The statistical geometry of material loops in turbulence.

Autor: Bentkamp L; Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077, Göttingen, Germany.; Theoretical Physics I, University of Bayreuth, Universitätsstraße 30, 95447, Bayreuth, Germany., Drivas TD; Mathematics Department, Stony Brook University, 100 Nicolls Rd., Stony Brook, NY, 11794, USA.; School of Mathematics, Institute for Advanced Study, 1 Einstein Dr., Princeton, NJ, 08540, USA., Lalescu CC; Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077, Göttingen, Germany.; Max Planck Computing and Data Facility, Gießenbachstraße 2, 85748, Garching b. München, Germany., Wilczek M; Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077, Göttingen, Germany. michael.wilczek@uni-bayreuth.de.; Theoretical Physics I, University of Bayreuth, Universitätsstraße 30, 95447, Bayreuth, Germany. michael.wilczek@uni-bayreuth.de.
Jazyk: angličtina
Zdroj: Nature communications [Nat Commun] 2022 Apr 19; Vol. 13 (1), pp. 2088. Date of Electronic Publication: 2022 Apr 19.
DOI: 10.1038/s41467-022-29422-1
Abstrakt: 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.
(© 2022. The Author(s).)
Databáze: MEDLINE
Externí odkaz: