Pattern formation by turbulent cascades.
Journal
Nature
ISSN: 1476-4687
Titre abrégé: Nature
Pays: England
ID NLM: 0410462
Informations de publication
Date de publication:
Mar 2024
Mar 2024
Historique:
received:
04
05
2023
accepted:
15
01
2024
medline:
21
3
2024
pubmed:
21
3
2024
entrez:
21
3
2024
Statut:
ppublish
Résumé
Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales at which the cascade is eventually arrested by dissipation
Identifiants
pubmed: 38509279
doi: 10.1038/s41586-024-07074-z
pii: 10.1038/s41586-024-07074-z
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
515-521Informations de copyright
© 2024. The Author(s).
Références
Cardy, J., Falkovich, G. & Gawędzki, K. Non-equilibrium Statistical Mechanics and Turbulence London Mathematical Society Lecture Note Series 355 (Cambridge Univ. Press, 2008).
Davidson, P. Turbulence: An Introduction for Scientists and Engineers (Oxford Univ. Press, 2015).
Falkovich, G., Gawędzki, K. & Vergassola, M. Particles and fields in fluid turbulence. Rev. Mod. Phys. 73, 913–975 (2001).
doi: 10.1103/RevModPhys.73.913
Alexakis, A. & Biferale, L. Cascades and transitions in turbulent flows. Phys. Rep. 767, 1–101 (2018).
doi: 10.1016/j.physrep.2018.08.001
Eyink, G. L. & Sreenivasan, K. R. Onsager and the theory of hydrodynamic turbulence. Rev. Mod. Phys. 78, 87–135 (2006).
doi: 10.1103/RevModPhys.78.87
Frisch, U. Turbulence: The Legacy of AN Kolmogorov (Cambridge Univ. Press, 1995).
Cross, M. C. & Hohenberg, P. C. Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993).
doi: 10.1103/RevModPhys.65.851
Avron, J. E. Odd viscosity. J. Stat. Phys. 92, 543–557 (1998).
doi: 10.1023/A:1023084404080
Fruchart, M., Scheibner, C. & Vitelli, V. Odd viscosity and odd elasticity. Annu. Rev. Condens. Matter Phys. 14, 471–510 (2023).
doi: 10.1146/annurev-conmatphys-040821-125506
Berdyugin, A. I. et al. Measuring Hall viscosity of graphene’s electron fluid. Science 364, 162–165 (2019).
pubmed: 30819929
doi: 10.1126/science.aau0685
Morrison, P. J., Caldas, I. L. & Tasso, H. Hamiltonian formulation of two-dimensional gyroviscous MHD. Z. Naturforsch. A Phys. Sci. 39, 1023–1027 (1984).
doi: 10.1515/zna-1984-1102
van Saarloos, W., Vitelli, V. & Zeravcic, Z. Soft Matter: Concepts, Phenomena and Applications (Princeton Univ. Press, 2023).
Diamond, P. H., Itoh, S.-I., Itoh, K. & Hahm, T. S. Zonal flows in plasma—a review. Plasma Phys. Control. Fusion 47, R35 (2005).
doi: 10.1088/0741-3335/47/5/R01
Sukoriansky, S., Dikovskaya, N. & Galperin, B. On the arrest of inverse energy cascade and the rhines scale. J. Atmos. Sci. 64, 3312–3327 (2007).
doi: 10.1175/JAS4013.1
Berloff, P., Kamenkovich, I. & Pedlosky, J. A mechanism of formation of multiple zonal jets in the oceans. J. Fluid Mech. 628, 395–425 (2009).
doi: 10.1017/S0022112009006375
Chekhlov, A., Orszag, S. A., Sukoriansky, S., Galperin, B. & Staroselsky, I. The effect of small-scale forcing on large-scale structures in two-dimensional flows. Physica D 98, 321–334 (1996).
doi: 10.1016/0167-2789(96)00102-9
Rhines, P. B. Geostrophic turbulence. Ann. Rev. Fluid Mech. 11, 401–441 (1979).
doi: 10.1146/annurev.fl.11.010179.002153
Legras, B., Villone, B. & Frisch, U. Dispersive stabilization of the inverse cascade for the kolmogorov flow. Phys. Rev. Lett. 82, 4440–4443 (1999).
doi: 10.1103/PhysRevLett.82.4440
Grianik, N., Held, I. M., Smith, K. S. & Vallis, G. K. The effects of quadratic drag on the inverse cascade of two-dimensional turbulence. Phys. Fluids 16, 73–78 (2004).
