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Turbulence theories and statistical closure approaches

Journal Article · Wed Jul 28 00:00:00 EDT 2021 · Physics Reports

DOI:https://doi.org/10.1016/j.physrep.2021.07.001· OSTI ID:1832324

Zhou, Ye ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range [A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, 30, 299, (1941); 32, 19, (1941)]. The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) [R.H. Kraichnan, J. Fluid Mech., 5, 497 (1959)] and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Finally, turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1832324

Report Number(s):: LLNL-JRNL--807019; 1009170

Journal Information:: Physics Reports, Journal Name: Physics Reports Journal Issue: na Vol. 935; ISSN 0370-1573

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Passive scalar turbulence in high dimensions Mazzino, Andrea; Muratore-Ginanneschi, Paolo Physical Review E, Vol. 63, Issue 1 https://doi.org/10.1103/PhysRevE.63.015302	journal	December 2000
Anomalous exponents to order ɛ 3 in the rapid-change model of passive scalar advection Adzhemyan, L. Ts.; Antonov, N. V.; Barinov, V. A. Physical Review E, Vol. 63, Issue 2 https://doi.org/10.1103/PhysRevE.63.025303	journal	January 2001
Mean-field approximation and a small parameter in turbulence theory Yakhot, Victor Physical Review E, Vol. 63, Issue 2 https://doi.org/10.1103/PhysRevE.63.026307	journal	January 2001
Anomalous scaling in two models of passive scalar advection: Effects of anisotropy and compressibility Antonov, N. V.; Honkonen, Juha Physical Review E, Vol. 63, Issue 3 https://doi.org/10.1103/PhysRevE.63.036302	journal	February 2001
Scaling laws and vortex profiles in two-dimensional decaying turbulence Laval, Jean-Philippe; Chavanis, Pierre-Henri; Dubrulle, Bérengère Physical Review E, Vol. 63, Issue 6 https://doi.org/10.1103/PhysRevE.63.065301	journal	May 2001
Kinetic theory of point vortices: Diffusion coefficient and systematic drift Chavanis, P. H. Physical Review E, Vol. 64, Issue 2 https://doi.org/10.1103/PhysRevE.64.026309	journal	July 2001
Statistical mechanics of the shallow water system Chavanis, P. H.; Sommeria, J. Physical Review E, Vol. 65, Issue 2 https://doi.org/10.1103/PhysRevE.65.026302	journal	January 2002
Subgrid scale and backscatter model for magnetohydrodynamic turbulence based on closure theory: Theoretical formulation Zhou, Ye; Schilling, Oleg; Ghosh, Sanjoy Physical Review E, Vol. 66, Issue 2 https://doi.org/10.1103/PhysRevE.66.026309	journal	August 2002
Energy transfer in Rayleigh-Taylor instability Cook, Andrew W.; Zhou, Ye Physical Review E, Vol. 66, Issue 2 https://doi.org/10.1103/PhysRevE.66.026312	journal	August 2002
Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: Two-loop approximation Adzhemyan, L. Ts.; Antonov, N. V.; Honkonen, J. Physical Review E, Vol. 66, Issue 3 https://doi.org/10.1103/PhysRevE.66.036313	journal	September 2002
Scaling exponents in anisotropic hydrodynamic turbulence L’vov, Victor S.; Procaccia, Itamar; Tiberkevich, Vasil Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/PhysRevE.67.026312	journal	February 2003
Weak inertial-wave turbulence theory Galtier, Sébastien Physical Review E, Vol. 68, Issue 1 https://doi.org/10.1103/PhysRevE.68.015301	journal	July 2003
Recovering isotropic statistics in turbulence simulations: The Kolmogorov 4/5th law Taylor, Mark A.; Kurien, Susan; Eyink, Gregory L. Physical Review E, Vol. 68, Issue 2 https://doi.org/10.1103/PhysRevE.68.026310	journal	August 2003
