- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Local linearity, coherent structures, and scale-to-scale coupling in turbulent flow

Lei Fang1, Sanjeeva Balasuriya2, and Nicholas T. Ouellette1,*

  • 1Department of Civil and Environmental Engineering, Stanford University, Stanford, California 94305, USA
  • 2School of Mathematical Sciences, University of Adelaide, Adelaide, South Australia 5005, Australia

  • *nto@stanford.edu
PDF

Phys. Rev. Fluids 4, 014501 – Published 4 January, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.014501

Abstract

Turbulent and other nonlinear flows are highly complex and time dependent, but are not fully random. To capture this spatiotemporal coherence, we introduce the idea of a linear neighborhood, defined as a region in an arbitrary flow field where the velocity gradient varies slowly in space over a finite time. Thus, by definition, the flow in a linear neighborhood can be approximated arbitrarily well by only a subset of the fluid-element trajectories inside it. This slow spatiotemporal variation also allows short-time prediction of the flow. We demonstrate that these linear neighborhoods are computable in real data using experimental measurements from a quasi-two-dimensional turbulent flow and find support for our theoretical arguments. We also show that our kinematically defined linear neighborhoods have an additional dynamical significance, in that the scale-to-scale spectral energy flux that is a hallmark of turbulent flows behaves differently inside the neighborhoods. Our results add additional support to the conjecture that turbulent flows locally tend to transport energy and momentum in space or in scale but not both simultaneously.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (37)