doi: 10.1063/1.1630054
Squire, J. et al. High-frequency heating of the solar wind triggered by low-frequency turbulence. Nat. Astron. 6, 715–723 (2022).
doi: 10.1038/s41550-022-01624-z
Meyrand, R., Squire, J., Schekochihin, A. & Dorland, W. On the violation of the zeroth law of turbulence in space plasmas. J. Plasma Phys. 87, 535870301 (2021).
doi: 10.1017/S0022377821000489
Miloshevich, G., Laveder, D., Passot, T. & Sulem, P. L. Inverse cascade and magnetic vortices in kinetic alfvén-wave turbulence. J. Plasma Phys. 87, 905870201 (2021).
doi: 10.1017/S0022377820001531
Krapivsky, P., Redner, S. & Ben-Naim, E. A Kinetic View of Statistical Physics (Cambridge Univ. Press, 2010).
Testik, F. Y. & Barros, A. P. Toward elucidating the microstructure of warm rainfall: a survey. Rev. Geophys. 45, RG2003 (2007).
doi: 10.1029/2005RG000182
Friedlander, S. K. Smoke, Dust, and Haze 2nd edn, Vol. 198 (Oxford Univ. Press, 2000).
Zakharov, V. E., L’vov, V. S. & Falkovich, G. Kolmogorov Spectra of Turbulence I: Wave Turbulence (Springer, 2012).
Nazarenko, S. Wave Turbulence (Springer, 2011).
Galtier, S. Physics of Wave Turbulence (Cambridge Univ. Press, 2022).
Newell, A. C. & Rumpf, B. Wave turbulence. Annu. Rev. Fluid Mech. 43, 59–78 (2011).
doi: 10.1146/annurev-fluid-122109-160807
Khain, T., Scheibner, C., Fruchart, M. & Vitelli, V. Stokes flows in three-dimensional fluids with odd and parity-violating viscosities. J. Fluid Mech. 934, A23 (2022).
doi: 10.1017/jfm.2021.1079
Beenakker, J. J. M. & McCourt, F. R. Magnetic and electric effects on transport properties. Annu. Rev. Phys. Chem. 21, 47–72 (1970).
doi: 10.1146/annurev.pc.21.100170.000403
Soni, V. et al. The odd free surface flows of a colloidal chiral fluid. Nat. Phys. 15, 1188–1194 (2019).
doi: 10.1038/s41567-019-0603-8
Biferale, L. et al. Coherent structures and extreme events in rotating multiphase turbulent flows. Phys. Rev. X 6, 041036 (2016).
Buzzicotti, M., Aluie, H., Biferale, L. & Linkmann, M. Energy transfer in turbulence under rotation. Phys. Rev. Fluids 3, 034802 (2018).
doi: 10.1103/PhysRevFluids.3.034802
Deusebio, E., Boffetta, G., Lindborg, E. & Musacchio, S. Dimensional transition in rotating turbulence. Phys. Rev. E 90, 023005 (2014).
doi: 10.1103/PhysRevE.90.023005
Smith, L. M. & Waleffe, F. Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence. Phys. Fluids 11, 1608–1622 (1999).
doi: 10.1063/1.870022
Zeman, O. A note on the spectra and decay of rotating homogeneous turbulence. Phys. Fluids 6, 3221–3223 (1994).
doi: 10.1063/1.868053
Mininni, P. D., Rosenberg, D. & Pouquet, A. Isotropization at small scales of rotating helically driven turbulence. J. Fluid Mech. 699, 263–279 (2012).
doi: 10.1017/jfm.2012.99
Kraichnan, R. H. Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8, 1385–1387 (1965).
doi: 10.1063/1.1761412
Zhou, Y. A phenomenological treatment of rotating turbulence. Phys. Fluids 7, 2092–2094 (1995).
doi: 10.1063/1.868457
Chakraborty, S. & Bhattacharjee, J. K. Third-order structure function for rotating three-dimensional homogeneous turbulent flow. Phys. Rev. E 76, 036304 (2007).
doi: 10.1103/PhysRevE.76.036304
Zhou, Y., Matthaeus, W. & Dmitruk, P. Colloquium: magnetohydrodynamic turbulence and time scales in astrophysical and space plasmas. Rev. Mod. Phys. 76, 1015–1035 (2004).
doi: 10.1103/RevModPhys.76.1015
Miri, M.-A. & Alu, A. Exceptional points in optics and photonics. Science 363, eaar7709 (2019).
