Skip to main content
SpringerLink
Log in

Response of open-channel flow to a sudden change from smooth to rough bed

  • Original Article
  • Published:
Environmental Fluid Mechanics Aims and scope Submit manuscript

Abstract

The turbulence characteristics in open-channel flow owing to a sudden change from smooth (upstream) to rough (downstream) bed are investigated experimentally using a Particle Image Velocimetry system. The upstream flow had a shear Reynolds number of 4.86, characterizing the hydraulically smooth flow, while the downstream flow had a shear Reynolds number greater than 70, characterizing the hydraulically rough flow. The Reynolds stress results reveal that for a given vertical distance, both the Reynolds shear and normal stresses in the downstream bed increase with the streamwise distance as compared to their upstream values. Their peaks appear at a distance of one-fifth of the flow depth from the bed. In addition, the bed shear stress enhances with the streamwise distance. The stress contours corroborate that the formation of a roughness-induced layer over the downstream bed thickens with the streamwise distance. The third-order correlations reveal that an arrival of slowly moving fluid streaks associated with an outward Reynolds stress diffusion prevails in the flow on the upstream bed, while an inrush of rapidly moving fluid streaks associated with an inward Reynolds stress diffusion governs the near-bed flow zone in the downstream bed. These results are in conformity with those obtained from the turbulent kinetic energy (TKE) fluxes and the bursting events. With regard to the TKE budget, the peaks of TKE production and dissipation rates appear near the downstream bed and are greater than those in the upstream bed. However, in the downstream bed, an enhanced negative TKE diffusion prevails near the bed.

Article highlights

  • Turbulent flow field on a sudden change from smooth to rough bed converting the flow from smooth to rough.

  • Formation of a roughness-induced layer over the downstream rough bed.

  • Understanding the effects of a sudden change in bed roughness on the turbulence characteristics from the perspectives of their time-averaged spatial fields.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Data availability

Data used in Figs. 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19 are available from the corresponding author by request.

Abbreviations

D 50 :

Median size of uniform gravel

d 50 :

Median size of sand

E D :

Normalized TKE dissipation rate

F :

Froude number

F ku :

Normalized streamwise TKE flux

F kw :

Normalized vertical TKE flux

f ku :

Streamwise TKE flux

f kw :

Vertical TKE flux

g :

Gravitational acceleration

H :

Hole size

h :

Flow depth

I :

Turbulence indicator

k :

Time-averaged TKE

k s :

Average roughness height

L :

Streamwise distance required to grow δ

m jk :

Third-order correlations

P D :

Normalized pressure energy diffusion rate

p′:

Pressure fluctuation

p d :

Pressure energy diffusion rate

Q i :

Quadrant i

R * :

Shear Reynolds number

S :

Streamwise bed slope

S i , H :

Fractional contribution of conditional Reynolds shear stress

T :

Sampling time

T D :

Normalized TKE diffusion rate

T P :

Normalized TKE production rate

t :

Time

t d :

TKE diffusion rate

t p :

TKE production rate

\(\overline{U}\) :

Time-averaged flow velocity

U a :

Depth-averaged streamwise velocity

U c :

Threshold streamwise velocity

U max :

Maximum streamwise velocity

\(\overline{u}\) :

Time-averaged streamwise velocity

u′:

Fluctuations of streamwise velocity

u * :

Shear velocity

u * x :

Local shear velocity at x

v d :

Viscous diffusion rate

\(\overline{w}\) :

Time-averaged vertical velocity

w′:

Fluctuations of vertical velocity

x :

Streamwise coordinate

z :

Vertical coordinate

z 0 :

Zero-velocity level

ν :

Coefficient of kinematic viscosity of water

Δ t :

Inter-frame time

Δz :

Depth of virtual bed level from bed surface or Nikuradse zero-plane displacement

δ :

Boundary layer thickness

δ 0 :

Roughness-induced layer thickness

ε :

TKE dissipation rate

κ :

Von Kármán coefficient

λ i , H :

Detecting function

ρ :

Mass density of water

τ 0 :

Bed shear stress

ω :

Instantaneous vorticity

References

  1. Elliott WP (1958) The growth of the atmospheric internal boundary layer. Trans Am Geophys Union 39(6):1048–1054

    Article  Google Scholar 

  2. Townsend AA (1965) Self-preserving flow inside a turbulent boundary layer. J Fluid Mech 22(4):773–797

    Article  Google Scholar 

  3. Townsend AA (1965) The response of a turbulent boundary layer to abrupt changes in surface conditions. J Fluid Mech 22(4):799–822

    Article  Google Scholar 

  4. Townsend AA (1966) The flow in a turbulent boundary layer after a change in surface roughness. J Fluid Mech 26(2):255–266

    Article  Google Scholar 

  5. Taylor PA (1969) On wind and shear stress profiles above a change in surface roughness. Q J R Met Soc 95(January):77–91

    Article  Google Scholar 

  6. Blom J, Wartena L (1969) The influence of changes in surface roughness on the development of the turbulent boundary layer in the lower layers of the atmosphere. J Atmos Sci 26(March):255–265

    Article  Google Scholar 

  7. Antonia RA, Luxton RE (1971) The response of a turbulent boundary layer to a step change in surface roughness. Part 1. Smooth to rough. J Fluid Mech 48(4):721–761

    Article  Google Scholar 

  8. Mulhearn PJ (1977) Relations between surface fluxes and mean profiles of velocity, temperature and concentration, downwind of a change in surface roughness. Q J R Met Soc 103(October):785–802

    Article  Google Scholar 

  9. Andreopoulos J, Wood DH (1982) The response of a turbulent boundary layer to a short length of surface roughness. J Fluid Mech 118(May):143–164

    Article  Google Scholar 

  10. Efros V, Krogstad P-Å (2011) Development of a turbulent boundary layer after a step from smooth to rough surface. Exp Fluids 51(July):1563–1575

    Article  Google Scholar 

  11. Nezu I, Tominaga A (1994) Response of velocity and turbulence to abrupt changes from smooth to rough beds in open-channel flow. In: Proceedings of the symposium on fundamentals and advancements in hydraulic measurements and experimentation, Buffalo, pp 195–204

  12. Chen X, Chiew Y-M (2003) Response of velocity and turbulence to sudden change of bed roughness in open-channel flow. J Hydraul Eng 129(1):35–43

    Article  Google Scholar 

  13. Monin AS, Yaglom AM (1971) Statistical fluid mechanics: mechanics of turbulence, vol 1. MIT Press, Cambridge

    Google Scholar 

  14. Buffin-Bélanger T, Roy A (2005) 1 min in the life of a river: selecting the optimal record length for the measurement of turbulence in fluvial boundary layers. Geomorphology 68(1–2):77–94

    Article  Google Scholar 

  15. Detert M, Nikora V, Jirka GH (2010) Synoptic velocity and pressure fields at the water–sediment interface of streambeds. J Fluid Mech 660(October):55–86

    Article  Google Scholar 

  16. Penna N, Padhi E, Dey S, Gaudio R (2021) Statistical characterization of unworked and water-worked gravel-bed roughness structures. J Hydraul Res 59(3):420–436

    Article  Google Scholar 

  17. Neill CR (1968) Note on initial movement of coarse uniform bed-material. J Hydraul Res 6(2):173–176

    Article  Google Scholar 

  18. Cook NJ (1997) The Deaves and Harris ABL model applied to heterogeneous terrain. J Wind Eng Ind Aerodyn 66(3):197–214

    Article  Google Scholar 

  19. Dey S, Das R (2012) Gravel-bed hydrodynamics: double-averaging approach. J Hydraul Eng 138(8):707–725

    Article  Google Scholar 

  20. Dey S, Das R, Gaudio R, Bose SK (2012) Turbulence in mobile-bed streams. Acta Geophys 60(6):1547–1588

    Article  Google Scholar 

  21. Shir CC (1972) A numerical computation of air flow over a sudden change of surface of surface roughness. J Atmos Sci 29(2):304–310

    Article  Google Scholar 

  22. Bou-Zeid E, Meneveau C, Parlange MB (2004) Large-eddy simulation of neutral atmospheric boundary layer flow over heterogeneous surfaces: blending height and effective surface roughness. Water Resour Res 40(2):W02505

    Article  Google Scholar 

  23. Rouhi A, Chung D, Hutchins N (2019) Direct numerical simulation of open-channel flow over smooth-to-rough and rough-to-smooth step changes. J Fluid Mech 866(May):450–486

    Article  Google Scholar 

  24. Antonia RA, Luxton RE (1972) The response of a turbulent boundary layer to a step change in surface roughness. Part 2. Rough-to-smooth. J Fluid Mech 53(4):737–757

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Padhi E, Penna N, Dey S, Gaudio R (2018) Hydrodynamics of water-worked and screeded gravel beds: a comparative study. Phys Fluids 30(8):085105

    Article  Google Scholar 

  27. Padhi E, Penna N, Dey S, Gaudio R (2018) Spatially-averaged dissipation rate in flows over water-worked and screeded gravel beds. Phys Fluids 30(12):125106

    Article  Google Scholar 

  28. Russo F, Basse NT (2016) Scaling of turbulence intensity for low-speed flow in smooth pipes. Flow Meas Instrum 52(December):101–114

    Article  Google Scholar 

  29. Basse NT (2017) Turbulence intensity and the friction factor for smooth- and rough-wall pipe flow. Fluids 2(2):1–13

    Article  Google Scholar 

  30. Dey S (2014) Fluvial hydrodynamics: hydrodynamic and sediment transport phenomena. Springer, Berlin

    Book  Google Scholar 

  31. Padhi E, Penna N, Dey S, Gaudio R (2019) Near-bed turbulence structures in water-worked and screeded gravel-bed flows. Phys Fluids 31(4):045107

    Article  Google Scholar 

  32. Dey S, Paul P, Fang H, Padhi E (2020) Hydrodynamics of flow over two-dimensional dunes. Phys Fluids 32(2):025106

    Article  Google Scholar 

  33. Mignot E, Hurther D, Barthelemy E (2009) On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow. J Fluid Mech 638(November):423–452

    Article  Google Scholar 

  34. Fang H, Han X, He G, Dey S (2018) Influence of permeable beds on hydraulically macro-rough flow. J Fluid Mech 847(May):552–590

    Article  Google Scholar 

  35. Reidenbach MA, Limm M, Hondzo M, Stacey MT (2010) Effects of bed roughness on boundary layer mixing and mass flux across the sediment-water interface. Water Resour Res 46(7):W07530

    Article  Google Scholar 

  36. Han X, He G, Fang H (2017) Double-averaging analysis of turbulent kinetic energy fluxes and budget based on large-eddy simulation. J Hydrodyn 29(4):567–574

    Article  Google Scholar 

  37. Fincham AM, Maxworthy T, Spedding GR (1966) Energy dissipation and vortex structure in freely decaying, stratified grid turbulence. Dyn Atmos Oceans 23(1–4):155–169

    Google Scholar 

  38. Nezu I, Nakagawa H (1993) Turbulence in open-channel flows. In: Balkema AA (ed) Rotterdam

  39. Dey S, Ravi Kishore G, Castro-Orgaz O, Ali SZ (2017) Hydrodynamics of submerged turbulent plane offset jets. Phys Fluids 29(6):065112

    Article  Google Scholar 

  40. Sarkar S, Papanicolao AN, Dey S (2016) Turbulence in a gravel-bed stream with an array of large gravel obstacles. J Hydraul Eng 142(11):04016052

    Article  Google Scholar 

  41. Lu SS, Willmarth WW (1973) Measurements of the structures of the Reynolds stress in a turbulent boundary layer. J Fluid Mech 60(3):481–511

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the financial support provided by the “SILA” PONa3_00341 project, “An Integrated System of Laboratories for the Environment”. SD also acknowledges the JC Bose Fellowship Award [funded by DST, Science and Engineering Research Board (SERB), Grant Reference No JCB/2018/000004] this collaborative work.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, 721302, India

    Vijit Rathore & Subhasish Dey

  2. Dipartimento di Ingegneria Civile, Università della Calabria, 87036, Rende, CS, Italy

    Nadia Penna & Roberto Gaudio

Authors
  1. Vijit Rathore
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nadia Penna
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Subhasish Dey
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Roberto Gaudio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Subhasish Dey.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interests,

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rathore, V., Penna, N., Dey, S. et al. Response of open-channel flow to a sudden change from smooth to rough bed. Environ Fluid Mech 22, 87–112 (2022). https://doi.org/10.1007/s10652-021-09830-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10652-021-09830-5

Keywords

Search

Navigation