Cascade time scales for energy and helicity in homogeneous isotropic turbulence Kurien, Susan; Taylor, Mark A.; Matsumoto, Takeshi Physical Review E, Vol. 69, Issue 6 https://doi.org/10.1103/PhysRevE.69.066313	journal	June 2004
Shell model for rotating turbulence Hattori, Y.; Rubinstein, R.; Ishizawa, A. Physical Review E, Vol. 70, Issue 4 https://doi.org/10.1103/PhysRevE.70.046311	journal	October 2004
Time-ordered fluctuation-dissipation relation for incompressible isotropic turbulence Kiyani, K.; McComb, W. D. Physical Review E, Vol. 70, Issue 6 https://doi.org/10.1103/PhysRevE.70.066303	journal	December 2004
Anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field: Two-loop approximation Adzhemyan, L. Ts.; Antonov, N. V.; Honkonen, J. Physical Review E, Vol. 71, Issue 1 https://doi.org/10.1103/PhysRevE.71.016303	journal	January 2005
Thermodynamics of magnetohydrodynamic flows with axial symmetry Leprovost, N.; Dubrulle, B.; Chavanis, P-H. Physical Review E, Vol. 71, Issue 3 https://doi.org/10.1103/PhysRevE.71.036311	journal	March 2005
Experiments and direct numerical simulations of two-dimensional turbulence Bruneau, C. H.; Kellay, H. Physical Review E, Vol. 71, Issue 4 https://doi.org/10.1103/PhysRevE.71.046305	journal	April 2005
Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy Hnatich, M.; Honkonen, J.; Jurcisin, M. Physical Review E, Vol. 71, Issue 6 https://doi.org/10.1103/PhysRevE.71.066312	journal	June 2005
Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence Alexakis, Alexandros; Mininni, Pablo D.; Pouquet, Annick Physical Review E, Vol. 72, Issue 4 https://doi.org/10.1103/PhysRevE.72.046301	journal	October 2005
Equilibrium theory of coherent vortex and zonal jet formation in a system of nonlinear Rossby waves Weichman, Peter B. Physical Review E, Vol. 73, Issue 3 https://doi.org/10.1103/PhysRevE.73.036313	journal	March 2006
Dynamics and thermodynamics of axisymmetric flows: Theory Leprovost, N.; Dubrulle, B.; Chavanis, P. -H. Physical Review E, Vol. 73, Issue 4 https://doi.org/10.1103/PhysRevE.73.046308	journal	April 2006
Large-scale flow effects, energy transfer, and self-similarity on turbulence Mininni, P. D.; Alexakis, A.; Pouquet, A. Physical Review E, Vol. 74, Issue 1 https://doi.org/10.1103/PhysRevE.74.016303	journal	July 2006
Third-order structure function for rotating three-dimensional homogeneous turbulent flow Chakraborty, Sagar; Bhattacharjee, J. K. Physical Review E, Vol. 76, Issue 3 https://doi.org/10.1103/PhysRevE.76.036304	journal	September 2007
Anomalous scaling of a passive scalar advected by a turbulent velocity field with finite correlation time and uniaxial small-scale anisotropy Jurčišinová, E.; Jurčišin, M. Physical Review E, Vol. 77, Issue 1 https://doi.org/10.1103/PhysRevE.77.016306	journal	January 2008
Sufficient condition for Gaussian departure in turbulence Tordella, Daniela; Iovieno, Michele; Bailey, Peter Roger Physical Review E, Vol. 77, Issue 1 https://doi.org/10.1103/PhysRevE.77.016309	journal	January 2008
Nonlocal interactions in hydrodynamic turbulence at high Reynolds numbers: The slow emergence of scaling laws Mininni, P. D.; Alexakis, A.; Pouquet, A. Physical Review E, Vol. 77, Issue 3 https://doi.org/10.1103/PhysRevE.77.036306	journal	March 2008
Spectral modeling of turbulent flows and the role of helicity Baerenzung, J.; Politano, H.; Ponty, Y. Physical Review E, Vol. 77, Issue 4 https://doi.org/10.1103/PhysRevE.77.046303	journal	April 2008
Spectral modeling of magnetohydrodynamic turbulent flows Baerenzung, J.; Politano, H.; Ponty, Y. Physical Review E, Vol. 78, Issue 2 https://doi.org/10.1103/PhysRevE.78.026310	journal	August 2008
