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Experimental test of the crossover between the inertial and the dissipative range in a turbulent swirling flow

Paul Debue, Denis Kuzzay, Ewe-Wei Saw, François Daviaud, and Bérengère Dubrulle

Léonie Canet and Vincent Rossetto

Nicolás Wschebor

  • SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France

  • Université Grenoble Alpes and CNRS, LPMMC, 38000 Grenoble, France

  • Instituto de Física, Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, 11000 Montevideo, Uruguay

Phys. Rev. Fluids 3, 024602 – Published 9 February, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.024602

Abstract

The kinetic energy spectrum of high-Reynolds turbulent swirling flows is experimentally studied. This spectrum, obtained from direct measurements in space, exhibits nearly two decades of Kolmogorov k5/3 decay in the inertial range of scales. Beyond this regime, in the dissipative range of scales, a crossover to a stretched exponential decay on scale k2/3 is observed, in full agreement with a recent theoretical prediction based on nonperturbative renormalization group theory.

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References (38)

  1. U. Frisch, Turbulence: The legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, UK, 1995).
  2. A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds number, Dokl. Akad. Nauk SSSR 30, 299 (1941).
  3. A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Proc. R. Soc. London, Ser. A 434, 9 (1991).
  4. L. Canet, V. Rossetto, N. Wschebor, and G. Balarac, Spatiotemporal velocity-velocity correlation function in fully developed turbulence, Phys. Rev. E 95, 023107 (2017).
  5. G. I. Taylor, The spectrum of turbulence, Proc. R. Soc. Lond. A Math. Phys. Sci. 164, 476 (1938).
  6. K. G. Wilson and J. Kogut, The renormalization group and the ε-expansion, Phys. Rep. C 12, 75 (1974).
  7. D. Forster, D. R. Nelson, and M. J. Stephen, Long-Time Tails and the Large-Eddy Behavior of a Randomly Stirred Fluid, Phys. Rev. Lett. 36, 867 (1976).
  8. D. Forster, D. R. Nelson, and M. J. Stephen, Large-distance and long-time properties of a randomly stirred fluid, Phys. Rev. A 16, 732 (1977).
  9. C. DeDominicis and P. C. Martin, Energy spectra of certain randomly-stirred fluids, Phys. Rev. A 19, 419 (1979).
  10. J. D. Fournier and U. Frisch, Remarks on the renormalization group in statistical fluid dynamics, Phys. Rev. A 28, 1000 (1983).
  11. L. T. Adzhemyan, N. V. Antonov, and A. N. Vasil'ev, The Field Theoretic Renormalization Group in Fully Developed Turbulence (Gordon and Breach, London, 1999).
  12. Y. Zhou, Renormalization group theory for fluid and plasma turbulence, Phys. Rep. 488, 1 (2010).
  13. P. Tomassini, An exact renormalization group analysis of 3D well developed turbulence, Phys. Lett. B 411, 117 (1997).
  14. C. Mejía-Monasterio and P. Muratore-Ginanneschi, Nonperturbative renormalization group study of the stochastic Navier-Stokes equation, Phys. Rev. E 86, 016315 (2012).
  15. A. A. Fedorenko, P. L. Doussal, and K. J. Wiese, Functional renormalization group approach to decaying turbulence, J. Stat. Mech.: Theory Exp. (2013) P04014.
  16. L. Canet, B. Delamotte, and N. Wschebor, Fully developed isotropic turbulence: Nonperturbative renormalization group formalism and fixed-point solution, Phys. Rev. E 93, 063101 (2016).
  17. C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301, 90 (1993).
