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For a traditional statement of this idea, consider for example the textbook of Landau & Lifschitz Landau and Lifshits 1959 , §31: “We therefore conclude that, for the large eddies which are the basis of any turbulent flow, the viscosity is unimportant and may be equated to zero, so that the motion of these eddies obeys Euler’s equation. In particular, it follows from this that there is no appreciable dissipation of energy in the large eddies”. The latter statement is only true, however, for the direct viscous dissipation of kinetic energy at inertial-range scales, whereas the energy in eddies at those scales, in fact, must be dissipated. The rate of decrease of energy for free-decay or rate of power-input for forced turbulence are objective facts that cannot depend upon the resolution of eddies in the inertial-range
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1994
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1995
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1996
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Russel E Caflisch, Isaac Klapper, and Gregory Steele, “Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD,” Communications in Mathematical Physics 184
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Katepalli R Sreenivasan, “An update on the energy dissipation rate in isotropic turbulence,” Physics of Fluids 10
1998
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Shiyi Chen, Robert E Ecke, Gregory L Eyink, Michael Rivera, Minping Wan, and Zuoli Xiao, “Physical mechanism of the two-dimensional inverse energy cascade,” Physical review letters 96
2006
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Gregory L Eyink and Hussein Aluie, “The breakdown of Alfvén’s theorem in ideal plasma flows: Necessary conditions and physical conjectures,” Physica D: Nonlinear Phenomena 223
2006
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Gregory L Eyink, “Turbulent diffusion of lines and circulations,” Physics Letters A 368
2007
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Peter Constantin and Gautam Iyer, “A stochastic lagrangian representation of the three-dimensional incompressible navier-stokes equations,” Communications on Pure and Applied Mathematics 61
2008
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Z Xiao, M Wan, S Chen, and GL Eyink, “Physical mechanism of the inverse energy cascade of two-dimensional turbulence: a numerical investigation,” Journal of Fluid Mechanics 619
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Denis Bernard, Krzysztof Gawȩdzki, and Antti Kupiainen, “Slow modes in passive advection,” Journal of Statistical Physics 90
1998
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Charles Meneveau and Joseph Katz, “Scale-invariance and turbulence models for large-eddy simulation,” Annu Rev Fluid Mech 32
2000
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Jean Duchon and Raoul Robert, “Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations,” Nonlinearity 13
2000
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V. N. Gribov, “Anomalies, as a manifestation of the high momentum collective motion in the vacuum,” in The Gribov Theory Of Quark Confinement , edited by J. Nyiri (World Scientific, 2001) pp. 74–91
2001
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Gregory L Eyink, “Dissipation in turbulent solutions of 2D Euler equations,” Nonlinearity 14
2001
Cited alongside, same era.
B.R. Pearson, P.-Å. Krogstad, and W. Van De Water, “Measurements of the turbulent energy dissipation rate,” Phys Fluids 14
2002
Cited alongside, same era.
Gregory L Eyink, “Local 4/5-law and energy dissipation anomaly in turbulence,” Nonlinearity 16
2002
Cited alongside, same era.
2009
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Gregory L Eyink, “Stochastic line motion and stochastic flux conservation for nonideal hydromagnetic models,” Journal of Mathematical Physics 50
2009
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Hussein Aluie and Gregory L Eyink, “Scale locality of magnetohydrodynamic turbulence,” Physical review letters 104
2010
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Camillo De Lellis and László Székelyhidi Jr, “The h h -principle and the equations of fluid dynamics,” B Am Math Soc 49
2012
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Camillo De Lellis and László Székelyhidi Jr, “Continuous dissipative Euler flows and a conjecture of Onsager,” in European Congress of Mathematics: Kraków, 2-7 July, 2012 , edited by R. Latała, A. Ruciński, P. Strzelecki, J. Światkowski, and D. Wrzosek (European Mathematical Society, Zurich, 2013) pp. 13–30
2013
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Hussein Aluie, “Scale decomposition in compressible turbulence,” Physica D: Nonlinear Phenomena 247
2013
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Gregory Eyink, Ethan Vishniac, Cristian Lalescu, Hussein Aluie, Kalin Kanov, Kai Bürger, Randal Burns, Charles Meneveau, and Alexander Szalay, “Flux-freezing breakdown in high-conductivity magnetohydrodynamic turbulence,” Nature 497
2013
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Gregory L Eyink and Theodore D Drivas, “Spontaneous stochasticity and anomalous dissipation for burgers equation,” Journal of Statistical Physics 158
2015
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Philip Isett, “A proof of Onsager’s conjecture,” https://arxiv.org/abs/1608.08301 (2016)
2016
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2017
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2017
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2017
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Hussein Aluie, “Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades,” New Journal of Physics 19
2017
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Theodore D Drivas and Gregory L Eyink, “A lagrangian fluctuation–dissipation relation for scalar turbulence. part i. flows with no bounding walls,” Journal of Fluid Mechanics 829
2017
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Gregory Eyink, “Cascades and dissipative anomalies in nearly collisionless plasma turbulence,” submitted to Phys. Rev. X (2018)
2018
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