pubmed: 30606818
doi: 10.1126/science.aar7709
Balmforth, N. J. & Young, Y. N. Stratified Kolmogorov flow. J. Fluid Mech. 450, 131–167 (2002).
doi: 10.1017/S0022111002006371
Boffetta, G., De Lillo, F., Mazzino, A. & Musacchio, S. A flux loop mechanism in two-dimensional stratified turbulence. Europhys. Lett. 95, 34001 (2011).
doi: 10.1209/0295-5075/95/34001
Politi, P. & Misbah, C. When does coarsening occur in the dynamics of one-dimensional fronts? Phys. Rev. Lett. 92, 090601 (2004).
pubmed: 15089457
doi: 10.1103/PhysRevLett.92.090601
Halatek, J. & Frey, E. Rethinking pattern formation in reaction–diffusion systems. Nat. Phys. 14, 507–514 (2018).
doi: 10.1038/s41567-017-0040-5
Cates, M. E. & Tailleur, J. Motility-induced phase separation. Annu. Rev. Condens. Matter Phys. 6, 219–244 (2015).
doi: 10.1146/annurev-conmatphys-031214-014710
Perlekar, P., Benzi, R., Clercx, H. J. H., Nelson, D. R. & Toschi, F. Spinodal decomposition in homogeneous and isotropic turbulence. Phys. Rev. Lett. 112, 014502 (2014).
pubmed: 24483904
doi: 10.1103/PhysRevLett.112.014502
Theurkauff, I., Cottin-Bizonne, C., Palacci, J., Ybert, C. & Bocquet, L. Dynamic clustering in active colloidal suspensions with chemical signaling. Phys. Rev. Lett. 108, 268303 (2012).
pubmed: 23005020
doi: 10.1103/PhysRevLett.108.268303
van der Linden, M. N., Alexander, L. C., Aarts, D. G. A. L. & Dauchot, O. Interrupted motility induced phase separation in aligning active colloids. Phys. Rev. Lett. 123, 098001 (2019).
pubmed: 31524482
doi: 10.1103/PhysRevLett.123.098001
Biferale, L. Shell models of energy cascade in turbulence. Annu. Rev. Fluid Mech. 35, 441–468 (2003).
doi: 10.1146/annurev.fluid.35.101101.161122
Ghashghaie, S., Breymann, W., Peinke, J., Talkner, P. & Dodge, Y. Turbulent cascades in foreign exchange markets. Nature 381, 767–770 (1996).
doi: 10.1038/381767a0
Bouchaud, J.-P. & Muzy, J.-F. in The Kolmogorov Legacy in Physics (eds Livi, R. & Vulpiani, A.) Vol. 636, 229–246 (Springer, 2003).
Biferale, L., Musacchio, S. & Toschi, F. Inverse energy cascade in three-dimensional isotropic turbulence. Phys. Rev. Lett. 108, 164501 (2012).
pubmed: 22680722
doi: 10.1103/PhysRevLett.108.164501
Słomka, J. & Dunkel, J. Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3d active fluids. Proc. Natl Acad. Sci. USA 114, 2119–2124 (2017).
pubmed: 28193853
pmcid: 5338532
doi: 10.1073/pnas.1614721114
Xia, H., Byrne, D., Falkovich, G. & Shats, M. Upscale energy transfer in thick turbulent fluid layers. Nat. Phys. 7, 321–324 (2011).
doi: 10.1038/nphys1910
Peyret, R. Spectral Methods for Incompressible Viscous Flow Vol. 148 (Springer, 2002).
Mahalov, A. & Zhou, Y. Analytical and phenomenological studies of rotating turbulence. Phys. Fluids 8, 2138–2152 (1996).
doi: 10.1063/1.868988
Waleffe, F. The nature of triad interactions in homogeneous turbulence. Phys. Fluids 4, 350–363 (1992).
doi: 10.1063/1.858309
Celani, A., Musacchio, S. & Vincenzi, D. Turbulence in more than two and less than three dimensions. Phys. Rev. Lett. 104, 184506 (2010).
pubmed: 20482182
doi: 10.1103/PhysRevLett.104.184506
Falkovich, G. Bottleneck phenomenon in developed turbulence. Phys. Fluids 6, 1411–1414 (1994).
doi: 10.1063/1.868255
Küchler, C., Bewley, G. & Bodenschatz, E. Experimental study of the bottleneck in fully developed turbulence. J. Stat. Phys. 175, 617–639 (2019).
doi: 10.1007/s10955-019-02251-1
Lohse, D. & Müller-Groeling, A. Bottleneck effects in turbulence: scaling phenomena in r versus p space. Phys. Rev. Lett. 74, 1747–1750 (1995).
