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Temporal Evolution of Vortical Structures in the Wall Region of Turbulent Channel Flow

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Abstract

Hairpin-like vortical structures that form in the wall region of turbulent channel flow are investigated. The analysis is performed by following a procedure in which the Navier-Stokes equations are first integrated by means of a computational code based on a mixed spectral-finite difference technique in the case of the flow in a plane channel. A DNS turbulent-flow database, representing the turbulent statistically steady state of the velocity field through 10 viscous time units, is computed and the vortex-detection method of the imaginary part of the complex eigenvalue pair of the velocity-gradient tensor is applied to the velocity field. As a result, hairpin-like vortical structures are educed. Flow visualizations are provided of the processes of evolution that characterize hairpin vortices in the wall region of turbulent channel flow. The relationship is investigated between vortex dynamics and 2nd- and 4th- quadrant events, showing that ejections and sweeps play a fundamental role in the way the morphological evolution of a hairpin vortex develops with time.

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References

  1. Kline, S.J., Reynolds, W.C., Schraub, F.A., Rundstadler, P.W.: The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773 (1967). doi:10.1017/S0022112067001740

    Article  ADS  Google Scholar 

  2. Antonia, R.A.: Conditional sampling in turbulence measurement. Annu. Rev. Fluid Mech. 13, 131–156 (1981). doi:10.1146/annurev.fl.13.010181.001023

    Article  ADS  Google Scholar 

  3. Willmarth, W.W., Ans Lu, S.S.: Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 65–92 (1972). doi:10.1017/S002211207200165X

    Article  ADS  Google Scholar 

  4. Blackwelder, R.F., Kaplan, R.E.: On the wall structure of the turbulent boundary layer. J. Fluid Mech. 76, 89–112 (1976). doi:10.1017/S0022112076003145

    Article  ADS  Google Scholar 

  5. Johansson, A.V., Alfredsson, P.H., Kim, J.: Evolution and dynamics of shear-layer structures in near-wall turbulence. J. Fluid Mech. 224, 579–599 (1991). doi:10.1017/S002211209100188X

    Article  MATH  ADS  Google Scholar 

  6. Theodorsen, T.: Mechanism of turbulence. In: Proc. 2nd Midwestern Fluid Mechanics Conf., Columbus, Ohio, pp. 1–18 (1952)

  7. Robinson, S.K.: Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639 (1991). doi:10.1146/annurev.fl.23.010191.003125

    Article  ADS  Google Scholar 

  8. Smith, C.R., Schwartz, S.P.: Observation of streamwise rotation in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 241–252 (1983)

    Google Scholar 

  9. Kasagi, N., Hirata, M., Nishino, K.: Streamwise pseudo-vortical structures and associated vorticity in the near-wall region of a wall-bounded turbulent shear flow. Exp. Fluids 4, 309–318 (1986). doi:10.1007/BF00266296

    Article  Google Scholar 

  10. Head, M.R., Bandyopadhyay, P.: New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–338 (1981). doi:10.1017/S0022112081001791

    Article  ADS  Google Scholar 

  11. Smith, C.R., Walker, J.D.A., Haidari, A.H., Soburn, U.: On the dynamics of near-wall turbulence. Philos. Trans. R. Soc. Lond. 336, 131–175 (1991). doi:10.1098/rsta.1991.0070

    Article  MATH  ADS  Google Scholar 

  12. Willmarth, W.W., Tu, B.J.: Structure of turbulence in the boundary layer near the wall. Phys. Fluids 10, S134–S137 (1967). doi:10.1063/1.1762431

    Article  ADS  Google Scholar 

  13. Offen, G.R., Kline, S.J.: A proposed model of the bursting process in turbulent boundary layers. J. Fluid Mech. 70, 209–228 (1975). doi:10.1017/S002211207500198X

    Article  ADS  Google Scholar 

  14. Praturi, A.K., Brodkey, R.S.: A stereoscopic visual study of coherent structures in turbulent shear flow. J. Fluid Mech. 89, 251–272 (1978). doi:10.1017/S0022112078002608

    Article  ADS  Google Scholar 

  15. Thomas, A.S.W., Bull, M.K.: On the role of wall-pressure fluctuations in deterministic motions in the turbulent boundary layer. J. Fluid Mech. 128, 283–322 (1983). doi:10.1017/S002211208300049X

