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Lagrangian view of time irreversibility of fluid turbulence

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  • Fluid Dynamics/The 6th Tsien Hsue Shen Memorial Lecture
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Abstract

A turbulent flow is maintained by an external supply of kinetic energy, which is eventually dissipated into heat at steep velocity gradients. The scale at which energy is supplied greatly differs from the scale at which energy is dissipated, the more so as the turbulent intensity (the Reynolds number) is larger. The resulting energy flux over the range of scales, intermediate between energy injection and dissipation, acts as a source of time irreversibility. As it is now possible to follow accurately fluid particles in a turbulent flow field, both from laboratory experiments and from numerical simulations, a natural question arises: how do we detect time irreversibility from these Lagrangian data? Here we discuss recent results concerning this problem. For Lagrangian statistics involving more than one fluid particle, the distance between fluid particles introduces an intrinsic length scale into the problem. The evolution of quantities dependent on the relative motion between these fluid particles, including the kinetic energy in the relative motion, or the configuration of an initially isotropic structure can be related to the equal-time correlation functions of the velocity field, and is therefore sensitive to the energy flux through scales, hence to the irreversibility of the flow. In contrast, for singleparticle Lagrangian statistics, the most often studied velocity structure functions cannot distinguish the “arrow of time”. Recent observations from experimental and numerical simulation data, however, show that the change of kinetic energy following the particle motion, is sensitive to time-reversal. We end the survey with a brief discussion of the implication of this line of work.

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Authors and Affiliations

  1. Center for Combustion Energy and Department of Thermal Engineering, Tsinghua University, Beijing, 100084, China

    HaiTao Xu

  2. Max Planck Institute for Dynamics & Self-Organization (MPIDS), Göttingen, D-37077, Germany

    HaiTao Xu, Alain Pumir & Eberhard Bodenschatz

  3. Ecole Normale Supérieure de Lyon, Lyon, F-69007, France

    Alain Pumir

  4. Institute for Nonlinear Dynamics, University of Göttingen, Göttingen, D-37077, Germany

    Eberhard Bodenschatz

  5. Laboratory of Atomic and Solid State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, 14853, USA

    Eberhard Bodenschatz

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  1. HaiTao Xu
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  2. Alain Pumir
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Correspondence to HaiTao Xu.

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Xu, H., Pumir, A. & Bodenschatz, E. Lagrangian view of time irreversibility of fluid turbulence. Sci. China Phys. Mech. Astron. 59, 614702 (2016). https://doi.org/10.1007/s11433-015-5736-x

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