Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-17T07:22:58.490Z Has data issue: false hasContentIssue false
  • English
  • Français

On the scaling of large-scale structures in smooth-bed turbulent open-channel flows

Published online by Cambridge University Press:  18 February 2020

C. Peruzzi Open the ORCID record for C. Peruzzi [Opens in a new window] ,
D. Poggi ,
L. Ridolfi  and
C. Manes
C. Peruzzi*
Affiliation:
Department of Environmental, Land and Infrastructure Engineering, Politecnico di Torino, 10129Turin, Italy
D. Poggi
Affiliation:
Department of Environmental, Land and Infrastructure Engineering, Politecnico di Torino, 10129Turin, Italy
L. Ridolfi
Affiliation:
Department of Environmental, Land and Infrastructure Engineering, Politecnico di Torino, 10129Turin, Italy
C. Manes
Affiliation:
Department of Environmental, Land and Infrastructure Engineering, Politecnico di Torino, 10129Turin, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper investigates the existence and scaling of the so-called large-scale and very-large-scale motions (LSMs and VLSMs) in non-uniform turbulent open-channel flows developing over a smooth bed in a laboratory flume. A laser Doppler anemometry system was employed to measure vertical profiles of longitudinal and bed-normal velocity statistics over a wide range of hydraulic conditions. Pre-multiplied spectra of the longitudinal velocity fluctuations revealed the existence of two peaks occurring at wavelengths consistent with those associated with LSMs and VLSMs as detected in the past literature pertaining to wall turbulence. However, contrary to so-called canonical wall flows (i.e. flat-plate boundary layers, pipe and closed-channel flows), the LSM and VLSM peaks observed in the open-channel flows investigated herein are detectable over a much larger extent of the wall-normal coordinate. Furthermore, the VLSM peak appears at von Kármán numbers $Re_{\unicode[STIX]{x1D70F}}$ as low as 725, whereas in other wall flows much higher values are normally required. Finally, as conjectured by a recent study on uniform rough-bed open-channel flows, the present paper confirms that LSM wavelengths scale nicely with the flow depth, whereas the channel aspect ratio (i.e. the ratio between channel width and flow depth) is the non-dimensional parameter controlling the scaling of VLSM wavelengths. The intensity and wavelengths of the VLSM peaks were also observed to depend on the spanwise coordinate. This result suggests that VLSMs might be dynamically linked to secondary currents, as these are also known to vary in strength and size across the channel width.

JFM classification

Turbulent Flows: Turbulent boundary layers Waves/Free-surface Flows: Hydraulics Boundary Layers: Boundary layer structure
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A1
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.CrossRefGoogle Scholar
Adrian, R. J. & Marusic, I. 2012 Coherent structures in flow over hydraulic engineering surfaces. J. Hydraul Res. 50 (5), 451–464.CrossRefGoogle Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Bagherimiyab, F. & Lemmin, U. 2018 Large-scale coherent flow structures in rough-bed open-channel flow observed in fluctuations of three-dimensional velocity, skin friction and bed pressure. J. Hydraul Res. 56 (6), 806–824.CrossRefGoogle Scholar
Balakumar, B. J. & Adrian, R. J. 2007 Large-and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365 (1852), 665–681.CrossRefGoogle ScholarPubMed
Bell, J. H. & Mehta, R. D. 1988 Contraction design for small low-speed wind tunnels. NASA STI/Recon Tech. Rep. 89, 13753.Google Scholar
Cameron, S. M., Nikora, V. I. & Marusic, I. 2019 Drag forces on a bed particle in open-channel flow: effects of pressure spatial fluctuations and very-large-scale motions. J. Fluid Mech. 863, 494–512.CrossRefGoogle Scholar
Cameron, S. M., Nikora, V. I. & Stewart, M. T. 2017 Very-large-scale motions in rough-bed open-channel flow. J. Fluid Mech. 814, 416–429.CrossRefGoogle Scholar
