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Influence of a wavy boundary on turbulence.

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Abstract

Measurements of turbulence with laser Doppler velocimetry (LDV) are compared for turbulent flows over a flat surface and a surface with sinusoidal waves of small wavelength. The wavy boundary was highly rough in that the flow separated. The Reynolds number based on the half-height of the channel and the bulk velocity was 46,000. The wavelength was 5 mm and the height to wavelength ratio was 0.1. The root-mean-squares of the velocity fluctuations are approximately equal if normalized with the friction velocity. This can be explained as a consequence of the approximate equality of the correlation coefficients of the Reynolds shear stress. Calculations with a direct numerical simulation (DNS) are used to show that the fluid interacts with the wall in quite different ways for flat and wavy surfaces. They show similarity in that large quadrant 2 events in the outer flow, for both cases, are associated with plumes that emerge from the wall region and extend over large distances. Measurements of skewness of the streamwise and wall-normal velocity fluctuations and quadrant analyses of the Reynolds shear stresses are qualitatively similar for flat and wavy surfaces. However, the skewness magnitudes and the ratio of the quadrant 2 to quadrant 4 contributions are larger for the wavy surface. Thus, there is evidence that turbulent structures are universal in the outer flow and for quantitative differences in the statistics that reflect differences in the way in which the fluid interacts with the wall.

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References

  • Andreopoulos J, Bradshaw P (1981) Measurements of turbulence structure in the boundary layer on a rough surface. Boundary-Layer Meteorol 20:201–213

    Google Scholar 

  • Brooke JW, Hanratty TJ (1993) Origin of turbulence-producing eddies in a channel flow. Phys Fluids A 5:1011–1022

    Article  CAS  Google Scholar 

  • Cherukat P, Na Y, Hanratty TJ, Mclaughlin JB (1998) Direct numerical simulation of a fully developed turbulent flow over a wavy wall. Theoret Comput Fluid Dyn 11:109–134

    Article  CAS  Google Scholar 

  • Chong MS, Perry AE, Cantwell BJ (1990) A general classification of three-dimensional flow fields. Phys Fluids A 2:765–777

    Article  Google Scholar 

  • Cohen LS, Hanratty TJ (1968) Effect of waves at a gas–liquid interface on a turbulent gas flow. J Fluid Mech 31:467 – 479

    Google Scholar 

  • Goodwin JW, Ottewill RH, Pelton R, Vianello G, Yateo DE (1978) Control of particle size in the formation of polymer lattices. Brit Polym J 10:173–180

    CAS  Google Scholar 

  • Grass AJ (1971) Structural features of turbulent flow over smooth and rough boundaries. J Fluid Mech 50:233–255

    Google Scholar 

  • Grass AJ, Stuart RJ, Mansour-Tehrani M (1993) Common vortical structure of turbulent flows over smooth and rough boundaries. AIAA J 31:837–847

    CAS  Google Scholar 

  • Günther A, Papavassilious DV, Warholic MD, Hanratty TJ (1998) Turbulent flow in a channel at a low Reynolds number. Exp Fluids 25:503–511

    Article  Google Scholar 

  • Hanjalic K, Launder BE (1972) Fully developed asymmetric flow in a plane channel. J Fluid Mech 51:301–335

    Google Scholar 

  • Hanratty TJ, Papavassiliou DV (1997) The role of wall vortices in producing turbulence. In: Panton RL (ed) Self-sustaining mechanisms of wall turbulence. Computational Mechanics Publications, Southampton, UK, pp 83–108

  • Heist DK, Hanratty TJ, Na Y (2000) Observations of the formation of streamwise vortices by rotation of arch vortices. Phys Fluids 12:2965–2975

    Article  CAS  Google Scholar 

  • Hudson JD, Dykhno L, Hanratty TJ (1996) Turbulence production in flow over a wavy wall. Exp Fluids 20:257–265

    CAS  Google Scholar 

  • Juang MS, Krieger IM (1976) Emulsifier-free emulsion polymerization with ionie comonomer. J Polym Sci 14:2089–2107