Development of anisotropy in incompressible magnetohydrodynamic turbulence Bigot, Barbara; Galtier, Sébastien; Politano, Hélène Physical Review E, Vol. 78, Issue 6 https://doi.org/10.1103/PhysRevE.78.066301	journal	December 2008
Locality and stability of the cascades of two-dimensional turbulence Gkioulekas, Eleftherios Physical Review E, Vol. 78, Issue 6 https://doi.org/10.1103/PhysRevE.78.066302	journal	December 2008
Anisotropic magnetohydrodynamic spectral transfer in the diffusion approximation Matthaeus, W. H.; Oughton, S.; Zhou, Y. Physical Review E, Vol. 79, Issue 3 https://doi.org/10.1103/PhysRevE.79.035401	journal	March 2009
Anomalous scaling and anisotropy in models of passively advected vector fields Arponen, Heikki Physical Review E, Vol. 79, Issue 5 https://doi.org/10.1103/PhysRevE.79.056303	journal	May 2009
Influence of anisotropy on anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field Jurčišinová, E.; Jurčišin, M.; Remecký, R. Physical Review E, Vol. 80, Issue 4 https://doi.org/10.1103/PhysRevE.80.046302	journal	October 2009
Lack of universality in decaying magnetohydrodynamic turbulence Lee, E.; Brachet, M. E.; Pouquet, A. Physical Review E, Vol. 81, Issue 1 https://doi.org/10.1103/PhysRevE.81.016318	journal	January 2010
Statistical mechanics of Beltrami flows in axisymmetric geometry: Theory reexamined Naso, Aurore; Monchaux, Romain; Chavanis, Pierre-Henri Physical Review E, Vol. 81, Issue 6 https://doi.org/10.1103/PhysRevE.81.066318	journal	June 2010
Evidence for the double cascade scenario in two-dimensional turbulence Boffetta, G.; Musacchio, S. Physical Review E, Vol. 82, Issue 1 https://doi.org/10.1103/PhysRevE.82.016307	journal	July 2010
Dissipation scales and anomalous sinks in steady two-dimensional turbulence Gkioulekas, Eleftherios Physical Review E, Vol. 82, Issue 4 https://doi.org/10.1103/PhysRevE.82.046304	journal	October 2010
Kraichnan’s random sweeping hypothesis in homogeneous turbulent convection He, Xiaozhou; Tong, Penger Physical Review E, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevE.83.037302	journal	March 2011
Rotating shallow water dynamics: Extra invariant and the formation of zonal jets Balk, Alexander M.; van Heerden, Francois; Weichman, Peter B. Physical Review E, Vol. 83, Issue 4 https://doi.org/10.1103/PhysRevE.83.046320	journal	April 2011
Effective merging dynamics of two and three fluid vortices: Application to two-dimensional decaying turbulence Sire, Clément; Chavanis, Pierre-Henri; Sopik, Julien Physical Review E, Vol. 84, Issue 5 https://doi.org/10.1103/PhysRevE.84.056317	journal	November 2011
Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere Herbert, C.; Dubrulle, B.; Chavanis, P. H. Physical Review E, Vol. 85, Issue 5 https://doi.org/10.1103/PhysRevE.85.056304	journal	May 2012
Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: Two-loop renormalization-group analysis of the Kazantsev-Kraichnan kinematic model Antonov, N. V.; Gulitskiy, N. M. Physical Review E, Vol. 85, Issue 6 https://doi.org/10.1103/PhysRevE.85.065301	journal	June 2012
Examination of the four-fifths law for longitudinal third-order moments in incompressible magnetohydrodynamic turbulence in a periodic box Yoshimatsu, Katsunori Physical Review E, Vol. 85, Issue 6 https://doi.org/10.1103/PhysRevE.85.066313	journal	June 2012
Nonperturbative renormalization group study of the stochastic Navier-Stokes equation Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo Physical Review E, Vol. 86, Issue 1 https://doi.org/10.1103/PhysRevE.86.016315	journal	July 2012
Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: Scaling functions and amplitude ratios in 1+1, 2+1, and 3+1 dimensions Kloss, Thomas; Canet, Léonie; Wschebor, Nicolás Physical Review E, Vol. 86, Issue 5 https://doi.org/10.1103/PhysRevE.86.051124	journal	November 2012
Wave-number–frequency spectrum for turbulence from a random sweeping hypothesis with mean flow Wilczek, M.; Narita, Y. Physical Review E, Vol. 86, Issue 6 https://doi.org/10.1103/PhysRevE.86.066308	journal	December 2012
Turbulent magnetic Prandtl number in helical kinematic magnetohydrodynamic turbulence: Two-loop renormalization group result Jurčišinová, E. ; Jurčišin, M.; Remecký, R. Physical Review E, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevE.87.043010	journal	April 2013
Anomalous scaling of the magnetic field in the compressible Kazantsev-Kraichnan model: Two-loop renormalization group analysis Jurčišinová, E.; Jurčišin, M. Physical Review E, Vol. 88, Issue 1 https://doi.org/10.1103/PhysRevE.88.011004	journal	July 2013
Fluctuations of a passive scalar in a turbulent mixing layer Attili, Antonio; Bisetti, Fabrizio Physical Review E, Vol. 88, Issue 3 https://doi.org/10.1103/PhysRevE.88.033013	journal	September 2013
Kardar-Parisi-Zhang equation with spatially correlated noise: A unified picture from nonperturbative renormalization group Kloss, Thomas; Canet, Léonie; Delamotte, Bertrand Physical Review E, Vol. 89, Issue 2 https://doi.org/10.1103/PhysRevE.89.022108	journal	February 2014
Turbulent Prandtl number of a passively advected vector field in helical environment: Two-loop renormalization group result Jurčišinová, E.; Jurčišin, M.; Zalom, P. Physical Review E, Vol. 89, Issue 4 https://doi.org/10.1103/PhysRevE.89.043023	journal	April 2014
Strong-coupling phases of the anisotropic Kardar-Parisi-Zhang equation Kloss, Thomas; Canet, Léonie; Wschebor, Nicolás Physical Review E, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevE.90.062133	journal	December 2014
Fully developed isotropic turbulence: Symmetries and exact identities Canet, Léonie; Delamotte, Bertrand; Wschebor, Nicolás Physical Review E, Vol. 91, Issue 5 https://doi.org/10.1103/PhysRevE.91.053004	journal	May 2015
Anomalous scaling of the magnetic field in the helical Kazantsev-Kraichnan model Jurčišinová, E.; Jurčišin, M. Physical Review E, Vol. 91, Issue 6 https://doi.org/10.1103/PhysRevE.91.063009	journal	June 2015
Bottlenecks in turbulent kinetic energy spectra predicted from structure function inflections using the Von Kármán-Howarth equation Katul, Gabriel G.; Manes, Costantino; Porporato, Amilcare Physical Review E, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRevE.92.033009	journal	September 2015
Functional renormalization group approach to the Kraichnan model Pagani, Carlo Physical Review E, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRevE.92.033016	journal	September 2015
Passive advection of a vector field: Anisotropy, finite correlation time, exact solution, and logarithmic corrections to ordinary scaling Antonov, N. V.; Gulitskiy, N. M. Physical Review E, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevE.92.043018	journal	October 2015
Fully developed isotropic turbulence: Nonperturbative renormalization group formalism and fixed-point solution Canet, Léonie; Delamotte, Bertrand; Wschebor, Nicolás Physical Review E, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevE.93.063101	journal	June 2016
Multilocality and fusion rules on the generalized structure functions in two-dimensional and three-dimensional Navier-Stokes turbulence Gkioulekas, Eleftherios Physical Review E, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevE.94.033105	journal	September 2016