pubmed: 10057747
doi: 10.1103/PhysRevLett.74.1747
Donzis, D. A. & Sreenivasan, K. R. The bottleneck effect and the kolmogorov constant in isotropic turbulence. J. Fluid Mech. 657, 171–188 (2010).
doi: 10.1017/S0022112010001400
Verma, M. K. & Donzis, D. Energy transfer and bottleneck effect in turbulence. J. Phys. A Math. Theor. 40, 4401 (2007).
doi: 10.1088/1751-8113/40/16/010
Sreenivasan, K. R. & Antonia, R. A. The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435–472 (1997).
doi: 10.1146/annurev.fluid.29.1.435
Leoni, P. C. D., Alexakis, A., Biferale, L. & Buzzicotti, M. Phase transitions and flux-loop metastable states in rotating turbulence. Phys. Rev. Fluids 5, 104603 (2020).
doi: 10.1103/PhysRevFluids.5.104603
Dunkel, J. et al. Fluid dynamics of bacterial turbulence. Phys. Rev. Lett. 110, 228102 (2013).
pubmed: 23767750
doi: 10.1103/PhysRevLett.110.228102
Wensink, H. H. et al. Meso-scale turbulence in living fluids. Proc. Natl Acad. Sci. USA 109, 14308–14313 (2012).
pubmed: 22908244
pmcid: 3437854
doi: 10.1073/pnas.1202032109
Alert, R., Casademunt, J. & Joanny, J.-F. Active turbulence. Annu.Rev. Condens. Matter Phys. 13, 143–170 (2022).
doi: 10.1146/annurev-conmatphys-082321-035957
Martínez-Prat, B., Ignés-Mullol, J., Casademunt, J. & Sagués, F. Selection mechanism at the onset of active turbulence. Nat. Phys. 15, 362–366 (2019).
doi: 10.1038/s41567-018-0411-6
Alert, R., Joanny, J.-F. & Casademunt, J. Universal scaling of active nematic turbulence. Nat. Phys. 16, 682–688 (2020).
doi: 10.1038/s41567-020-0854-4
Carenza, L. N., Biferale, L. & Gonnella, G. Multiscale control of active emulsion dynamics. Phys. Rev. Fluids 5, 011302 (2020).
doi: 10.1103/PhysRevFluids.5.011302
Słomka, J. & Dunkel, J. Generalized Navier-Stokes equations for active suspensions. Eur. Phys. J. Special Topics 224, 1349–1358 (2015).
doi: 10.1140/epjst/e2015-02463-2
Rorai, C., Toschi, F. & Pagonabarraga, I. Coexistence of active and hydrodynamic turbulence in two-dimensional active nematics. Phys. Rev. Lett. 129, 218001 (2022).
pubmed: 36461968
doi: 10.1103/PhysRevLett.129.218001
Bratanov, V., Jenko, F. & Frey, E. New class of turbulence in active fluids. Proc. Natl Acad. Sci. USA 112, 15048–15053 (2015).
pubmed: 26598708
pmcid: 4679023
doi: 10.1073/pnas.1509304112
Mukherjee, S., Singh, R. K., James, M. & Ray, S. S. Intermittency, fluctuations and maximal chaos in an emergent universal state of active turbulence. Nat. Phys. 19, 891–897 (2023).
doi: 10.1038/s41567-023-01990-z
Linkmann, M., Boffetta, G., Marchetti, M. C. & Eckhardt, B. Phase transition to large scale coherent structures in two-dimensional active matter turbulence. Phys. Rev. Lett. 122, 214503 (2019).
pubmed: 31283308
doi: 10.1103/PhysRevLett.122.214503
Kiran, K. V., Gupta, A., Verma, A. K. & Pandit, R. Irreversibility in bacterial turbulence: Insights from the mean-bacterial-velocity model. Phys. Rev. Fluids 8, 023102 (2023).
doi: 10.1103/PhysRevFluids.8.023102
Marston, J. & Tobias, S. Recent developments in theories of inhomogeneous and anisotropic turbulence. Annu. Rev. Fluid Mech. 55, 351–375 (2023).
doi: 10.1146/annurev-fluid-120720-031006
Parker, J. B. & Krommes, J. A. Generation of zonal flows through symmetry breaking of statistical homogeneity. New J. Phys. 16, 035006 (2014).
doi: 10.1088/1367-2630/16/3/035006
Constantinou, N. C. & Parker, J. B. Magnetic suppression of zonal flows on a beta plane. Astrophys. J. 863, 46 (2018).