    Article  CAS  Google Scholar 

  • Krogstad PA, Antonia RA, Browne LWB (1992) Comparison between rough and smooth wall turbulent boundary layers. J Fluid Mech 245:599–617

    CAS  Google Scholar 

  • Krogstad PA, Antonia RA (1994) Structure of turbulent boundary layers on smooth and rough walls. J Fluid Mech 277:1–21

    Google Scholar 

  • Krogstad PA, Antonia RA (1999) Surface roughness effects in turbulent boundary layers. Exp Fluids 27:450–460

    Google Scholar 

  • Liu ZC, Adrian RJ, Hanratty TJ (2000) Large-scale modes of turbulent channel flow: transport and structure. TAM Report No.929, UILU-ENG-2000–6004, ISSN 0073 5264

  • Liu ZC, Landreth CC, Adrian RJ, Hanratty TJ (1991) High resolution measurement of turbulent structure in a channel with particle image velocimetry. Exp Fluids 10:301–312

    Google Scholar 

  • Lu SS, Willmarth WW (1973) Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J Fluid Mech 60:481–511

    Google Scholar 

  • Mazouz A, Labraga L, Tournier C (1994) Behavior of the Reynolds stress on rough walls. Exp Fluids 17:39–44

    Google Scholar 

  • Miya M (1966) Effect of waves on turbulence. PhD Thesis, University of Illinois, Urbana

  • Na Y, Hanratty TJ, Liu ZC (2001) The use of DNS to define stress producing events for turbulent flow over a smooth wall. Flow, Turb Combust 66:495–512

    Google Scholar 

  • Niederschulte MA, Adrian RJ, Hanratty TJ (1990) Measurement of turbulent flow in a channel at low Reynolds numbers. Exp Fluids 9:222–231

    CAS  Google Scholar 

  • Perry AE, Lim KL, Henbest SM (1987) An experimental study of the turbulence structure in smooth- and rough-wall boundary layers. J Fluid Mech 177:437–466

    CAS  Google Scholar 

  • Pimenta MM; Moffat RJ; Kays WM (1979) The structure of a boundary layer on a rough wall with blowing and heat transfer. J Heat Transfer 101:193–198

    Google Scholar 

  • Raupach MR (1981) Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers. J Fluid Mech 108:363–382

    Google Scholar 

  • Raupach MR, Antonia RA, Rajagopalan S (1991) Rough-wall turbulent boundary layers. Appl Mech Rev 44:1–25

    Google Scholar 

  • Schlichting H (1979) Boundary-layer theory, 7th edn. McGraw-Hill, New York

  • Shafi HS, Antonia RA (1997) Small-scale characteristics of a turbulent boundary layer over a rough wall. J Fluid Mech 342:263–293

    Article  CAS  Google Scholar 

  • Warholic MD (1997) Modification of turbulent channel flow by passive and additive devices. PhD thesis, University of Illinois, Urbana

  • Warholic MD, Schmidt GM, Hanratty TJ (1999) The influence of a drag-reducing surfactant on a turbulent velocity field. J Fluid Mech 388:1–20

    Article  CAS  Google Scholar 

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Acknowledgement

This work was supported by the Natural Science Foundation under Grant NSF CTS 98-06265. We also acknowledge the support and facilities of the National Center for Supercomputing Applications at the University of Illinois in Urbana, Illinois.

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Authors and Affiliations

  1. Department of Chemical Engineering, University of Illinois, Urbana, IL, 61801, USA

    S. Nakagawa & T. J. Hanratty

  2. Department of Mechanical Engineering, Konkuk University, 143-701, Seoul, Korea

    Y. Na

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  1. S. Nakagawa
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  2. Y. Na
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  3. T. J. Hanratty
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Correspondence to T. J. Hanratty.

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Nakagawa, S., Na, Y. & Hanratty, T.J. Influence of a wavy boundary on turbulence. . Exp Fluids 35, 422–436 (2003). https://doi.org/10.1007/s00348-003-0681-2

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  • DOI: https://doi.org/10.1007/s00348-003-0681-2

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