Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 111, Issue 21, Pages 7558-7563Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1321682111
Keywords
nonequilibrium systems; turbulent mixing; direct and inverse turbulent energy cascades; nonequilibrium statistical mechanics; Lagrangian description
Categories
Funding
- Max Planck Society
- Humboldt Foundation
- European Cooperation in Science and Technology Action Particles in Turbulence [MP0806]
- German Science Foundation [XU/91-3]
- Minerva Foundation
- Bi-National Science Foundation
- Agency of Natural Resources Grant Turbulent Evaporation and Condensation 2
- Australian Research Council [DP110101525, DE120100364]
- Australian Research Council [DE120100364] Funding Source: Australian Research Council
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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 away 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.
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