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The statistical properties of turbulence differ in an essential way from those of systems in or near thermal equilibrium because of the flux of energy between vastly different scales at which energy is supplied and at which it is dissipated. We elucidate this difference by studying experimentally and numerically the fluctuations of the energy of a small fluid particle moving in a turbulent fluid. We demonstrate how the fundamental property of detailed balance is broken, so that the probabilities of forward and backward transitions are not equal for turbulence. In physical terms, we found that in a large set of flow configurations, fluid elements decelerate faster than accelerate, a feature known all too well from driving in dense traffic. The statistical signature of rare "flight-crash" events, associated with fast particle deceleration, provides a way to quantify irreversibility in a turbulent flow. Namely, we find that the third moment of the power fluctuations along a trajectory, nondimensionalized by the energy flux, displays a remarkable power law as a function of the Reynolds number, both in two and in three spatial dimensions. This establishes a relation between the irreversibility of the system and the range of active scales. We speculate that the breakdown of the detailed balance characterized here is a general feature of other systems very far from equilibrium, displaying a wide range of spatial scales.

@article{ title = {Flight-crash events in turbulence}, type = {article}, year = {2014}, keywords = {Lagrangian description,direct and inverse turbulent energy cascades,nonequilibrium statistical mechanics,nonequilibrium systems,turbulent mixing}, pages = {7558-7563}, volume = {111}, websites = {http://www.ncbi.nlm.nih.gov/pubmed/24794529,http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=PMC4040622,http://www.pnas.org/cgi/doi/10.1073/pnas.1321682111}, month = {4}, publisher = {National Academy of Sciences}, id = {fda3961e-245e-3a03-a910-a65e04ccf982}, created = {2021-04-09T15:23:34.122Z}, file_attached = {false}, profile_id = {75799766-8e2d-3c98-81f9-e3efa41233d0}, group_id = {c9329632-2a50-3043-b803-cadc8dbdfc3f}, last_modified = {2021-04-09T15:23:34.122Z}, read = {false}, starred = {false}, authored = {false}, confirmed = {false}, hidden = {false}, source_type = {article}, private_publication = {false}, abstract = {The statistical properties of turbulence differ in an essential way from those of systems in or near thermal equilibrium because of the flux of energy between vastly different scales at which energy is supplied and at which it is dissipated. We elucidate this difference by studying experimentally and numerically the fluctuations of the energy of a small fluid particle moving in a turbulent fluid. We demonstrate how the fundamental property of detailed balance is broken, so that the probabilities of forward and backward transitions are not equal for turbulence. In physical terms, we found that in a large set of flow configurations, fluid elements decelerate faster than accelerate, a feature known all too well from driving in dense traffic. The statistical signature of rare "flight-crash" events, associated with fast particle deceleration, provides a way to quantify irreversibility in a turbulent flow. Namely, we find that the third moment of the power fluctuations along a trajectory, nondimensionalized by the energy flux, displays a remarkable power law as a function of the Reynolds number, both in two and in three spatial dimensions. This establishes a relation between the irreversibility of the system and the range of active scales. We speculate that the breakdown of the detailed balance characterized here is a general feature of other systems very far from equilibrium, displaying a wide range of spatial scales.}, bibtype = {article}, author = {Xu, Haitao and Pumir, Alain and Falkovich, Gregory and Bodenschatz, Eberhard and Shats, Michael and Xia, Hua and Francois, Nicolas and Boffetta, Guido}, doi = {10.1073/pnas.1321682111}, journal = {Proceedings of the National Academy of Sciences}, number = {21} }

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