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Annual Review of Fluid Mechanics

Volume 57, 2025

Turbulence from an Observer Perspective

Abstract

Turbulence is often studied by tracking its spatiotemporal evolution and analyzing the dynamics of its different scales. The dual to this perspective is that of an observer who starts from measurements, or observations, of turbulence and attempts to identify their back-in-time origin, which is the foundation of data assimilation. This back-in-time search must contend with the action of chaos, which obfuscates the interpretation of the observations. When the available measurements satisfy a critical resolution threshold, the influence of chaos can be entirely mitigated and turbulence can be synchronized to the exact state–space trajectory that generated the observations. The critical threshold offers a new interpretation of the Taylor microscale, one that underscores its causal influence. Below the critical threshold, the origin of measurements becomes less definitive in regions where the flow is inconsequential to the observations. In contrast, flow events that influence the measurements, or are within their domain of dependence, are accurately captured. The implications for our understanding of wall turbulence are explored, starting with the highest density of measurements that entirely tame chaos and proceeding all the way to an isolated measurement of wall stress. The article concludes with a discussion of future opportunities and a call to action.

Keyword(s): data assimilation, measurement domain of dependence, state estimation, turbulence observability
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2025-01-22
2025-04-25
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Literature Cited

  1. Abe H, Kawamura H, Choi H. 2004.. Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to Reτ= 640. . J. Fluids Eng. 126:(5):835–43
     [Crossref] [Google Scholar]
  2. Arun R, Bae HJ, McKeon BJ. 2023.. Towards real-time reconstruction of velocity fluctuations in turbulent channel flow. . Phys. Rev. Fluids 8:(6):064612
     [Crossref] [Google Scholar]
  3. Bandak D, Mailybaev AA, Eyink GL, Goldenfeld N. 2024.. Spontaneous stochasticity amplifies even thermal noise to the largest scales of turbulence in a few eddy turnover times. . Phys. Rev. Lett. 132:(10):104002
     [Crossref] [Google Scholar]
  4. Besse N, Frisch U. 2017.. Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces. . J. Fluid. Mech. 825::412–78
     [Crossref] [Google Scholar]
  5. Blonigan PJ. 2017.. Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing. . J. Comput. Phys. 348::803–26
     [Crossref] [Google Scholar]
  6. Buchta DA, Laurence SJ, Zaki TA. 2022.. Assimilation of wall-pressure measurements in high-speed flow over a cone. . J. Fluid Mech. 947::R2
     [Crossref] [Google Scholar]
  7. Buchta DA, Zaki TA. 2021.. Observation-infused simulations of high-speed boundary-layer transition. . J. Fluid Mech. 916::A44
     [Crossref] [Google Scholar]
  8. Chandramoorthy N, Fernandez P, Talnikar C, Wang Q. 2019.. Feasibility analysis of ensemble sensitivity computation in turbulent flows. . AIAA J. 57:(10):4514–26
     [Crossref] [Google Scholar]
  9. Charney J, Halem M, Jastrow R. 1969.. Use of incomplete historical data to infer the present state of the atmosphere. . J. Atmos. Sci. 26:(5):1160–63
     [Crossref] [Google Scholar]
  10. Chevalier M, Hœpffner J, Bewley TR, Henningson DS. 2006.. State estimation in wall-bounded flow systems. Part 2. Turbulent flows. . J. Fluid Mech. 552::167–87
     [Crossref] [Google Scholar]
  11. Clark Di Leoni P, Mazzino A, Biferale L. 2020.. Synchronization to big data: Nudging the Navier-Stokes equations for data assimilation of turbulent flows. . Phys. Rev. X 10:(1):011023