Cameron, S. M., Nikora, V. I., Stewart, M. T. & Zampiron, A. 2018 Large and very large scale motions in rough-bed open-channel flow. In E3S Web of Conferences – River Flow 2018, vol. 40, p. 05061. EDP Sciences.Google Scholar
Cardoso, A. H., Graf, W. H. & Gust, G. 1989 Uniform flow in a smooth open channel. J. Hydraul Res. 27 (5), 603–616.CrossRefGoogle Scholar
Cardoso, A. H., Graf, W. H. & Gust, G. 1991 Steady gradually accelerating flow in a smooth open channel. J. Hydraul Res. 29 (4), 525–543.CrossRefGoogle Scholar
Cellino, M. & Lemmin, U. 2004 Influence of coherent flow structures on the dynamics of suspended sediment transport in open-channel flow. J. Hydraul Res. 130 (11), 1077–1088.CrossRefGoogle Scholar
Chamorro, L. P., Hill, C., Morton, S., Ellis, C., Arndt, R. E. A. & Sotiropoulos, F. 2013 On the interaction between a turbulent open channel flow and an axial-flow turbine. J. Fluid Mech. 716, 658–670.CrossRefGoogle Scholar
Clauser, F. H. 1956 The turbulent boundary layer. Adv. Appl. Maths 4, 1–51.Google Scholar
Cossu, C. & Hwang, Y. 2017 Self-sustaining processes at all scales in wall-bounded turbulent shear flows. Phil. Trans. R. Soc. Lond. A 375 (2089), 20160088.Google ScholarPubMed
Da Silva, A. M. F. & Yalin, M. S. 2017 Fluvial Processes, 2nd edn. CRC Press.CrossRefGoogle Scholar
Dantec Dynamics 2011 LDA and PDA – Reference Manual. Dantec Dynamics A/S.Google Scholar
De Graaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
De Silva, C. M., Kevin, K., Baidya, R., Hutchins, N. & Marusic, I. 2018 Large coherence of spanwise velocity in turbulent boundary layers. J. Fluid Mech. 847, 161–185.CrossRefGoogle Scholar
Del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41–L44.CrossRefGoogle Scholar
Del Álamo, J. C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 5–26.CrossRefGoogle Scholar
Durst, F., Jovanovi, J. & Sender, J. 1995 LDA measurements in the near-wall region of a turbulent pipe flow. J. Fluid Mech. 295, 305–335.CrossRefGoogle Scholar
Escudier, M. P., Nickson, A. K. & Poole, R. J. 2009 Turbulent flow of viscoelastic shear-thinning liquids through a rectangular duct: quantification of turbulence anisotropy. J. Non-Newtonian Fluid Mech. 160 (1), 2–10.CrossRefGoogle Scholar
Franca, M. J. & Lemmin, U. 2015 Detection and reconstruction of large-scale coherent flow structures in gravel-bed rivers. Earth Surf. Process. Landf. 40 (1), 93–104.CrossRefGoogle Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46.CrossRefGoogle Scholar
Ghesemi, A., Fox, J. & Husic, A. 2019 Predicting macroturbulence energy and timescales for flow over a gravel bed: experimental results and scaling laws. Geomorphology 332, 122–137.CrossRefGoogle Scholar
Grinvald, D. I. & Nikora, V. I. 1988 River Turbulence. Hydrometeoizdat.Google Scholar
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
Henderson, F. M. 1966 Open Channel Flow. Macmillan Publishing Co. Inc.Google Scholar
Hommema, S. & Adrian, R. 2002 Similarity of apparently random structures in the outer region of wall turbulence. Exp. Fluids 33 (1), 5–12.CrossRefGoogle Scholar
Hurther, D., Lemmin, U. & Terray, E. A. 2007 Turbulent transport in the outer region of rough-wall open-channel flows: the contribution of large coherent shear stress structures (LC3S). J. Fluid Mech. 574, 465–493.CrossRefGoogle Scholar
Hutchins, N., Hambleton, W. T. & Marusic, I. 2005 Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers. J. Fluid Mech. 541, 21–54.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647–664.CrossRefGoogle Scholar
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136.CrossRefGoogle Scholar
Hwang, Y. & Bengana, Y. 2016 Self-sustaining process of minimal attached eddies in turbulent channel flow. J. Fluid Mech. 795, 708–738.CrossRefGoogle Scholar
Hwang, Y. & Cossu, C. 2010 Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett. 105 (4), 044505.CrossRefGoogle ScholarPubMed
Hwang, Y., Willis, A. P. & Cossu, C. 2016 Invariant solutions of minimal large-scale structures in turbulent channel flow for Re 𝜏 up to 1000. J. Fluid Mech. 802, R1.CrossRefGoogle Scholar