doi: 10.3847/1538-4357/aace53
Gürcan, O. D. & Diamond, P. H. Zonal flows and pattern formation. J. Phys. A Math. Theor. 48, 293001 (2015).
doi: 10.1088/1751-8113/48/29/293001
Parker, J. B. & Krommes, J. A. Zonal flow as pattern formation. Phys. Plasmas 20, 100703 (2013).
doi: 10.1063/1.4828717
Constantinou, N. C., Farrell, B. F. & Ioannou, P. J. Emergence and equilibration of jets in beta-plane turbulence: applications of stochastic structural stability theory. J. Atmos. Sci. 71, 1818–1842 (2014).
doi: 10.1175/JAS-D-13-076.1
Tuckerman, L. S., Chantry, M. & Barkley, D. Patterns in wall-bounded shear flows. Annu. Rev. Fluid Mech. 52, 343–367 (2020).
doi: 10.1146/annurev-fluid-010719-060221
Prigent, A., Grégoire, G., Chaté, H., Dauchot, O. & van Saarloos, W. Large-scale finite-wavelength modulation within turbulent shear flows. Phys. Rev. Lett. 89, 014501 (2002).
pubmed: 12097045
doi: 10.1103/PhysRevLett.89.014501
Duguet, Y., Schlatter, P. & Henningson, D. S. Formation of turbulent patterns near the onset of transition in plane couette flow. J. Fluid Mech. 650, 119–129 (2010).
doi: 10.1017/S0022112010000297
Kashyap, P. V., Duguet, Y. & Dauchot, O. Linear instability of turbulent channel flow. Phys. Rev. Lett. 129, 244501 (2022).
pubmed: 36563243
doi: 10.1103/PhysRevLett.129.244501
Vallis, G. K. & Maltrud, M. E. Generation of mean flows and jets on a beta plane and over topography. J. Phys. Oceanogr. 23, 1346–1362 (1993).
doi: 10.1175/1520-0485(1993)023<1346:GOMFAJ>2.0.CO;2
Galtier, S. Weak inertial-wave turbulence theory. Phys. Rev. E 68, 015301 (2003).
doi: 10.1103/PhysRevE.68.015301
Galperin, B., Sukoriansky, S. & Dikovskaya, N. Zonostrophic turbulence. Phys. Scr. 2008, 014034 (2008).
doi: 10.1088/0031-8949/2008/T132/014034
Meyrand, R., Galtier, S. & Kiyani, K. H. Direct evidence of the transition from weak to strong magnetohydrodynamic turbulence. Phys. Rev. Lett. 116, 105002 (2016).
pubmed: 27015486
doi: 10.1103/PhysRevLett.116.105002
McCourt, F. Nonequilibrium Phenomena in Polyatomic Gases (Oxford Univ. Press, 1990).
Avron, J. E., Seiler, R. & Zograf, P. G. Viscosity of quantum hall fluids. Phys. Rev. Lett. 75, 697–700 (1995).
pubmed: 10060091
doi: 10.1103/PhysRevLett.75.697
Ganeshan, S. & Abanov, A. G. Odd viscosity in two-dimensional incompressible fluids. Phys. Rev. Fluids 2, 094101 (2017).
doi: 10.1103/PhysRevFluids.2.094101
Nakagawa, Y. The kinetic theory of gases for the rotating system. J. Phys. Earth 4, 105–111 (1956).
doi: 10.4294/jpe1952.4.105
Chapman, S. & Cowling, T.The Mathematical Theory of Non-uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases (Cambridge Univ. Press, 1990).
Lingam, M., Morrison, P. J. & Wurm, A. A class of three-dimensional gyroviscous magnetohydrodynamic models. J. Plasma Phys. 86, 835860501 (2020).
doi: 10.1017/S0022377820001038
Hoyos, C. & Son, D. T. Hall viscosity and electromagnetic response. Phys. Rev. Lett. 108, 066805 (2012).
pubmed: 22401104
doi: 10.1103/PhysRevLett.108.066805
Read, N. Non-Abelian adiabatic statistics and hall viscosity in quantum hall states and p
doi: 10.1103/PhysRevB.79.045308
Vollhardt, D. & Wolfle, P. The Superfluid Phases of Helium 3 (Dover, 2013).
Wiegmann, P. & Abanov, A. G. Anomalous hydrodynamics of two-dimensional vortex fluids. Phys. Rev. Lett. 113, 034501 (2014).
pubmed: 25083647
doi: 10.1103/PhysRevLett.113.034501
Zhao, Z., Yang, M., Komura, S. & Seto, R. Odd viscosity in chiral passive suspensions. Front. Phys. https://doi.org/10.3389/fphy.2022.951465 (2022).