Helical turbulent Prandtl number in the A model of passive vector advection Hnatič, M.; Zalom, P. Physical Review E, Vol. 94, Issue 5 https://doi.org/10.1103/PhysRevE.94.053113	journal	November 2016
Reynolds number scaling of velocity increments in isotropic turbulence Iyer, Kartik P.; Sreenivasan, Katepalli R.; Yeung, P. K. Physical Review E, Vol. 95, Issue 2 https://doi.org/10.1103/PhysRevE.95.021101	journal	February 2017
Spatiotemporal velocity-velocity correlation function in fully developed turbulence Canet, Léonie; Rossetto, Vincent; Wschebor, Nicolás Physical Review E, Vol. 95, Issue 2 https://doi.org/10.1103/PhysRevE.95.023107	journal	February 2017
Turbulent compressible fluid: Renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M. Physical Review E, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevE.95.033120	journal	March 2017
Simultaneous influence of helicity and compressibility on anomalous scaling of the magnetic field in the Kazantsev-Kraichnan model Jurčišinová, E.; Jurčišin, M.; Menkyna, M. Physical Review E, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevE.95.053210	journal	May 2017
Generation of anisotropy in turbulent flows subjected to rapid distortion Clark, Timothy T.; Kurien, Susan; Rubinstein, Robert Physical Review E, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevE.97.013112	journal	January 2018
Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M. Physical Review E, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevE.97.033101	journal	March 2018
Scale-similar clustering of heavy particles in the inertial range of turbulence Ariki, Taketo; Yoshida, Kyo; Matsuda, Keigo Physical Review E, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevE.97.033109	journal	March 2018
Directional change of tracer trajectories in rotating Rayleigh-Bénard convection Alards, Kim M. J.; Rajaei, Hadi; Kunnen, Rudie P. J. Physical Review E, Vol. 97, Issue 6 https://doi.org/10.1103/PhysRevE.97.063105	journal	June 2018
Spectral energy scaling in precessing turbulence Khlifi, A.; Salhi, A.; Nasraoui, S. Physical Review E, Vol. 98, Issue 1 https://doi.org/10.1103/PhysRevE.98.011102	journal	July 2018
Multiscale velocity correlations in turbulence and Burgers turbulence: Fusion rules, Markov processes in scale, and multifractal predictions Friedrich, Jan; Margazoglou, Georgios; Biferale, Luca Physical Review E, Vol. 98, Issue 2 https://doi.org/10.1103/PhysRevE.98.023104	journal	August 2018
Cancellation exponents in isotropic turbulence and magnetohydrodynamic turbulence Zhai, X. M.; Sreenivasan, K. R.; Yeung, P. K. Physical Review E, Vol. 99, Issue 2 https://doi.org/10.1103/PhysRevE.99.023102	journal	February 2019
Artificial neural network approach to large-eddy simulation of compressible isotropic turbulence Xie, Chenyue; Wang, Jianchun; Li, Ke Physical Review E, Vol. 99, Issue 5 https://doi.org/10.1103/PhysRevE.99.053113	journal	May 2019
Internal gravity waves in the energy and flux budget turbulence-closure theory for shear-free stably stratified flows Kleeorin, N.; Rogachevskii, I.; Soustova, I. A. Physical Review E, Vol. 99, Issue 6 https://doi.org/10.1103/PhysRevE.99.063106	journal	June 2019
Energy spectrum in high-resolution direct numerical simulations of turbulence Ishihara, Takashi; Morishita, Koji; Yokokawa, Mitsuo Physical Review Fluids, Vol. 1, Issue 8 https://doi.org/10.1103/PhysRevFluids.1.082403	journal	December 2016
Competing turbulent cascades and eddy-wave interactions in shallow water equilibria Weichman, Peter B. Physical Review Fluids, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevFluids.2.034701	journal	March 2017