Jackson, R. G. 1976 Sedimentological and fluid-dynamic implications of the turbulent bursting phenomenon in geophysical flows. J. Fluid Mech. 77 (3), 531–560.CrossRefGoogle Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.CrossRefGoogle Scholar
Jirka, G. H., Herlina, H. & Niepelt, A. 2010 Gas transfer at the air–water interface: experiments with different turbulence forcing mechanisms. Exp. Fluids 49 (1), 319–327.CrossRefGoogle Scholar
Katul, G. G. 2019 The anatomy of large-scale motion in atmospheric boundary layers. J. Fluid Mech. 858, 1–4.CrossRefGoogle Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.CrossRefGoogle Scholar
Kirkgöz, M. S. 1989 Turbulent velocity profiles for smooth and rough open channel flow. J. Hydraul. Engng 115 (11), 1543–1561.CrossRefGoogle Scholar
Kirkgöz, M. S. & Ardic˛lioğlu, M. 1997 Velocity profiles of developing and developed open channel flow. J. Hydraul. Engng 123 (12), 1099–1105.CrossRefGoogle Scholar
Kironoto, B. A. 1998 The universality of the Kármán constant on non-uniform open-channel flow. 11th Cong. of APD-IAHR 2, 579–586.Google Scholar
Kironoto, B. A. & Graf, W. H. 1995 Turbulence characteristics in rough non-uniform open-channel flow. In Proc., Instn. Civ. Engrs. Water, Maritime, and Energy, vol. 112, pp. 336–348.Google Scholar
Knight, D. W., Demetriou, J. D. & Hamed, M. E. 1984 Boundary shear in smooth rectangular channels. J. Hydraul. Engng 110 (4), 405–422.CrossRefGoogle Scholar
López, F. & García, M. H. 1999 Wall similarity in turbulent open-channel flow. J. Engng Mech. 125 (7), 789–796.CrossRefGoogle Scholar
Manes, C., Poggi, D. & Ridolfi, L. 2011 Turbulent boundary layers over permeable walls: scaling and near-wall structure. J. Fluid Mech. 687, 141–170.CrossRefGoogle Scholar
Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22 (6), 065103.CrossRefGoogle Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.CrossRefGoogle Scholar
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147–156.CrossRefGoogle Scholar
Moog, D. B. & Jirka, G. H. 1999 Air–water gas transfer in uniform channel flow. J. Hydraul. Engng 125 (1), 3–10.CrossRefGoogle Scholar
Nakagawa, H. & Nezu, I. 1981 Structure of space–time correlations of bursting phenomena in an open-channel flow. J. Fluid Mech. 104, 1–43.CrossRefGoogle Scholar
Nepf, H. M. 2012 Flow and transport in regions with aquatic vegetation. Annu. Rev. Fluid Mech. 44, 123–142.CrossRefGoogle Scholar
Nezu, I. 2005 Open-channel flow turbulence and its research prospect in the 21st century. J. Hydraul. Engng 131 (4), 229–246.CrossRefGoogle Scholar
Nezu, I. & Nakagawa, H. 1993 Turbulence in Open-Channel Flows. A. A. Balkema.Google Scholar
Nezu, I. & Rodi, W. 1986 Open-channel flow measurements with a laser Doppler anemometer. J. Hydraul. Engng 112 (5), 335–355.CrossRefGoogle Scholar
Nikora, V. I. & Goring, D. 2000 Eddy convection velocity and Taylor’s hypothesis of ‘frozen’ turbulence in a rough-bed open-channel flow. J. Hydrosci. Hydraul. Engng 18 (2), 75–91.Google Scholar
Onitsuka, K., Akiyama, J. & Matsuoka, S. 2009 Prediction of velocity profiles and Reynolds stress distributions in turbulent open-channel flows with adverse pressure gradient. J. Hydraul Res. 47 (1), 58–65.CrossRefGoogle Scholar
Poggi, D., Katul, G. G., Albertson, J. D. & Ridolfi, L. 2007 An experimental investigation of turbulent flows over a hilly surface. Phys. Fluids 19 (3), 036601.CrossRefGoogle Scholar
Poggi, D., Porporato, A. & Ridolfi, L. 2002 An experimental contribution to near-wall measurements by means of a special laser Doppler anemometry technique. Exp. Fluids 32 (3), 366–375.CrossRefGoogle Scholar
Poggi, D., Porporato, A. & Ridolfi, L. 2003 Analysis of the small-scale structure of turbulence on smooth and rough walls. Phys. Fluids 15 (1), 35–46.CrossRefGoogle Scholar
Pu, J. H., Tait, S., Guo, Y., Huang, Y. & Hanmaiahgari, P. R. 2018 Dominant features in three-dimensional turbulence structure: comparison of non-uniform accelerating and decelerating flows. Environ. Fluid Mech. 18 (2), 395–416.CrossRefGoogle Scholar