Banerjee, D., Souslov, A., Abanov, A. G. & Vitelli, V. Odd viscosity in chiral active fluids. Nat. Commun. 8, 1573 (2017).
pubmed: 29146894
pmcid: 5691086
doi: 10.1038/s41467-017-01378-7
Han, M. et al. Fluctuating hydrodynamics of chiral active fluids. Nat. Phys. 17, 1260–1269 (2021).
doi: 10.1038/s41567-021-01360-7
Markovich, T. & Lubensky, T. C. Odd viscosity in active matter: microscopic origin and 3d effects. Phys. Rev. Lett. 127, 048001 (2021).
pubmed: 34355935
doi: 10.1103/PhysRevLett.127.048001
Fruchart, M., Han, M., Scheibner, C. & Vitelli, V. The odd ideal gas: Hall viscosity and thermal conductivity from non-Hermitian kinetic theory. Preprint at https://doi.org/10.48550/arXiv.2202.02037 (2022).
Tsai, J.-C., Ye, F., Rodriguez, J., Gollub, J. P. & Lubensky, T. C. A chiral granular gas. Phys. Rev. Lett. 94, 214301 (2005).
pubmed: 16090323
doi: 10.1103/PhysRevLett.94.214301
Grzybowski, B. A., Stone, H. A. & Whitesides, G. M. Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid–air interface. Nature 405, 1033–1036 (2000).
pubmed: 10890439
doi: 10.1038/35016528
Yan, J., Bae, S. C. & Granick, S. Rotating crystals of magnetic Janus colloids. Soft Matter 11, 147–153 (2015).
pubmed: 25372218
doi: 10.1039/C4SM01962H
Bililign, E. S. et al. Motile dislocations knead odd crystals into whorls. Nat. Phys. 18, 212–218 (2021).
doi: 10.1038/s41567-021-01429-3
Tan, T. H. et al. Odd dynamics of living chiral crystals. Nature 607, 287–293 (2022).
pubmed: 35831595
doi: 10.1038/s41586-022-04889-6
Petroff, A. P., Wu, X.-L. & Libchaber, A. Fast-moving bacteria self-organize into active two-dimensional crystals of rotating cells. Phys. Rev. Lett. 114, 158102 (2015).
pubmed: 25933342
doi: 10.1103/PhysRevLett.114.158102
Ivlev, A., Löwen, H., Morfill, G. & Royall, C. P. Complex Plasmas and Colloidal Dispersions (World Scientific, 2012).
Ivlev, A. V. et al. Statistical mechanics where Newton’s third law is broken. Phys. Rev. X 5, 011035 (2015).
Denk, J., Huber, L., Reithmann, E. & Frey, E. Active curved polymers form vortex patterns on membranes. Phys. Rev. Lett. 116, 178301 (2016).
pubmed: 27176542
doi: 10.1103/PhysRevLett.116.178301
Liebchen, B. & Levis, D. Collective behavior of chiral active matter: Pattern formation and enhanced flocking. Phys. Rev. Lett. 119, 058002 (2017).
pubmed: 28949732
doi: 10.1103/PhysRevLett.119.058002
Connaughton, C., Nazarenko, S. & Quinn, B. Rossby and drift wave turbulence and zonal flows: the Charney–Hasegawa–Mima model and its extensions. Phys. Rep. 604, 1–71 (2015).
doi: 10.1016/j.physrep.2015.10.009
Boffetta, G., Lillo, F. D. & Musacchio, S. Inverse cascade in charney-hasegawa-mima turbulence. Europhys. Lett. 59, 687–693 (2002).
doi: 10.1209/epl/i2002-00180-y
Tassi, E., Chandre, C. & Morrison, P. J. Hamiltonian derivation of the Charney–Hasegawa–Mima equation. Phys. Plasmas 16, 082301 (2009).
doi: 10.1063/1.3194275
Hasegawa, A. & Mima, K. Stationary spectrum of strong turbulence in magnetized nonuniform plasma. Phys. Rev. Lett. 39, 205–208 (1977).
doi: 10.1103/PhysRevLett.39.205
Charney, J. G. Geostrophic turbulence. J. Atmos. Sci. 28, 1087–1095 (1971).
doi: 10.1175/1520-0469(1971)028<1087:GT>2.0.CO;2
Horton, W. Drift waves and transport. Rev. Mod. Phys. 71, 735–778 (1999).
doi: 10.1103/RevModPhys.71.735
Pedlosky, J. Geophysical Fluid Dynamics (Springer, 1979).