     [Google Scholar]
  12. Constantin P, Iyer G. 2008.. A stochastic Lagrangian representation of the 3-dimensional incompressible Navier-Stokes equations. . Pure Appl. Math. 61::330–45
     [Crossref] [Google Scholar]
  13. Courtier P, Derber J, Errico R, Louis JF, Vukićević T. 1993.. Important literature on the use of adjoint, variational methods and the Kalman filter in meteorology. . Tellus A Dyn. Meteorol. Oceanogr. 45:(5):342–57
     [Crossref] [Google Scholar]
  14. Dimet FXL, Talagrand O. 1986.. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. . Tellus A Dyn. Meteorol. Oceanogr. 38:(2):97–110
     [Crossref] [Google Scholar]
  15. Encinar MP, Jiménez J. 2019.. Logarithmic-layer turbulence: a view from the wall. . Phys. Rev. Fluids 4:(11):114603
     [Crossref] [Google Scholar]
  16. Eyink G, Haine T, Lea D. 2004.. Ruelle's linear response formula, ensemble adjoint schemes and Lévy flights. . Nonlinearity 17:(5):1867–89
     [Crossref] [Google Scholar]
  17. Eyink GL, Gupta A, Zaki TA. 2020.. Stochastic Lagrangian dynamics of vorticity. Part 1. General theory for viscous, incompressible fluids. . J. Fluid Mech. 901::A2
     [Crossref] [Google Scholar]
  18. Fowler M, Zaki TA, Meneveau C. 2023.. A multi-time-scale wall model for large-eddy simulations and applications to non-equilibrium channel flows. . J. Fluid Mech. 974::A51
     [Crossref] [Google Scholar]
  19. Fratantonio D, Lai CCK, Charonko J, Prestridge K. 2021.. Beyond Taylor's hypothesis: a novel volumetric reconstruction of velocity and density fields for variable-density and shear flows. . Exp. Fluids 62:(4):84
     [Crossref] [Google Scholar]
  20. Graham MD, Floryan D. 2021.. Exact coherent states and the nonlinear dynamics of wall-bounded turbulent flows. . Annu. Rev. Fluid Mech. 53::227–53
     [Crossref] [Google Scholar]
  21. Grötzbach G. 1987.. Direct numerical and large eddy simulation of turbulent channel flows. . In Encyclopedia of Fluid Mechanics, Vol. 6:: Complex Flow Phenomena and Modeling, ed. NP Cheremisinoff , pp. 1337–91. Houston:: Gulf
     [Google Scholar]
  22. Hamilton JM, Kim J, Waleffe F. 1995.. Regeneration mechanisms of near-wall turbulence structures. . J. Fluid Mech. 287::317–48
     [Crossref] [Google Scholar]
  23. Hansen C, Yang XI, Abkar M. 2023.. A pod-mode-augmented wall model and its applications to flows at non-equilibrium conditions. . J. Fluid Mech. 975::A24
     [Crossref] [Google Scholar]
  24. Hunt J, Durbin P. 1999.. Perturbed vortical layers and shear sheltering. . Fluid Dyn. Res. 24:(6):375–404
     [Crossref] [Google Scholar]
  25. Hutchins N, Nickels TB, Marusic I, Chong MS. 2009.. Hot-wire spatial resolution issues in wall-bounded turbulence. . J. Fluid. Mech. 635::103–36
     [Crossref] [Google Scholar]
  26. Hwang J, Lee J, Sung HJ, Zaki TA. 2016.. Inner–outer interactions of large-scale structures in turbulent channel flow. . J. Fluid Mech. 790::128–57
     [Crossref] [Google Scholar]
  27. Illingworth SJ, Monty JP, Marusic I. 2018.. Estimating large-scale structures in wall turbulence using linear models. . J. Fluid Mech. 842::146–62
     [Crossref] [Google Scholar]
  28. Jiménez J. 2013.. How linear is wall-bounded turbulence?. Phys. Fluids 25:(11):110814
     [Crossref] [Google Scholar]
  29. Jiménez J. 2018.. Machine-aided turbulence theory. . J. Fluid Mech. 854::R1
     [Crossref] [Google Scholar]
  30. Jiménez J, Pinelli A. 1999.. The autonomous cycle of near-wall turbulence. . J. Fluid Mech. 389::335–59
     [Crossref] [Google Scholar]
  31. Kennedy RE, Laurence SJ, Smith MS, Marineau EC. 2018.. Investigation of the second-mode instability at Mach 14 using calibrated schlieren. . J. Fluid Mech. 845::R2
