 237, Issue 14-17
Degrees of locality of energy transfer in the inertial range
journal, May 1993
- Zhou, Ye
- Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 5
Growth of correlations in magnetohydrodynamic turbulence
journal, June 1986
- Pouquet, A.; Meneguzzi, M.; Frisch, U.
- Physical Review A, Vol. 33, Issue 6
Rigorous new limits on magnetic helicity dissipation in the solar corona
journal, September 1984
- Berger, Mitchell A.
- Geophysical & Astrophysical Fluid Dynamics, Vol. 30, Issue 1-2
Real-Space Renormalization
book, January 1982
- Burkhardt, Theodore W.; van Leeuwen, J. M. J.
- Topics in Current Physics
Berechnung der mittleren Lorentz-Feldstärke für ein elektrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte beeinflußter Bewegung
journal, January 1966
- Steenbeck, M.; Krause, F.; Rädler, K. -H.
- Zeitschrift für Naturforschung A, Vol. 21, Issue 4
Scale-Invariance and Turbulence Models for Large-Eddy Simulation
journal, January 2000
- Meneveau, Charles; Katz, Joseph
- Annual Review of Fluid Mechanics, Vol. 32, Issue 1
Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields
journal, November 1974
- Taylor, J. B.
- Physical Review Letters, Vol. 33, Issue 19
Nonlocal interactions in hydrodynamic turbulence at high Reynolds numbers: The slow emergence of scaling laws
journal, March 2008
- Mininni, P. D.; Alexakis, A.; Pouquet, A.
- Physical Review E, Vol. 77, Issue 3
Hydrodynamic and hydromagnetic energy spectra from large eddy simulations
journal, July 2006
- Haugen, Nils Erland L.; Brandenburg, Axel
- Physics of Fluids, Vol. 18, Issue 7
Realizability conditions for the turbulent stress tensor in large-eddy simulation
journal, November 1994
- Vreman, Bert; Geurts, Bernard; Kuerten, Hans
- Journal of Fluid Mechanics, Vol. 278
On the Inverse Cascade of Magnetic Helicity
journal, March 2006
- Alexakis, Alexandros; Mininni, Pablo D.; Pouquet, Annick
- The Astrophysical Journal, Vol. 640, Issue 1
A Global Three-Dimensional Radiation Magneto-Hydrodynamic Simulation of Super-Eddington Accretion Disks
journal, November 2014
- Jiang, Yan-Fei; Stone, James M.; Davis, Shane W.
- The Astrophysical Journal, Vol. 796, Issue 2
Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter
journal, November 2009
- Aluie, Hussein; Eyink, Gregory L.
- Physics of Fluids, Vol. 21, Issue 11
Turbulent General Magnetic Reconnection
journal, July 2015
- Eyink, G. L.
- The Astrophysical Journal, Vol. 807, Issue 2
Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence
journal, October 2005
- Alexakis, Alexandros; Mininni, Pablo D.; Pouquet, Annick
- Physical Review E, Vol. 72, Issue 4
An analysis of the energy transfer and the locality of nonlinear interactions in turbulence
journal, August 2007
- Domaradzki, J. Andrzej; Carati, Daniele
- Physics of Fluids, Vol. 19, Issue 8
Inertial-Range Spectrum of Hydromagnetic Turbulence
journal, January 1965
- Kraichnan, Robert H.
- Physics of Fluids, Vol. 8, Issue 7
Introduction to magnetic helicity
journal, December 1999
- Berger, Mitchell A.
- Plasma Physics and Controlled Fusion, Vol. 41, Issue 12B
Shell-to-shell energy transfer in magnetohydrodynamics. II. Kinematic dynamo
journal, October 2005
- Mininni, Pablo; Alexakis, Alexandros; Pouquet, Annick
- Physical Review E, Vol. 72, Issue 4
On the scaling of the turbulence energy dissipation rate
journal, January 1984
- Sreenivasan, K. R.
- Physics of Fluids, Vol. 27, Issue 5
Turbulence: the filtering approach
journal, May 1992
- Germano, M.
- Journal of Fluid Mechanics, Vol. 238
Extragalactic magnetic fields
journal, April 1994
- Kronberg, P. P.
- Reports on Progress in Physics, Vol. 57, Issue 4
Magnetic fields in galaxies and beyond
journal, January 1997
- Zweibel, Ellen G.; Heiles, Carl
- Nature, Vol. 385, Issue 6612
General relativistic MHD simulations of black hole accretion disks and jets
journal, July 2007
- Hawley, John F.; Beckwith, Kris; Krolik, Julian H.
- Astrophysics and Space Science, Vol. 311, Issue 1-3
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- Lees, Aarne; Aluie, Hussein
- Fluids, Vol. 4, Issue 2
Convolutions on the sphere: commutation with differential operators
journal, January 2019
- Aluie, Hussein
- GEM - International Journal on Geomathematics, Vol. 10, Issue 1
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journal, January 2020
- Lazarian, Alex; Eyink, Gregory L.; Jafari, Amir
- Physics of Plasmas, Vol. 27, Issue 1
Topology and stochasticity of turbulent magnetic fields
journal, July 2019
- Jafari, Amir; Vishniac, Ethan
- Physical Review E, Vol. 100, Issue 1
Energy Transfer in Incompressible Magnetohydrodynamics: The Filtered Approach
journal, September 2019
- Coburn, Jesse T.; Sorriso-Valvo, Luca
- Fluids, Vol. 4, Issue 3, p. 163
Partial Invariants, Large-scale Dynamo Action, and the Inverse Transfer of Magnetic Helicity
journal, December 2019
- Rathmann, Nicholas M.; Ditlevsen, Peter D.
- The Astrophysical Journal, Vol. 887, Issue 1
Do Androids Dream of Magnetic Fields? Using Neural Networks to Interpret the Turbulent Interstellar Medium
journal, September 2019
- Peek, J. E. G.; Burkhart, Blakesley
- The Astrophysical Journal, Vol. 882, Issue 1