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The statistical geometry of material loops in turbulence

Author

Listed:
  • Lukas Bentkamp

    (Max Planck Institute for Dynamics and Self-Organization
    University of Bayreuth)

  • Theodore D. Drivas

    (Stony Brook University
    Institute for Advanced Study)

  • Cristian C. Lalescu

    (Max Planck Institute for Dynamics and Self-Organization
    Max Planck Computing and Data Facility)

  • Michael Wilczek

    (Max Planck Institute for Dynamics and Self-Organization
    University of Bayreuth)

Abstract

Material elements – which are lines, surfaces, or volumes behaving as passive, non-diffusive markers – provide an inherently geometric window into the intricate dynamics of chaotic flows. Their stretching and folding dynamics has immediate implications for mixing in the oceans or the atmosphere, as well as the emergence of self-sustained dynamos in astrophysical settings. Here, we uncover robust statistical properties of an ensemble of material loops in a turbulent environment. Our approach combines high-resolution direct numerical simulations of Navier-Stokes turbulence, stochastic models, and dynamical systems techniques to reveal predictable, universal features of these complex objects. We show that the loop curvature statistics become stationary through a dynamical formation process of high-curvature folds, leading to distributions with power-law tails whose exponents are determined by the large-deviations statistics of finite-time Lyapunov exponents of the flow. This prediction applies to advected material lines in a broad range of chaotic flows. To complement this dynamical picture, we confirm our theory in the analytically tractable Kraichnan model with an exact Fokker-Planck approach.

Suggested Citation

  • Lukas Bentkamp & Theodore D. Drivas & Cristian C. Lalescu & Michael Wilczek, 2022. "The statistical geometry of material loops in turbulence," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
  • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-29422-1
    DOI: 10.1038/s41467-022-29422-1
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    Cited by:

    1. Zijie Xu & Leo N. Y. Cao & Chengyu Li & Yingjin Luo & Erming Su & Weizhe Wang & Wei Tang & Zhaohui Yao & Zhong Lin Wang, 2023. "Digital mapping of surface turbulence status and aerodynamic stall on wings of a flying aircraft," Nature Communications, Nature, vol. 14(1), pages 1-11, December.

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