Rhines, P. B. Waves and turbulence on a beta-plane. J. Fluid Mech. 69, 417–443 (1975).
doi: 10.1017/S0022112075001504
Burns, K. J., Vasil, G. M., Oishi, J. S., Lecoanet, D. & Brown, B. P. Dedalus: a flexible framework for numerical simulations with spectral methods. Phys. Rev. Res. 2, 023068 (2020).
doi: 10.1103/PhysRevResearch.2.023068
Balk, A. M. A new invariant for rossby wave systems. Phys. Lett. A 155, 20–24 (1991).
doi: 10.1016/0375-9601(91)90501-X
Balk, A. M., Nazarenko, S. V. & Zakharov, V. E. New invariant for drift turbulence. Phys. Lett. A 152, 276–280 (1991).
doi: 10.1016/0375-9601(91)90105-H
Nazarenko, S. & Quinn, B. Triple cascade behavior in quasigeostrophic and drift turbulence and generation of zonal jets. Phys. Rev. Lett. 103, 118501 (2009).
pubmed: 19792408
doi: 10.1103/PhysRevLett.103.118501
Sahoo, G., Alexakis, A. & Biferale, L. Discontinuous transition from direct to inverse cascade in three-dimensional turbulence. Phys. Rev. Lett. 118, 164501 (2017).
pubmed: 28474929
doi: 10.1103/PhysRevLett.118.164501
Smoluchowski, M. Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen. Z. Phys. 17, 557–585 (1916).
Kolmogorov, A. N. On the logarithmically normal law of distribution of the size of particles under pulverization. Dokl. Akad. Nauk SSSR 31, 99–101 (1941).
Gorokhovski, M. & Herrmann, M. Modeling primary atomization. Annu. Rev. Fluid Mech. 40, 343–366 (2008).
doi: 10.1146/annurev.fluid.40.111406.102200
Brilliantov, N. et al. Size distribution of particles in saturn’s rings from aggregation and fragmentation. Proc. Natl Acad. Sci. USA 112, 9536–9541 (2015).
pubmed: 26183228
pmcid: 4534276
doi: 10.1073/pnas.1503957112
Cheng, Z. & Redner, S. Kinetics of fragmentation. J. Phys. A Math. Gen. 23, 1233–1258 (1990).
doi: 10.1088/0305-4470/23/7/028
Brilliantov, N. V., Otieno, W. & Krapivsky, P. L. Nonextensive supercluster states in aggregation with fragmentation. Phys. Rev. Lett. 127, 250602 (2021).
pubmed: 35029448
doi: 10.1103/PhysRevLett.127.250602
Leyvraz, F. Scaling theory and exactly solved models in the kinetics of irreversible aggregation. Phys. Rep. 383, 95–212 (2003).
doi: 10.1016/S0370-1573(03)00241-2
Wattis, J. A. An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach. Physica D 222, 1–20 (2006).
doi: 10.1016/j.physd.2006.07.024
Ramkrishna, D. & Singh, M. R. Population balance modeling: current status and future prospects. Annu. Rev. Chem. Biomol. Eng. 5, 123–146 (2014).
pubmed: 24606333
doi: 10.1146/annurev-chembioeng-060713-040241
Connaughton, C., Rajesh, R. & Zaboronski, O. Stationary Kolmogorov solutions of the Smoluchowski aggregation equation with a source term. Phys. Rev. E 69, 061114 (2004).
doi: 10.1103/PhysRevE.69.061114
Connaughton, C., Rajesh, R. & Zaboronski, O. Cluster-cluster aggregation as an analogue of a turbulent cascade: Kolmogorov phenomenology, scaling laws and the breakdown of self-similarity. Physica D 222, 97–115 (2006).
doi: 10.1016/j.physd.2006.08.005
Connaughton, C., Dutta, A., Rajesh, R., Siddharth, N. & Zaboronski, O. Stationary mass distribution and nonlocality in models of coalescence and shattering. Phys. Rev. E 97, 022137 (2018).
pubmed: 29548142
doi: 10.1103/PhysRevE.97.022137
Srivastava, R. C. Size distribution of raindrops generated by their breakup and coalescence. J. Atmos. Sci. 28, 410–415 (1971).
doi: 10.1175/1520-0469(1971)028<0410:SDORGB>2.0.CO;2
Testik, F. & Gebremichael, M. E. Rainfall: State of the Science, Geophysical Monograph Series (Wiley, 2013).