Rashidi, M. 1997 Burst–interface interactions in free surface turbulent flows. Phys. Fluids 9 (11), 3485–3501.CrossRefGoogle Scholar
Rashidi, M. & Banerjee, S. 1988 Turbulence structure in free-surface channel flows. Phys. Fluids 31 (9), 2491–2503.CrossRefGoogle Scholar
Rawat, S., Cossu, C., Hwang, Y. & Rincon, F. 2015 On the self-sustained nature of large-scale motions in turbulent Couette flow. J. Fluid Mech. 782, 515–540.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601–639.CrossRefGoogle Scholar
Rodríguez, J. F. & García, M. H. 2008 Laboratory measurements of 3-D flow patterns and turbulence in straight open channel with rough bed. J. Hydraul Res. 46 (4), 454–465.CrossRefGoogle Scholar
Roussinova, V., Biswas, N. & Balachandar, R. 2008 Revisiting turbulence in smooth uniform open channel flow. J. Hydraul Res. 46 (sup1), 36–48.CrossRefGoogle Scholar
Roy, A. G., Buffin-Belanger, T., Lamarre, H. & Kirkbride, A. D. 2004 Size, shape and dynamics of large-scale turbulent flow structures in a gravel-bed river. J. Fluid Mech. 500, 1–27.CrossRefGoogle Scholar
Shen, C. & Lemmin, U. 1999 Application of an acoustic particle flux profiler in particleladen open-channel flow. J. Hydraul Res. 37 (3), 407–419.CrossRefGoogle Scholar
Shvidchenko, A. B. & Pender, G. 2001 Macroturbulent structure of open-channel flow over gravel beds. Water Resour. Res. 37 (3), 709–719.CrossRefGoogle Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2014 Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up 𝛿+ ≈ 2000. Phys. Fluids 26 (10), 105109.CrossRefGoogle Scholar
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Song, T. & Chiew, Y. M. 2001 Turbulence measurement in nonuniform open-channel flow using acoustic Doppler velocimeter (ADV). J. Engng Mech. 127 (3), 219–232.CrossRefGoogle Scholar
Steffler, P. M., Rajaratnam, N. & Peterson, A. W. 1985 LDA measurements in open channel. J. Hydraul Res. 111 (1), 119–130.CrossRefGoogle Scholar
Sukhodolov, A. N., Nikora, V. I. & Katolikov, V. M. 2011 Flow dynamics in alluvial channels: the legacy of Kirill V. Grishanin. J. Hydraul Res. 49 (3), 285–292.CrossRefGoogle Scholar
Tamburrino, A. & Gulliver, J. S. 1999 Large flow structures in a turbulent open channel flow. J. Hydraul Res. 37 (3), 363–380.CrossRefGoogle Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164 (919), 476–490.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Tominaga, A., Nezu, I., Ezaki, K. & Nakagawa, H. 1989 Three-dimensional turbulent structure in straight open channel flows. J. Hydraul Res. 27 (1), 149–173.CrossRefGoogle Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.CrossRefGoogle Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11 (1), 97–120.CrossRefGoogle Scholar
Trinci, G., Harvey, G. L., Henshaw, A. J., Bertoldi, W. & Hölker, F. 2017 Life in turbulent flows: interactions between hydrodynamics and aquatic organisms in rivers. Wiley Interdiscip. Rev.: Water 4 (3), e1213.Google Scholar
Venditti, J. G., Best, J. L., Church, M. & Hardy, R. J. 2013 Coherent Flow Structures at Earth’s Surface. John Wiley & Sons.CrossRefGoogle Scholar
Wang, G. & Richter, D. H. 2019 Two mechanisms of modulation of very-large-scale motions by inertial particles in open channel flow. J. Fluid Mech. 868, 538–559.CrossRefGoogle Scholar
Wang, Z. Q. & Cheng, N. S. 2005 Secondary flows over artificial bed strips. Adv. Water Resour. 28 (5), 441–450.CrossRefGoogle Scholar
Wei, T. & Willmarth, W. 1989 Reynolds-number effects on the structure of a turbulent channel flow. J. Fluid Mech. 204, 57–95.CrossRefGoogle Scholar
Zhong, Q., Chen, Q., Wang, H., Li, D. & Wang, X. 2016 Statistical analysis of turbulent super-streamwise vortices based on observations of streaky structures near the free surface in the smooth open channel flow. Water Resour. Res. 52 (5), 3563–3578.CrossRefGoogle Scholar
Zhong, Q., Li, D., Chen, Q. & Wang, X. 2015 Coherent structures and their interactions in smooth open channel flows. Environ. Fluid Mech. 15 (3), 653–672.CrossRefGoogle Scholar