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Symmetry breaking in a turbulent environment

Alexandros Alexakis and François Pétrélis

Santiago J. Benavides

Kannabiran Seshasayanan

  • Laboratoire de Physique de l'École Normale Supérieure, CNRS, PSL Research University, Sorbonne Université, Université de Paris, F-75005 Paris, France

  • Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • Service de Physique de l'Etat Condensé, CNRS UMR 3680, CEA Saclay, 91191 Gif-sur-Yvette, France and Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721 302, India

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Phys. Rev. Fluids 6, 024605 – Published 15 February, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.024605

Abstract

In this work we investigate symmetry breaking in the presence of a turbulent environment. The transition from a symmetric state to a symmetry-breaking state is demonstrated using two examples: (1) the transition of a two-dimensional flow to a three-dimensional flow as the fluid layer thickness is varied and (2) the dynamo instability in a thin layer flow as the magnetic Reynolds number is varied. We show that these examples have similar critical exponents that differ from the mean-field predictions. The critical behavior can be related to the multiplicative nature of the fluctuations and can be predicted in certain limits using results from the statistical properties of random interfaces. Our results indicate the possibility of existence of a new class of out-of-equilibrium phase transition controlled by the multiplicative noise.

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References (28)

  1. S. K. Ma, Modern Theory of Critical Phenomena Frontiers in Physics (Benjamin, Reading, MA, 1976).
  2. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group Frontiers in Physics (Westview Press, Boulder, 1992).
  3. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, International Series of Monographs on Physics Vol. 113 (Clarendon Press, Oxford, 2002).
  4. K. A. Takeuchi, M. Kuroda, H. Chaté, and M. Sano, Directed Percolation Criticality in Turbulent Liquid Crystals, Phys. Rev. Lett. 99, 234503 (2007).
  5. G. Lemoult, L. Shi, K. Avila, S. V. Jalikop, M. Avila, and B. Hof, Directed percolation phase transition to sustained turbulence in Couette flow, Nat. Phys. 12, 254 (2016).
  6. M. Sano and K. Tamai, A universal transition to turbulence in channel flow, Nat. Phys. 12, 249 (2016).
  7. M. Chantry, L. S. Tuckerman, and D. Barkley, Universal continuous transition to turbulence in a planar shear flow, J. Fluid Mech. 824, R1 (2017).
  8. A. Alexakis and L. Biferale, Cascades and transitions in turbulent flows, Phys. Rep. 767, 1 (2018).
  9. D. Byrne and J. A. Zhang, Height-dependent transition from 3-D to 2-D turbulence in the hurricane boundary layer, Geophys. Res. Lett. 40, 1439 (2013).
  10. R. M. B. Young and P. L. Read, Forward and inverse kinetic energy cascades in Jupiter's turbulent weather layer, Nat. Phys. 13, 1135 (2017).
  11. J. Pedlosky, Geophysical Fluid Dynamics (Springer-Verlag, New York, 1987).
  12. S. J. Benavides and A. Alexakis, Critical transitions in thin layer turbulence, J. Fluid Mech. 822, 364 (2017).
  13. H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, 1978).
  14. K. Seshasayanan and F. Pétrélis, Growth rate distribution and intermittency in kinematic turbulent dynamos: Which moment predicts the dynamo onset? Europhys. Lett. 122, 64004 (2018).
  15. K. Seshasayanan, B. Gallet, and A. Alexakis, Transition to Turbulent Dynamo Saturation, Phys. Rev. Lett. 119, 204503 (2017).
  16. A. Alexakis, S. Fauve, C. Gissinger, and F. Pétrélis, Effect of fluctuations on mean-field dynamos, J. Plasma Phys. 84, 735840401 (2018).
  17. H. Fujisaka and T. Yamada, A new intermittency in coupled dynamical systems, Prog. Theor. Phys. 74, 918 (1985).
  18. N. Platt, E. A. Spiegel, and C. Tresser, On-Off Intermittency: A Mechanism for Bursting, Phys. Rev. Lett. 70, 279 (1993).
  19. M. A. Munoz, Multiplicative noise in non-equilibrium phase transitions: A tutorial, arXiv:cond-mat/0303650 (2003).
  20. U. C. Täuber, Critical dynamics: A Field Theory Approach to Equilibrium and Non-equilibrium Scaling Behavior (Cambridge University Press, 2014).
  21. M. Henkel, H. Hinrichsen, S. Lübeck, and M. Pleimling, Non-equilibrium Phase Transitions, Vol. 1 (Springer, 2008).
  22. Y. Tu, G. Grinstein, and M. A. Muñoz, Systems with Multiplicative Noise: Critical Behavior from KPZ Equation and Numerics, Phys. Rev. Lett. 78, 274 (1997).
  23. M. Kardar, G. Parisi, and Y.-C. Zhang, Dynamic Scaling of Growing Interfaces, Phys. Rev. Lett. 56, 889 (1986).
  24. T. Halpin-Healy and Y.-C. Zhang, Kinetic roughening phenomena, stochastic growth, directed polymers and all that: Aspects of multidisciplinary statistical mechanics, Phys. Rep. 254, 215 (1995).
  25. W. Genovese, M. A. Muñoz, and J. M. Sancho, Nonequilibrium transitions induced by multiplicative noise, Phys. Rev. E 57, R2495 (1998).
  26. Barber, M. N., in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Leibovitz (Academic, London, 1983), Vol. 8, pp. 146–259.
  27. F. Pétrélis and A. Alexakis, Anomalous Exponents at the Onset of an Instability, Phys. Rev. Lett. 108, 014501 (2012).
  28. A. Alexakis and F. Pétrélis, Critical exponents in zero dimensions, J. Stat. Phys. 149, 738 (2012).

Outline

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Phys. Rev. Fluids 6, 024605– Published 15 February, 2021
  • Received 19 April 2020
  • Accepted 28 January 2021
Article part of CHORUS
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