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POD analysis of the instability mode of a low-speed streak in a laminar boundary layer

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Abstract

The instability of one single low-speed streak in a zero-pressure-gradient laminar boundary layer is investigated experimentally via both hydrogen bubble visualization and planar particle image velocimetry (PIV) measurement. A single low-speed streak is generated and destabilized by the wake of an interference wire positioned normal to the wall and in the upstream. The downstream development of the streak includes secondary instability and self-reproduction process, which leads to the generation of two additional streaks appearing on either side of the primary one. A proper orthogonal decomposition (POD) analysis of PIV measured velocity field is used to identify the components of the streak instability in the POD mode space: for a sinuous/varicose type of POD mode, its basis functions present anti-symmetric/symmetric distributions about the streak centerline in the streamwise component, and the symmetry condition reverses in the spanwise component. It is further shown that sinuous mode dominates the turbulent kinematic energy (TKE) through the whole streak evolution process, the TKE content first increases along the streamwise direction to a saturation value and then decays slowly. In contrast, varicose mode exhibits a sustained growth of the TKE content, suggesting an increasing competition of varicose instability against sinuous instability.

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References

  1. Kim, H.T., Kline, S.J., Reynolds, W.C.: The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50, 133–160 (1971)

    Article  Google Scholar 

  2. Brandt, L., Lange, H.C.: Streak interactions and breakdown in boundary layer flows. Phys. Fluids 20, 024107 (2008)

    Article  MATH  Google Scholar 

  3. Schoppa, W., Hussain, F.: Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Matsubara, M., Alfredsson, P.H.: Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149–168 (2001)

    Article  MATH  Google Scholar 

  5. Zheng, X.B., Jiang, N.: The spatial-temporal evolution of coherent structures in log law region of turbulent boundary layer. Acta Mech. Sin. 31, 16–24 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kline, S.J., Reynolds, W.C., Schraub, F.A., et al.: The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773 (1967)

    Article  Google Scholar 

  7. Wang, S.F., Jia, F.: Some characteristics of low-speed streaks under sheared air-water interfaces. Acta Mech. Sin. 17, 115–124 (2001)

    Article  Google Scholar 

  8. Pan, C., Wang, J.J.: Progress in bypass transition induced by free-stream disturbance. Adv. Mech. 41, 668–685 (2011). (in Chinese)

    Google Scholar 

  9. Westin, K.J.A., Boiko, A.V., Klingmann, B.G.B., et al.: Experiments in a boundary layer subjected to free stream turbulence. Part 1. Boundary layer structure and receptivity. J. Fluid Mech. 281, 193–218 (1994)

    Article  Google Scholar 

  10. Hunt, C.R., Durbin, P.A., Kevlahan, N.K.R., et al.: Non-local effects of shear in turbulent flows. In: Proceedings of the 6th European turbulence conference, Lausanne, Switzerland, 2–5 July (1996)

  11. Klebanoff, P.S.: Effect of freestream turbulence on the laminar boundary layer. Bull. Am. Phys. Soc. 10, 1323 (1971)

    Google Scholar 

  12. Blackwelder, R.F., Eckelmann, H.: Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech. 94, 577–594 (1979)

    Article  Google Scholar 

  13. Smith, C.R., Schwartz, S.P.: Observation of streamwise rotation in the nearc-wall region of a turbulent boundary layer. Phys. Fluids 26, 641–652 (1983)

    Article  Google Scholar 

  14. Hultgren, L.S., Gustavsson, L.H.: Algebraic growth of disturbances in a laminar boundary layer. Phys. Fluids 24, 1000–1004 (1981)

    Article  MATH  Google Scholar 

  15. Butler, K.M., Farrell, B.F.: Three dimensional optimal perturbations in viscous shear flow. Phys. Fluids A Fluid Dyn. 4, 1637–1650 (1992)

    Article  Google Scholar 

  16. Ellingsen, T., Palm, E.: Stability of linear flow. Phys. Fluids 18, 487–488 (1975)

    Article  MATH  Google Scholar 

  17. Andersson, P., Berggren, M., Henningson, D.S.: Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11, 134–150 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wundrow, D.W., Goldstein, M.E.: Effect on a laminar boundary layer of small-amplitude streamwise vorticity in the upstream flow. J. Fluid Mech. 426, 229–262 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  19. Goldstein, M.E., Leib, S.J., Cowley, S.J.: Distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate. J. Fluid Mech. 237, 231–260 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  20. Ricco, P., Luo, J., Wu, X.: Evolution and instability of unsteady nonlinear streaks generated by free-stream vortical disturbances. J. Fluid Mech. 677, 1–38 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Dong, M., Wu, X.: On continuous spectra of the orr-sommerfeld/squire equations and entrainment of free-stream vortical disturbances. J. Fluid Mech. 732, 616–659 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. Brandt, L., Henningson, D.S.: Transition of streamwise streaks in zero-pressure-gradient boundary layers. J. Fluid Mech. 472, 229–261 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  23. Asai, M., Minagawa, M., Nishioka, M.: The instability and breakdown of a near-wall low-speed streak. J. Fluid Mech. 455, 289–314 (2002)