    Article  ADS  Google Scholar 

  16. Acarlar, M.S., Smith, C.R.: A study of hairpin vortices in a laminar boundary layer, Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 43–83 (1987). doi:10.1017/S0022112087000284

    Article  ADS  Google Scholar 

  17. Panton, R.L.: Overview of the self-sustaining mechanisms of wall turbulence. Prog. Aerosp. Sci. 37, 341–383 (2001). doi:10.1016/S0376–0421(01)00009–4

    Article  Google Scholar 

  18. Alfonsi, G.: Coherent structures of turbulence: methods of eduction and results. Appl. Mech. Rev. 59, 307–323 (2006). doi:10.1115/1.2345370

    Article  Google Scholar 

  19. Perry, A.E., Chong, M.S.: A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19, 125–155 (1987). doi:10.1146/annurev.fl.19.010187.001013

    Article  ADS  Google Scholar 

  20. Hunt, J.C.R., Wray, A.A., Moin, P.: Eddies, streams and convergence zones in turbulent flows. In: Proc. 1988 Summer Program, Center for Turbulence Research, NASA Ames/Stanford University, pp. 193–208 (1988)

  21. Zhou, J., Adrian, R.J., Balachandar, S., Kendall, T.M.: Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396 (1999). doi:10.1017/S002211209900467X

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. Jeong, J., Hussain, F.: On the definition of a vortex. J. Fluid Mech. 285, 69–94 (1995). doi:10.1017/S0022112095000462

    Article  MATH  ADS  MathSciNet  Google Scholar 

  23. Chakraborty, P., Balachandar, S., Adrian, R.J.: On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189–214 (2005). doi:10.1017/S0022112005004726

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. Chakraborty, P., Balachandar, S., Adrian, R.J.: Local vortex identification criteria: inter-relationships and a unified outlook. In: Proc. IUTAM Symp. on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamics, pp. 111–115 (2006)

  25. Alfonsi, G., Passoni, G., Pancaldo, L., Zampaglione, D.: A spectral-finite difference solution of the Navier-Stokes equations in three dimensions. Int. J. Numer. Methods Fluids 28, 129–142 (1998). doi:10.1002/(SICI)1097–0363(19980715)28:1<129::AID-FLD707>3.0.CO;2–4

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. Passoni, G., Alfonsi, G., Galbiati, M.: Analysis of hybrid algorithms for the Navier-Stokes equations with respect to hydrodynamic stability theory. Int. J. Numer. Methods Fluids 38, 1069–1089 (2002). doi:10.1002/fld.259

    Article  MATH  ADS  MathSciNet  Google Scholar 

  27. Kim, J., Moin, P., Moser, R.D.: Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166 (1987). doi:10.1017/S0022112087000892

    Article  MATH  ADS  Google Scholar 

  28. Lyons, S.L., Hanratty, T.J., McLaughlin, J.B.: Large-scale computer simulation of fully developed turbulent channel flow with heath transfer. Int. J. Numer. Methods Fluids 13, 999–1028 (1991). doi:10.1002/fld.1650130805

    Article  MATH  ADS  Google Scholar 

  29. Rutledge, J., Sleicher, C.A.: Direct simulation of turbulent flow and heath transfer in a channel. Part I: smooth walls. Int. J. Numer. Methods Fluids 16, 1051–1078 (1993). doi:10.1002/fld.1650161203

    Article  MATH  ADS  Google Scholar 

  30. Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to Re τ  = 590. Phys. Fluids 11, 943–945 (1999). doi:10.1063/1.869966

    Article  MATH  ADS  Google Scholar 

  31. Grötzbach, G.: Spatial resolution requirements for direct numerical simulation of the Rayleigh-Bénard convection. J. Comput. Phys. 49, 241–264 (1983). doi:10.1016/0021–9991(83)90125–0

    Article  MATH  ADS  Google Scholar 

  32. Dean, R.B.: Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. ASME J. Fluids Eng. 100, 215–223 (1978)

    Google Scholar 

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Correspondence to Giancarlo Alfonsi.

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Alfonsi, G., Primavera, L. Temporal Evolution of Vortical Structures in the Wall Region of Turbulent Channel Flow. Flow Turbulence Combust 83, 61–79 (2009). https://doi.org/10.1007/s10494-008-9189-4

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  • DOI: https://doi.org/10.1007/s10494-008-9189-4

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