Anisotropic spectral modeling for unstably stratified homogeneous turbulence Briard, Antoine; Iyer, Manasa; Gomez, Thomas Physical Review Fluids, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevFluids.2.044604	journal	April 2017
Multiscale anisotropic fluctuations in sheared turbulence with multiple states Iyer, Kartik P.; Bonaccorso, Fabio; Biferale, Luca Physical Review Fluids, Vol. 2, Issue 5 https://doi.org/10.1103/PhysRevFluids.2.052602	journal	May 2017
Hierarchy of antiparallel vortex tubes in spatially periodic turbulence at high Reynolds numbers Goto, Susumu; Saito, Yuta; Kawahara, Genta Physical Review Fluids, Vol. 2, Issue 6 https://doi.org/10.1103/PhysRevFluids.2.064603	journal	June 2017
Influence of zero-modes on the inertial-range anisotropy of Rayleigh-Taylor and unstably stratified homogeneous turbulence Soulard, Olivier; Gréa, Benoît-Joseph Physical Review Fluids, Vol. 2, Issue 7 https://doi.org/10.1103/PhysRevFluids.2.074603	journal	July 2017
Large-scale sweeping of small-scale eddies in turbulence: A filtering approach Drivas, Theodore D.; Johnson, Perry L.; Lalescu, Cristian C. Physical Review Fluids, Vol. 2, Issue 10 https://doi.org/10.1103/PhysRevFluids.2.104603	journal	October 2017
Extended scale invariance in the vortices of freely evolving two-dimensional turbulence Burgess, B. H.; Dritschel, D. G.; Scott, R. K. Physical Review Fluids, Vol. 2, Issue 11 https://doi.org/10.1103/PhysRevFluids.2.114702	journal	November 2017
Experimental test of the crossover between the inertial and the dissipative range in a turbulent swirling flow Debue, Paul; Kuzzay, Denis; Saw, Ewe-Wei Physical Review Fluids, Vol. 3, Issue 2 https://doi.org/10.1103/PhysRevFluids.3.024602	journal	February 2018
Effects of finite spatial and temporal resolution in direct numerical simulations of incompressible isotropic turbulence Yeung, P. K.; Sreenivasan, K. R.; Pope, S. B. Physical Review Fluids, Vol. 3, Issue 6 https://doi.org/10.1103/PhysRevFluids.3.064603	journal	June 2018
Energy spectrum in the dissipation range Khurshid, Sualeh; Donzis, Diego A.; Sreenivasan, K. R. Physical Review Fluids, Vol. 3, Issue 8 https://doi.org/10.1103/PhysRevFluids.3.082601	journal	August 2018
Scale locality of the energy cascade using real space quantities Doan, N. A. K.; Swaminathan, N.; Davidson, P. A. Physical Review Fluids, Vol. 3, Issue 8 https://doi.org/10.1103/PhysRevFluids.3.084601	journal	August 2018
Evolution of anisotropy in direct numerical simulations of MHD turbulence in a strong magnetic field on elongated periodic domains Zhai, X. M.; Yeung, P. K. Physical Review Fluids, Vol. 3, Issue 8 https://doi.org/10.1103/PhysRevFluids.3.084602	journal	August 2018
Mandala-inspired representation of the turbulent energy cascade Bassenne, Maxime; Bae, Hyunji Jane; Lozano-Durán, Adrián Physical Review Fluids, Vol. 3, Issue 10 https://doi.org/10.1103/PhysRevFluids.3.100505	journal	October 2018
Large-scale structure of velocity and passive scalar fields in freely decaying homogeneous anisotropic turbulence Yoshimatsu, Katsunori; Kaneda, Yukio Physical Review Fluids, Vol. 3, Issue 10 https://doi.org/10.1103/PhysRevFluids.3.104601	journal	October 2018
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Onset criteria for freely decaying isotropic turbulence Yoffe, S. R.; McComb, W. D. Physical Review Fluids, Vol. 3, Issue 10 https://doi.org/10.1103/PhysRevFluids.3.104605	journal	October 2018
Inertial range skewness of the longitudinal velocity derivative in locally isotropic turbulence Sukoriansky, S.; Kit, E.; Zemach, E. Physical Review Fluids, Vol. 3, Issue 11 https://doi.org/10.1103/PhysRevFluids.3.114605	journal	November 2018