     [Crossref] [Google Scholar]
  32. Lalescu CC, Meneveau C, Eyink GL. 2013.. Synchronization of chaos in fully developed turbulence. . Phys. Rev. Lett. 110:(8):084102
     [Crossref] [Google Scholar]
  33. Lea DJ, Allen MR, Haine TWN. 2000.. Sensitivity analysis of the climate of a chaotic system. . Tellus A Dyn. Meteorol. Oceanogr. 52:(5):523–32
     [Crossref] [Google Scholar]
  34. Lea DJ, Haine TWN, Allen MR, Hansen JA. 2002.. Sensitivity analysis of the climate of a chaotic ocean circulation model. . Q. J. R. Meteorol. Soc. 128:(586):2587–605
     [Crossref] [Google Scholar]
  35. Lee JH, Kevin , Monty JP, Hutchins N. 2016.. Validating under-resolved turbulence intensities for PIV experiments in canonical wall-bounded turbulence. . Exp. Fluids 57::129
     [Crossref] [Google Scholar]
  36. Li Y, Zhang J, Dong G, Abdullah NS. 2020.. Small-scale reconstruction in three-dimensional Kolmogorov flows using four-dimensional variational data assimilation. . J. Fluid Mech. 885::A9
     [Crossref] [Google Scholar]
  37. Lorenz EN. 1963.. Deterministic nonperiodic flow. . J. Atmos. Sci. 20:(2):130–41
     [Crossref] [Google Scholar]
  38. Lorenz EN. 1972.. Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas? Paper presented at the 139th Meeting of the American Association for the Advancement of Science, Washington, DC:, Dec. 29
    [Google Scholar]
  39. Luchini P. 2017.. Receptivity to thermal noise of the boundary layer over a swept wing. . AIAA J. 55:(1):121–30
     [Crossref] [Google Scholar]
  40. Lumley JL. 1967.. The structure of inhomogeneous turbulence. . In Atmospheric Turbulence and Wave Propagation, ed. AM Yaglom, VI Tatarski , pp. 166–78. Moscow:: Nauka
     [Google Scholar]
  41. Mathis R, Hutchins N, Marusic I. 2009.. Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. . J. Fluid Mech. 628::311–37
     [Crossref] [Google Scholar]
  42. McKeon BJ, Sharma AS. 2010.. A critical-layer framework for turbulent pipe flow. . J. Fluid Mech. 658::336–82
     [Crossref] [Google Scholar]
  43. Meneveau C. 2020.. A note on fitting a generalised Moody diagram for wall modelled large-eddy simulations. . J. Turbul. 21:(11):650–73
     [Crossref] [Google Scholar]
  44. Meneveau C, Katz J. 2000.. Scale-invariance and turbulence models for large-eddy simulation. . Annu. Rev. Fluid Mech. 32::1–32
     [Crossref] [Google Scholar]
  45. Moin P, Mahesh K. 1998.. Direct numerical simulation: a tool in turbulence research. . Annu. Rev. Fluid Mech. 30::539–78
     [Crossref] [Google Scholar]
  46. Mons V, Chassaing JC, Gomez T, Sagaut P. 2016.. Reconstruction of unsteady viscous flows using data assimilation schemes. . J. Comput. Phys. 316::255–80
     [Crossref] [Google Scholar]
  47. Mons V, Du Y, Zaki TA. 2021.. Ensemble-variational assimilation of statistical data in large-eddy simulation. . Phys. Rev. Fluids 6:(10):104607
     [Crossref] [Google Scholar]
  48. Moser RD, Kim J, Mansour NN. 1999.. Direct numerical simulation of turbulent channel flow up to Reτ = 590. . Phys. Fluids 11:(4):943–45
     [Crossref] [Google Scholar]
  49. Ni A, Talnikar C. 2019.. Adjoint sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS). . J. Comput. Phys. 395::690–709
     [Crossref] [Google Scholar]
  50. Ni A, Wang Q. 2017.. Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS). . J. Comput. Phys. 347::56–77
     [Crossref] [Google Scholar]
  51. Nikitin N. 2018.. Characteristics of the leading Lyapunov vector in a turbulent channel flow. . J. Fluid Mech. 849::942–67
     [Crossref] [Google Scholar]
  52. Nikolaidis MA, Ioannou PJ. 2022.. Synchronization of low Reynolds number plane Couette turbulence. . J. Fluid Mech. 933::A5
     [Crossref] [Google Scholar]