    Article  MATH  Google Scholar 

  24. Wu, X., Luo, J.: Linear and nonlinear instabilities of a blasius boundary layer perturbed by streamwise vortices. Part 1. Steady streaks. J. Fluid Mech. 483, 225–248 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  25. Adrian, R.J., Meinhart, C.D., Tomkins, C.D.: Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  26. Wang, Y.S., Huang, W.X., Xu, C.X.: On hairpin vortex generation from near-wall streamwise vortices. Acta Mech. Sin. 31, 139–152 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  27. Mans, J.: Streak development and breakdown during bypass transition. [Ph.D. Thesis], Eindhoven University of Technology, The Netherlands (2007)

  28. Wang, J.J., Pan, C., Zhang, P.F.: On the instability and reproduction mechanism of a laminar streak. J. Turbul. 10, 1–27 (2009)

    Article  Google Scholar 

  29. Deng, S.C., Pan, C., Wang, J.J.: Dynamics of low-speed streak evolution and interaction in laminar boundary layer. Acta Mech. Sin. 30, 636–645 (2014)

    Article  Google Scholar 

  30. Chernoray, V.G., Kozlov, V.V., Lofdahl, L., et al.: Visualization of sinusoidal and varicose instabilities of streaks in a boundary layer. J. Visual. 9, 437–444 (2006)

    Article  Google Scholar 

  31. Hwang, Y.: Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254–289 (2015)

    Article  Google Scholar 

  32. Wu, X., Choudhari, M.: Linear and nonlinear instabilities of a blasius boundary layer perturbed by streamwise vortices. Part 2. Intermittent instability induced by long-wavelength klebanoff modes. J. Fluid Mech. 483, 249–286 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  33. Mans, J., de Lange, H.C., van Steenhoven, A.A.: Sinuous breakdown in a flat plate boundary layer exposed to free-stream turbulence. Phys. Fluids 19, 088101 (2007)

    Article  MATH  Google Scholar 

  34. Mans, J., Kadijk, E.C., de Lange, H.C., et al.: Breakdown in a boundary layer exposed to free-stream turbulence. Exp. Fluids 39, 1071–1083 (2005)

    Article  Google Scholar 

  35. He, G., Wang, J., Pan, C.: Initial growth of a disturbance in a boundary layer influenced by a circular cylinder wake. J. Fluid Mech. 718, 116–130 (2013)

    Article  MATH  Google Scholar 

  36. He, G.S., Wang, J.J., Pan, C., et al.: Vortex dynamics for flow over a circular cylinder in proximity to a wall. J. Fluid Mech. 812, 698–720 (2017)

    Article  MathSciNet  Google Scholar 

  37. Scarano, F., Riethmuller, M.L.: Advances in iterative multigrid piv image processing. Exp. Fluids 29, 51–60 (2000)

    Article  Google Scholar 

  38. Pan, C., Wang, H.P., Wang, J.J.: Phase identification of quasi-periodic flow measured by particle image velocimetry with a low sampling rate. Meas. Sci. Technol. 24, 055305 (2013)

    Article  Google Scholar 

  39. Arndt, R.E.A., Long, D.F., Glauser, M.N.: The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet. J. Fluid Mech. 340, 1–33 (1997)

    Article  Google Scholar 

  40. Citriniti, J.H., George, W.K.: Reconstruction of the global velocity field in the axisymmetric mixing layer utilizing the proper orthogonal decomposition. J. Fluid Mech. 418, 137–166 (2000)

    Article  MATH  Google Scholar 

  41. Iqbal, M.O., Thomas, F.O.: Coherent structure in a turbulent jet via a vector implementation of the proper orthogonal decomposition. J. Fluid Mech. 571, 281–326 (2007)

    Article  MATH  Google Scholar 

  42. Yang, H., Zhang, X., Ran, L., et al.: Coherent structures and wavepackets in subsonic transitional turbulent jets. Acta Mech. Sin. 33, 10–19 (2017)

    Article  Google Scholar 

  43. Lumley, J.L.: The structures of inhomogeneous turbulent flow. In: Proceedings of the international colloquium on the fine scale structure of the atmosphere and its influence on radio wave propagation, A.M. Yaglom and V.I. Tararsky, Nauka, Moscow (1967)

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 11372001, 11672020, and 11490552) and the Fundamental Research Funds for the Central Universities of China (Grant YWF-16-JCTD-A-05).

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Authors and Affiliations

  1. Fluid Mechanics Key Laboratory of Ministry of Education, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Si-Chao Deng, Chong Pan, Jin-Jun Wang & Akira Rinoshika

  2. Department of Mechanical Systems Engineering, Yamagata University, Yamagata, 992-8510, Japan

    Akira Rinoshika

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  1. Si-Chao Deng
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  2. Chong Pan
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  3. Jin-Jun Wang
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  4. Akira Rinoshika
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Correspondence to Chong Pan.

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Deng, SC., Pan, C., Wang, JJ. et al. POD analysis of the instability mode of a low-speed streak in a laminar boundary layer. Acta Mech. Sin. 33, 981–991 (2017). https://doi.org/10.1007/s10409-017-0681-8

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  • DOI: https://doi.org/10.1007/s10409-017-0681-8

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