Two-point spectral model for variable-density homogeneous turbulence Pal, Nairita; Kurien, Susan; Clark, Timothy Physical Review Fluids, Vol. 3, Issue 12 https://doi.org/10.1103/PhysRevFluids.3.124608	journal	December 2018
Condensate in quasi-two-dimensional turbulence Musacchio, S.; Boffetta, G. Physical Review Fluids, Vol. 4, Issue 2 https://doi.org/10.1103/PhysRevFluids.4.022602	journal	February 2019
No return to reflection symmetry in freely decaying homogeneous turbulence Yoshimatsu, Katsunori; Kaneda, Yukio Physical Review Fluids, Vol. 4, Issue 2 https://doi.org/10.1103/PhysRevFluids.4.024611	journal	February 2019
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Strong vorticity fluctuations and antiferromagnetic correlations in axisymmetric fluid equilibria Weichman, Peter B. Physical Review Fluids, Vol. 4, Issue 5 https://doi.org/10.1103/PhysRevFluids.4.054703	journal	May 2019
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Statistical Dynamical Closures and Subgrid Modeling for Inhomogeneous QG and 3D Turbulence Frederiksen, Jorgen S. Entropy, Vol. 14, Issue 1 https://doi.org/10.3390/e14010032	journal	January 2012
Reduced Models of Point Vortex Systems Maack, Jonathan; Turkington, Bruce Entropy, Vol. 20, Issue 12 https://doi.org/10.3390/e20120914	journal	November 2018
The predictability of a flow which possesses many scales of motion Lorenz, Edward N. Tellus, Vol. 21, Issue 3 https://doi.org/10.3402/tellusa.v21i3.10086	journal	January 1969
Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects Le Dimet, FranÇois-Xavier; Talagrand, Olivier Tellus A: Dynamic Meteorology and Oceanography, Vol. 38, Issue 2 https://doi.org/10.3402/tellusa.v38i2.11706	journal	January 1986
The effects of closure-based eddy diffusion on the climate and spectra of a GCM Frederiksen, Jorgen S.; Dix, Martin R.; Davies, Antony G. Tellus A: Dynamic Meteorology and Oceanography, Vol. 55, Issue 1 https://doi.org/10.3402/tellusa.v55i1.12081	journal	January 2003
Scale-Dependent Normalized Amplitude and weak Spectral Anisotropy of Magnetic Field Fluctuations in the Solar wind Turbulence Wang, Xin; Tu, Chuanyi; Marsch, Eckart The Astrophysical Journal, Vol. 816, Issue 1 https://doi.org/10.3847/0004-637X/816/1/15	journal	December 2015
Theory and Transport of Nearly Incompressible Magnetohydrodynamic Turbulence Zank, G. P.; Adhikari, L.; Hunana, P. The Astrophysical Journal, Vol. 835, Issue 2 https://doi.org/10.3847/1538-4357/835/2/147	journal	January 2017
A Model of Rotating Convection in Stellar and Planetary Interiors. I. Convective Penetration Augustson, K. C.; Mathis, S. The Astrophysical Journal, Vol. 874, Issue 1 https://doi.org/10.3847/1538-4357/ab0b3d	journal	March 2019
No Evidence for Critical Balance in Field-aligned Alfvénic Solar Wind Turbulence Telloni, Daniele; Carbone, Francesco; Bruno, Roberto The Astrophysical Journal, Vol. 887, Issue 2 https://doi.org/10.3847/1538-4357/ab517b	journal	December 2019
Critical Balance and the Physics of Magnetohydrodynamic Turbulence Oughton, S.; Matthaeus, W. H. The Astrophysical Journal, Vol. 897, Issue 1 https://doi.org/10.3847/1538-4357/ab8f2a	journal	June 2020
Spectral Features in Field-aligned Solar Wind Turbulence from Parker Solar Probe Observations Zhao, L. -L.; Zank, G. P.; Adhikari, L. The Astrophysical Journal, Vol. 898, Issue 2 https://doi.org/10.3847/1538-4357/ab9b7e	journal	July 2020
Spectral Anisotropy in 2D plus Slab Magnetohydrodynamic Turbulence in the Solar Wind and Upper Corona Zank, G. P.; Nakanotani, M.; Zhao, L. -L. The Astrophysical Journal, Vol. 900, Issue 2 https://doi.org/10.3847/1538-4357/abad30	journal	September 2020