  53. Pecora LM, Carroll TL. 1990.. Synchronization in chaotic systems. . Phys. Rev. Lett. 64:(8):821–24
     [Crossref] [Google Scholar]
  54. Phillips OM. 1969.. Shear-flow turbulence. . Annu. Rev. Fluid Mech. 1::245–64
     [Crossref] [Google Scholar]
  55. Pikovsky A, Rosenblum M, Kurths J. 2001.. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge, UK:: Cambridge Univ. Press
     [Google Scholar]
  56. Piomelli U, Ferziger J, Moin P, Kim J. 1989.. New approximate boundary conditions for large eddy simulations of wall-bounded flows. . Phys. Fluids A Fluid Dyn. 1:(6):1061–68
     [Crossref] [Google Scholar]
  57. Reynolds O. 1895.. IV. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. . Philos. Trans. R. Soc. Lond. A 186::123–64
     [Crossref] [Google Scholar]
  58. Sasaki K, Vinuesa R, Cavalieri AVG, Schlatter P, Henningson DS. 2019.. Transfer functions for flow predictions in wall-bounded turbulence. . J. Fluid Mech. 864::708–45
     [Crossref] [Google Scholar]
  59. Scarano F, Moore P. 2012.. An advection-based model to increase the temporal resolution of PIV time series. . Exp. Fluids 52:(4):919–33
     [Crossref] [Google Scholar]
  60. Schumann U. 1975.. Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. . J. Comput. Phys. 18:(4):376–404
     [Crossref] [Google Scholar]
  61. Suzuki T, Hasegawa Y. 2017.. Estimation of turbulent channel flow at Reτ= 100 based on the wall measurement using a simple sequential approach. . J. Fluid Mech. 830::760–96
     [Crossref] [Google Scholar]
  62. Thomson W. 1868.. VI.–On vortex motion. . Trans. R. Soc. Edinburgh 25:(1):217–60
     [Crossref] [Google Scholar]
  63. Vela-Martín A. 2021.. The synchronisation of intense vorticity in isotropic turbulence. . J. Fluid Mech. 913::R8
     [Crossref] [Google Scholar]
  64. Wang M, Eyink GL, Zaki TA. 2022.. Origin of enhanced skin friction at the onset of boundary-layer transition. . J. Fluid Mech. 941::A32
     [Crossref] [Google Scholar]
  65. Wang M, Wang Q, Zaki TA. 2019.. Discrete adjoint of fractional-step incompressible Navier-Stokes solver in curvilinear coordinates and application to data assimilation. . J. Comput. Phys. 396::427–50
     [Crossref] [Google Scholar]
  66. Wang M, Zaki TA. 2021.. State estimation in turbulent channel flow from limited observations. . J. Fluid Mech. 917::A9
     [Crossref] [Google Scholar]
  67. Wang M, Zaki TA. 2022.. Synchronization of turbulence in channel flow. . J. Fluid Mech. 943::A4
     [Crossref] [Google Scholar]
  68. Wang Q, Wang M, Zaki TA. 2022.. What is observable from wall data in turbulent channel flow?. J. Fluid Mech. 941::A48
     [Crossref] [Google Scholar]
  69. Yoshida K, Yamaguchi J, Kaneda Y. 2005.. Regeneration of small eddies by data assimilation in turbulence. . Phys. Rev. Lett. 94:(1):014501
     [Crossref] [Google Scholar]
  70. You J, Zaki TA. 2019.. Conditional statistics and flow structures in turbulent boundary layers buffeted by free-stream disturbances. . J. Fluid Mech. 866::526–66
     [Crossref] [Google Scholar]
  71. Zaki TA, Saha S. 2009.. On shear sheltering and the structure of vortical modes in single- and two-fluid boundary layers. . J. Fluid Mech. 626::111–47
     [Crossref] [Google Scholar]
  72. Zaki TA, Wang M. 2021.. From limited observations to the state of turbulence: fundamental difficulties of flow reconstruction. . Phys. Rev. Fluids 6:(10):100501
     [Crossref] [Google Scholar]
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Turbulence from an Observer Perspective
Annual Review of Fluid Mechanics 57, 311 (2025); https://doi.org/10.1146/annurev-fluid-030424-114735
/content/journals/10.1146/annurev-fluid-030424-114735
/content/journals/10.1146/annurev-fluid-030424-114735
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