  18. J. Berges, N. Tetradis, and C. Wetterich, Non-perturbative renormalization flow in quantum field theory and statistical physics, Phys. Rep. 363, 223 (2002).
  19. B. Delamotte, in An introduction to the Non-perturbative Renormalization Group in Renormalization Group and Effective Field Theory Approaches to Many-Body Systems, edited by J. Polonyi and A. Schwenk, Lecture Notes in Physics, Vol. 852 (Springer, Berlin, 2012).
  20. P. Kopietz, L. Bartosch, and F. Schütz, Introduction to the Functional Renormalization Group, Lecture Notes in Physics, Vol. 798 (Springer, Berlin, 2010).
  21. N. V. Antonov, S. V. Borisenok, and V. I. Girina, Renormalisation group in the theory of fully developed turbulence. Composite operators of canonical dimension 8, Theor. Math. Phys. 106, 75 (1996).
  22. A. Berera and D. Hochberg, Gauge Symmetry and Slavnov-Taylor Identities for Randomly Stirred Fluids, Phys. Rev. Lett. 99, 254501 (2007).
  23. L. Canet, B. Delamotte, and N. Wschebor, Fully developed isotropic turbulence. Symmetries and exact identities, Phys. Rev. E 91, 053004 (2015).
  24. F. Ravelet, A. Chiffaudel, and F. Daviaud, Supercritical transition to turbulence in an inertially-driven von Kármán closed flow, J. Fluid Mech. 601, 339 (2008).
  25. B. Saint-Michel, B. Dubrulle, L. Mari, F. Ravelet, and F. Daviaud, Evidence for Forcing-Dependent Steady States in a Turbulent Swirling Flow, Phys. Rev. Lett. 111, 234502 (2013).
  26. Y. Zhou, Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations, Phys. Plasmas 14, 082701 (2007).
  27. E. W. Saw, D. Kuzzay, D. Faranda, A. Guittonneau, F. Daviaud, C. Wiertel-Gasquet, V. Padilla, and B. Dubrulle, Experimental characterization of extreme events of inertial dissipation in a turbulent swirling flow, Nat. Commun. 7, 12466 (2016).
  28. N. Ouellette, H. Xu, M. Bourgoin, and E. Bodenschatz, Small-scale anisotropy in Lagrangian turbulence, New J. Phys. 8, 102 (2006).
  29. Y. Zhou, W. H. Matthaeus, and P. Dmitruk, Colloquium: Magnetohydrodynamic turbulence and time scales in astrophysical and space plasmas, Rev. Mod. Phys. 76, 1015 (2004).
  30. http://turbulence.pha.jhu.edu.
  31. E. Herbert, F. Daviaud, B. Dubrulle, S. Nazarenko, and A. Naso, Dual non-Kolmogorov cascades in a von Kármán flow, EPL 100, 44003 (2012).
  32. Y. Li, E. Perlman, M. Wan, Y. Yang, R. Burns, C. Meneveau, S. Chen, A. Szalay, and G. Eyink, A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence, J. Turbulence 9, N31 (2008).
  33. E. Perlman, R. Burns, Y. Li, and C. Meneveau, Data Exploration of Turbulence Simulations using a Database Cluster, in Proceedings of the 2007 ACM/IEEE Conference on Supercomputing, SC '07 (ACM, New York, 2007), pp. 23:1–23:11.
  34. D. Kuzzay, D. Faranda, and B. Dubrulle, Global vs local energy dissipation: The energy cycle of the turbulent von Kármán flow, Phys. Fluids 27, 075105 (2015).
  35. E.-W. Saw, P. Debue, D. Kuzzay, F. Daviaud, and B. Dubrulle, On the universality of anomalous scaling exponents of structure functions in turbulent flows, J. Fluid Mech. 837, 657 (2018).
  36. http://www.fast.u-psud.fr/pivmat/.
  37. J. M. Foucaut, J. Carlier, and M. Stanislas, PIV optimization for the study of turbulent flow using spectral analysis, Meas. Sci. Technol. 15, 1046 (2004).
  38. M. Farge and K. Schneider, Wavelets: Application to turbulence, in Encyclopedia of Mathematical Physics. edited by J. P. Françoise, G. L. Naber, and T. S. Tsun (Academic, Oxford, 2006), pp. 408–20.

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