A Solar Coronal Hole and Fast Solar Wind Turbulence Model and First-orbit Parker Solar Probe (PSP) Observations Adhikari, L.; Zank, G. P.; Zhao, L. -L. The Astrophysical Journal, Vol. 901, Issue 2 https://doi.org/10.3847/1538-4357/abb132	journal	September 2020
The Formation of Electron Outflow Jets with Power-law Energy Distribution in Guide-field Magnetic Reconnection Che, H.; Zank, G. P.; Benz, A. O. The Astrophysical Journal, Vol. 908, Issue 1 https://doi.org/10.3847/1538-4357/abcf29	journal	February 2021
Numerical Study on the Validity of the Taylor Hypothesis in Space Plasmas Perri, Silvia; Servidio, Sergio; Vaivads, Andris The Astrophysical Journal Supplement Series, Vol. 231, Issue 1 https://doi.org/10.3847/1538-4365/aa755a	journal	July 2017
High-resolution UV/Optical/IR Imaging of Jupiter in 2016–2019 Wong, Michael H.; Simon, Amy A.; Tollefson, Joshua W. The Astrophysical Journal Supplement Series, Vol. 247, Issue 2 https://doi.org/10.3847/1538-4365/ab775f	journal	April 2020
On the Limitations of Taylor’s Hypothesis in Parker Solar Probe’s Measurements near the Alfvén Critical Point Bourouaine, Sofiane; Perez, Jean C. The Astrophysical Journal, Vol. 858, Issue 2 https://doi.org/10.3847/2041-8213/aabccf	journal	May 2018
On the Interpretation of Parker Solar Probe Turbulent Signals Bourouaine, Sofiane; Perez, Jean C. The Astrophysical Journal, Vol. 879, Issue 1 https://doi.org/10.3847/2041-8213/ab288a	journal	July 2019
Interpreting Solar Wind Turbulent Spectra beyond Taylor’s Hypothesis Bourouaine, Sofiane; Perez, Jean C. The Astrophysical Journal, Vol. 893, Issue 2 https://doi.org/10.3847/2041-8213/ab7fb1	journal	April 2020
Scaling of Turbulent Viscosity and Resistivity: Extracting a Scale-dependent Turbulent Magnetic Prandtl Number Bian, Xin; Shang, Jessica K.; Blackman, Eric G. The Astrophysical Journal Letters, Vol. 917, Issue 1 https://doi.org/10.3847/2041-8213/ac0fe5	journal	August 2021
On the double cascades of energy and enstrophy in two dimensional turbulence. Part 2. Approach to the KLB limit and interpretation of experimental evidence Gkioulekas, Eleftherios; Tung, Ka Kit Discrete and Continuous Dynamical Systems - Series B, Vol. 5, Issue 1 https://doi.org/10.3934/dcdsb.2005.5.103	journal	November 2004
Energy Spectrum of Turbulent Velocity Pulsations at Arbitrary Values of Fluid Viscosity Teodorovich, Edward V. Journal of Modern Physics, Vol. 11, Issue 10 https://doi.org/10.4236/jmp.2020.1110092	journal	January 2020
A note on Taylor's hypothesis under large-scale flow variation Wilczek, M.; Xu, H.; Narita, Y. Nonlinear Processes in Geophysics, Vol. 21, Issue 3 https://doi.org/10.5194/npg-21-645-2014	journal	January 2014
Theoretical comparison of subgrid turbulence in atmospheric and oceanic quasi-geostrophic models Kitsios, Vassili; Frederiksen, Jorgen S.; Zidikheri, Meelis J. Nonlinear Processes in Geophysics, Vol. 23, Issue 2 https://doi.org/10.5194/npg-23-95-2016	journal	January 2016
Error Growth in Three-Dimensional Homogeneous Turbulence Yoshimatsu, Katsunori; Ariki, Taketo Journal of the Physical Society of Japan, Vol. 88, Issue 12 https://doi.org/10.7566/JPSJ.88.124401	journal	December 2019

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
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Exascale computer
Geophysical turbulence
Intermittency
Large eddy simulation
Machine learning
Physics
Plasma and magnetohydrodynamics (MHD) turbulence
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Rayleigh–Taylor and Richtmyer–Meshkov instabilities
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