Pumir, A. & Wilkinson, M. Collisional aggregation due to turbulence. Annu. Rev. Condens. Matter Phys. 7, 141–170 (2016).
doi: 10.1146/annurev-conmatphys-031115-011538
Babler, M. U., Biferale, L. & Lanotte, A. S. Breakup of small aggregates driven by turbulent hydrodynamical stress. Phys. Rev. E 85, 025301 (2012).
doi: 10.1103/PhysRevE.85.025301
Grabowski, W. W. & Wang, L.-P. Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45, 293–324 (2013).
doi: 10.1146/annurev-fluid-011212-140750
Villermaux, E. Fragmentation. Annu. Rev. Fluid Mech. 39, 419–446 (2007).
doi: 10.1146/annurev.fluid.39.050905.110214
Falkovich, G., Fouxon, A. & Stepanov, M. G. Acceleration of rain initiation by cloud turbulence. Nature 419, 151–154 (2002).
pubmed: 12226661
doi: 10.1038/nature00983
Bec, J., Biferale, L., Cencini, M., Lanotte, A. S. & Toschi, F. Intermittency in the velocity distribution of heavy particles in turbulence. J. Fluid Mech. 646, 527–536 (2010).
doi: 10.1017/S0022112010000029
Rackauckas, C. & Nie, Q. DifferentialEquations.jl – a performant and feature-rich ecosystem for solving differential equations in Julia. J. Open Res. Softw. 5, 15 (2017).
doi: 10.5334/jors.151
Ball, R. C., Connaughton, C., Jones, P. P., Rajesh, R. & Zaboronski, O. Collective oscillations in irreversible coagulation driven by monomer inputs and large-cluster outputs. Phys. Rev. Lett. 109, 168304 (2012).
pubmed: 23215141
doi: 10.1103/PhysRevLett.109.168304
Matveev, S. A., Krapivsky, P. L., Smirnov, A. P., Tyrtyshnikov, E. E. & Brilliantov, N. V. Oscillations in aggregation-shattering processes. Phys. Rev. Lett. 119, 260601 (2017).
pubmed: 29328699
doi: 10.1103/PhysRevLett.119.260601
Politi, P. & Misbah, C. Nonlinear dynamics in one dimension: A criterion for coarsening and its temporal law. Phys. Rev. E 73, 036133 (2006).
doi: 10.1103/PhysRevE.73.036133
Ginot, F., Theurkauff, I., Detcheverry, F., Ybert, C. & Cottin-Bizonne, C. Aggregation-fragmentation and individual dynamics of active clusters. Nat. Commun. 9, 696 (2018).
pubmed: 29449564
pmcid: 5814572
doi: 10.1038/s41467-017-02625-7
Brauns, F., Weyer, H., Halatek, J., Yoon, J. & Frey, E. Wavelength selection by interrupted coarsening in reaction-diffusion systems. Phys. Rev. Lett. 126, 104101 (2021).
pubmed: 33784126
doi: 10.1103/PhysRevLett.126.104101
Ferraro, M., Mangini, F., Zitelli, M. & Wabnitz, S. On spatial beam self-cleaning from the perspective of optical wave thermalization in multimode graded-index fibers. Adv. Phys. X 8, 2228018 (2023).
Loman, T. et al. Catalyst: fast and flexible modeling of reaction networks. PLoS Comput. Biol. 19, e1011530 (2023).
Gaspard, P. The Statistical Mechanics of Irreversible Phenomena (Cambridge Univ. Press, 2022).
Kondepudi, D. & Prigogine, I. Modern Thermodynamics: From Heat Engines to Dissipative Structures (Wiley, 2014).
Schnakenberg, J. Network theory of microscopic and macroscopic behavior of master equation systems. Rev. Mod. Phys. 48, 571–585 (1976).
doi: 10.1103/RevModPhys.48.571
Rao, R. & Esposito, M. Nonequilibrium thermodynamics of chemical reaction networks: Wisdom from stochastic thermodynamics. Phys. Rev. X 6, 041064 (2016).
de Wit, X. M., Fruchart, M., Khain, T., Toschi, F. & Vitelli, V. Repository for: “Pattern formation by turbulent cascades”. Zenodo https://doi.org/10.5281/zenodo.10371195 (2023).
Ascher, U. M., Ruuth, S. J. & Spiteri, R. J. Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Numer. Math. 25, 151–167 (1997).
doi: 10.1016/S0168-9274(97)00056-1