  1. G. Haller, Lagrangian coherent structures, Annu. Rev. Fluid Mech. 47, 137 (2015).
  2. S. Balasuriya, N. T. Ouellette, and I. I. Rypina, Generalized Lagrangian coherent structures, Physica D 372, 31 (2018).
  3. D. H. Kelley and N. T. Ouellette, Spatiotemporal persistence of spectral fluxes in two-dimensional weak turbulence, Phys. Fluids 23, 115101 (2011).
  4. N. T. Ouellette, On the dynamical role of coherent structures in turbulence, C. R. Phys. 13, 866 (2012).
  5. A. Hadjighasem, M. Farazmand, D. Blazevski, G. Froyland, and G. Haller, A critical comparison of Lagrangian methods for coherent structure detection, Chaos 27, 053104 (2017).
  6. S. Balasuriya, Barriers and Transport in Unsteady Flows: A Melnikov Approach (SIAM, Philadelphia, 2016).
  7. G. Haller and G. Yuan, Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D 147, 352 (2000).
  8. G. Haller, Lagrangian coherent structures from approximate velocity data, Phys. Fluids 14, 1851 (2002).
  9. E. Aurell, G. Boffetta, A. Crisanti, G. Paladin, and A. Vulpiani, Predictability in the large: An extension of the concept of Lyapunov exponent, J. Phys. A: Math. Gen. 30, 1 (1997).
  10. I. Mezić, S. Loire, V. A. Fonoberov, and P. Hogan, A new mixing diagnostic and Gulf oil spill movement, Science 330, 486 (2010).
  11. S. Balasuriya and G. Gottwald, Estimating stable and unstable sets and their role as transport barriers in stochastic flows, Phys. Rev. E 98, 013106 (2018).
  12. T. Ma and E. Bollt, Differential geometry perspective of shape coherence and curvature evolution by finite-time nonhyperbolic splitting, SIAM J. Appl. Dyn. Syst. 13, 1106 (2014).
  13. G. Froyland, Statistically optimal almost-invariant sets, Physica D 200, 205 (2005).
  14. G. Froyland and K. Padberg, Almost-invariant sets and invariant manifolds—Connecting probabilistic and geometric descriptions of coherent structures in flows, Physica D 238, 1507 (2009).
  15. G. Froyland and K. Padberg-Gehle, A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data, Chaos 25, 087406 (2015).
  16. A. Hadjighasem, D. Karrasch, H. Teramoto, and G. Haller, Spectral-clustering approach to Lagrangian vortex detection, Phys. Rev. E 93, 063107 (2016).
  17. K. L. Schlueter-Kuck and J. O. Dabiri, Coherent structure coloring: identification of coherent structures from sparse data using graph theory, J. Fluid Mech. 811, 468 (2017).
  18. S. Balasuriya, R. Kalampattel, and N. T. Ouellette, Hyperbolic neighbourhoods as organizers of finite-time exponential stretching, J. Fluid Mech. 807, 509 (2016).
  19. L. Fang and N. T. Ouellette, Advection and the Efficiency of Spectral Energy Transfer in Two-Dimensional Turbulence, Phys. Rev. Lett. 117, 104501 (2016).
  20. J. G. Ballouz and N. T. Ouellette, Tensor geometry in the turbulent cascade, J. Fluid Mech. 835, 1048 (2018).
  21. L. Fang and N. T. Ouellette, Multiple stages of decay in two-dimensional turbulence, Phys. Fluids 29, 111105 (2017).
  22. Y. Liao and N. T. Ouellette, Spatial structure of spectral transport in two-dimensional flow, J. Fluid Mech. 725, 281 (2013).
  23. D. H. Kelley and N. T. Ouellette, Onset of three-dimensionality in electromagnetically forced thin-layer flows, Phys. Fluids 23, 045103 (2011).
  24. L. Fang and N. T. Ouellette, Influence of lateral boundaries on transport in quasi-two-dimensional flow, Chaos 28, 023113 (2018).
  25. N. T. Ouellette, H. Xu, and E. Bodenschatz, A quantitative study of three-dimensional Lagrangian particle tracking algorithms, Exp. Fluids 40, 301 (2006).
  26. N. T. Ouellette, P. J. J. O'Malley, and J. P. Gollub, Transport of Finite-Sized Particles in Chaotic Flow, Phys. Rev. Lett. 101, 174504 (2008).
  27. G. A. Voth, G. Haller, and J. P. Gollub, Experimental Measurements of Stretching Fields in Fluid Mixing, Phys. Rev. Lett. 88, 254501 (2002).
  28. A. Okubo, Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences, Deep-Sea Res. Oceanogr. Abstr. 17, 445 (1970).
  29. J. Weiss, The dynamics of enstrophy transfer in two-dimensional hydrodynamics, Physica D 48, 273 (1991).
  30. M. Germano, Turbulence: The filtering approach, J. Fluid Mech. 238, 325 (1992).
  31. S. Liu, C. Meneveau, and J. Katz, On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet, J. Fluid Mech. 275, 83 (1994).
  32. G. L. Eyink, Local energy flux and the refined similarity hypothesis, J. Stat. Phys. 78, 335 (1995).
  33. M. K. Rivera, W. B. Daniel, S. Y. Chen, and R. E. Ecke, Energy and Enstrophy Transfer in Decaying Two-Dimensional Turbulence, Phys. Rev. Lett. 90, 104502 (2003).
  34. S. Chen, R. E. Ecke, G. L. Eyink, M. Rivera, M. Wan, and Z. Xiao, Physical Mechanism of the Two-Dimensional Inverse Energy Cascade, Phys. Rev. Lett. 96, 084502 (2006).
  35. Z. Xiao, M. Wan, S. Chen, and G. L. Eyink, Physical mechanism the inverse energy cascade of two-dimensional turbulence: A numerical approach, J. Fluid Mech. 619, 1 (2009).
  36. Y. Liao and N. T. Ouellette, Geometry of scale-to-scale energy and enstrophy transport in two-dimensional flow, Phys. Fluids 26, 045103 (2014).
  37. Y. Liao and N. T. Ouellette, Long-range ordering of turbulent stresses in two-dimensional flow, Phys. Rev. E 91, 063004 (2015).

Outline

Information

Phys. Rev. Fluids 4, 014501– Published 4 January, 2019
  • Received 20 July 2018
Article part of CHORUS
Crossmark - Check for updates button

©2019 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation