Skip to main content
SpringerLink
Log in

Turbulence characteristics in wall-wake flows downstream of wall-mounted and near-wall horizontal cylinders

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

Abstract

Turbulent characteristics in wall-wake flows downstream of wall-mounted and near-wall cylinders are investigated. The distributions of the defect of streamwise velocity, Reynolds shear stress and turbulence intensities exhibit a certain degree of self-preserving characteristic when they are scaled by their respective peak defect values. For the velocity defect distributions, the vertical distances are scaled by the half-width of peak defect velocity. However, for the distributions of the defects of the Reynolds shear stress and the turbulence intensities, the vertical distances are scaled by the half-width of Reynolds shear stress defect. The peak defects of all the quantities reduce with longitudinal distance signifying the recovery of the upstream distributions of the individual quantities. The third-order correlations reveal that for the wall-mounted cylinder, a streamwise acceleration associated with a downward flux of streamwise Reynolds normal stress (SRNS) in the inner-layer of wall-wake composes sweeps and a streamwise deceleration associated with an upward flux of SRNS in the outer-layer forms ejections. On the other hand, for the near-wall cylinder, a streamwise deceleration associated with a downward flux of SRNS in the inner-layer of wall-wake flow and the gap flow produces the inward interaction events, while the outer-layer characteristic is similar to that of wall-mounted cylinder. The turbulent kinetic energy (TKE) budget in the wake flow demonstrates strong negative pressure energy diffusion in addition to a strong TKE dissipation and diffusion and that in the gap flow exhibits a minor positive peak of pressure energy diffusion and a minor negative peak of TKE diffusion.

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

Similar content being viewed by others

Abbreviations

D :

Cylinder diameter (L)

d 50 :

Median size of sand (L)

E D :

Nondimensional TKE dissipation rate (–)

\( \mathsf{F} \) :

Flow Froude number, \( \overline{U} \)/(gh)0.5 (–)

F ii :

Power spectral density function (L2T−1)

f :

Frequency (T−1)

f kw :

Vertical flux of TKE, \( \overline{{kw^{\prime}}} \) (L3T−3)

g :

Acceleration due to gravity (LT−2)

h :

Flow depth (L)

k :

TKE, 0.5(\( \overline{{u^{\prime}u^{\prime}}} \) + \( \overline{{v^{\prime}v^{\prime}}} \) + \( \overline{{w^{\prime}w^{\prime}}} \)) (L2T−2)

k s :

Roughness height (L)

k w :

Wave number (L−1)

M jk :

Third-order correlations (–)

P D :

Nondimensional pressure energy diffusion rate (–)

p′:

Fluctuations of hydrostatic pressure relative to mass density of fluid (L2T−2)

p D :

Pressure energy diffusion rate (L2T−3)

\( \mathsf{R} \) :

Reynolds number characterized by cylinder diameter, \( \overline{U} \) D/υ (–)

\( \mathsf{R}_{\text{*}} \) :

Shear-particle Reynolds number, u*ks/υ (–)

S uu :

Spectral density as a function of kw (L3T−2)

T D :

Nondimensional TKE diffusion rate (–)

T P :

Nondimensional TKE production rate (–)

t D :

TKE diffusion rate (L2T−3)

t P :

TKE production rate (L2T−3)

U :

Time-average approaching velocity at an elevation z (LT−1)

\( \overline{U} \) :

Depth-averaged approaching velocity (LT−1)

u :

Time-averaged streamwise velocity component (LT−1)

u′:

Fluctuations of streamwise velocity (LT−1)

u * :

Approaching shear velocity (LT−1)

v :

Time-averaged transverse velocity component (LT−1)

v′:

Fluctuations of spanwise velocity (LT−1)

v D :

Viscous diffusion rate (L2T−3)

w :

Time-averaged vertical velocity component (LT−1)

w′:

Fluctuations of vertical velocity (LT−1)

x :

Streamwise distance (L)

y :

Spanwise distance (L)

z :

Vertical distance (L)

z 1 :

Height of occurrence of half of maximum velocity defect (L)

z 2 :

Height of occurrence of half of peak RSS defect (L)

Δu :

Velocity defect, U(z) − u(z) (LT−1)

Δz :

Gap thickness (L)

Δτ :

RSS defect relative to mass density of fluid, τ(z)|upstream − τ(z)|downstream (L2T−2)

Δσ u :

Streamwise turbulence intensity defect, σu(z)|upstream − σu(z)|downstream (LT−1)

Δσ w :

Vertical turbulence intensity defect, σw(z)|upstream − σw(z)|downstream (LT−1)

ε :

TKE dissipation rate (L2T−3)

ρ :

Mass density of fluid (ML−3)

σ u :

Streamwise turbulence intensity (LT−1)

σ w :

Vertical turbulence intensity (LT−1)

τ :

RSS relative to mass density of fluid (L2T−2)

υ :

Kinematic viscosity of fluid (L2T−1)

m :

Peak value

References

  1. Schlichting H (1979) Boundary layer theory. McGraw-Hill Book Company, New York

    Google Scholar 

  2. Angrilli F, Bergamaschi S, Cossalter V (1982) Investigation of wall induced modifications to vortex shedding from a circular cylinder. J Fluids Eng 104(4):518–522

    Article  Google Scholar 

  3. Grass AJ, Raven PWJ, Stuart RJ, Bray JA (1984) The influence of boundary layer velocity gradients and bed proximity on vortex shedding from free spanning pipelines. J Energy Resour Technol 106(1):70–78

    Article  Google Scholar 

  4. Lei C, Cheng L, Kavanagh K (1999) Re-examination of the effect of a plane boundary on force and vortex shedding of a circular cylinder. J Wind Eng Ind Aerodyn 80(3):263–286

    Article  Google Scholar 

  5. Price SJ, Sumner D, Smith JG, Leong K, Paidoussis MP (2002) Flow visualisation around a circular cylinder near to a plane wall. J Fluids Struct 16(2):175–191

    Article  Google Scholar 

  6. Testik FY, Voropayev SI, Fernando HJS (2005) Flow around a short horizontal bottom cylinder under steady and oscillatory flows. Phys Fluids 17(4):047103

    Article  Google Scholar 

  7. Smith HD, Foster DL (2007) Three-dimensional flow around a bottom–mounted short cylinder. J Hydraul Eng 133(5):534–544

    Article  Google Scholar 

  8. Wang XK, Tan SK (2008) Near-wake flow characteristics of a circular cylinder close to a wall. J Fluids Struct 24(5):605–627

    Article  Google Scholar 

  9. Lin WJ, Lin C, Hsieh SC, Dey S (2009) Flow characteristics around a circular cylinder placed horizontally above a plane boundary. J Eng Mech 135(7):697–716

    Article  Google Scholar 

  10. Kahraman A, Ozgoren M, Sahin B (2012) Flow structure from a horizontal cylinder coincident with a free surface in shallow water flow. Therm Sci 16(1):93–107

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Ozdil NFT, Akilli H (2015) Investigation of flow structure around a horizontal cylinder at different elevations in shallow water. Ocean Eng 96(March):56–67

    Article  Google Scholar 

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

    Book  Google Scholar 

  14. Goring DG, Nikora VI (2002) Despiking acoustic Doppler velocimeter data. J Hydraul Eng 128(1):117–126

    Article  Google Scholar 

  15. Lacey RWJ, Roy AG (2008) Fine-scale characterization of the turbulent shear layer of an instream pebble cluster. J Hydraul Eng 134(7):925–936

    Article  Google Scholar 

  16. Blanckaert K, Lemmin U (2006) Means of noise reduction in acoustic turbulence measurements. J Hydraul Res 44(1):1–17

    Article  Google Scholar 

  17. Dey S, Sarkar S, Bose SK, Tait S, Castro-Orgaz O (2011) Wall-wake flows downstream of a sphere placed on a plane rough wall. J Hydraul Eng 137(10):1173–1189

    Article  Google Scholar 

  18. Sadeque MAF, Rajaratnam N, Loewen MR (2009) Shallow turbulent wakes behind bed-mounted cylinders in open channels. J Hydraul Res 47(6):727–743

    Article  Google Scholar 

  19. Sforza PM, Mons RF (1970) Wall-wake: flow behind a leading edge obstacle. AIAA J 8(2):2162–2167

    Google Scholar 

  20. Schmeeckle MW, Nelson JM (2003) Direct numerical simulation of bedload transport using a local, dynamic boundary condition. Sedimentology 50(2):279–301

    Article  Google Scholar 

  21. Dey S, Sarkar A (2006) Response of velocity and turbulence in submerged wall jets to abrupt changes from smooth to rough beds and its application to scour downstream of an apron. J Fluid Mech 556:387–419

    Article  Google Scholar 

  22. Dey S, Sarkar A (2008) Characteristics of turbulent flow in submerged jumps on rough beds. J Eng Mech 134(1):49–59

    Article  Google Scholar 

  23. Dey S, Nath TK, Bose SK (2010) Submerged wall jets subjected to injection and suction from the wall. J Fluid Mech 653:57–97

    Article  Google Scholar 

  24. Gad-El-Hak M, Bandyopadhyay PR (1994) Reynolds number effects in wall-bounded turbulent flows. Appl Mech Rev 47(8):307–365

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Nakagawa H, Nezu I (1977) Prediction of the contributions to the Reynolds stress from bursting events in open-channel flows. J Fluid Mech 80:99–128

    Article  Google Scholar 

  27. Nezu I, Nakagawa H (1993) Turbulence in open-channel flows. Balkema, Rotterdam

    Google Scholar 

  28. Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge

    Book  Google Scholar 

  29. Monin AS, Yaglom AM (2007) Statistical fluid mechanics, volume II: mechanics of turbulence. Dover Publications, New York

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  32. Sarkar S, Dey S (2010) Double-averaging turbulence characteristics in flows over a gravel-bed. J Hydraul Res 48(6):801–809

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Subhasish Dey & Rajashree Lodh

  2. Physics and Applied Mathematics Unit, Indian Statistical Institute Kolkata, Kolkata, West Bengal, 700108, India

    Subhasish Dey & Sankar Sarkar

  3. Department of Hydraulic Engineering, State Key Laboratory of Hydro-Science and Engineering, Tsinghua University, Beijing, 100084, China

    Subhasish Dey

Authors
  1. Subhasish Dey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rajashree Lodh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sankar Sarkar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Subhasish Dey.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dey, S., Lodh, R. & Sarkar, S. Turbulence characteristics in wall-wake flows downstream of wall-mounted and near-wall horizontal cylinders. Environ Fluid Mech 18, 891–921 (2018). https://doi.org/10.1007/s10652-018-9573-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10652-018-9573-0

Keywords

Search

Navigation