Research Papers: Fundamental Issues and Canonical Flows

High-Order Velocity Moments of Turbulent Boundary Layers in Seepage Affected Alluvial Channel

[+] Author and Article Information
Anurag Sharma

Department of Civil Engineering,
Indian Institute of Technology,
Guwahati 781039, India
e-mail: anurag.sharma@iitg.ac.in

Bimlesh Kumar

Department of Civil Engineering,
Indian Institute of Technology,
Guwahati 781039, India
e-mail: bimk@iitg.ac.in

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 10, 2017; final manuscript received January 28, 2018; published online March 29, 2018. Assoc. Editor: Daniel Livescu.

J. Fluids Eng 140(8), 081204 (Mar 29, 2018) (8 pages) Paper No: FE-17-1575; doi: 10.1115/1.4039253 History: Received September 10, 2017; Revised January 28, 2018

In this work, we have performed the flume study to analyze the high-order velocity moments of turbulent boundary layer with and without downward seepage. Sediment transport experiments were done in the laboratory for no seepage (NS), 10% seepage (10%S), and 15% seepage (15%S) cases. Measures of streamwise velocity variance were found increasing with seepage, which lead to increase in sediment transport with seepage. Results show that the variance of streamwise velocity fluctuation follows logarithmic law with distance away from the bed, within inner layer. This observation is also valid for even-order moments obtained in this work. The results show that the (2p-order moments)1/p also follows logarithmic law. The slopes Ap in the turbulent boundary layer seem fairly unaffected to NS and seepage flow but follows nonuniversal behavior for NS and seepage runs. The computed slope based on the Gaussian statistics does not agree well with the slope obtained from the experimental data and computed slope are reliable with sub-Gaussian performance for NS flow and super-Gaussian behavior for seepage flow.

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Bennett, S. J. , and Best, J. L. , 1995, “ Particle Size and Velocity Discrimination in a Sediment-Laden Turbulent Flow Using Phase Doppler Anemometry,” ASME J. Fluids Eng., 117(3), pp. 505–511. [CrossRef]
Sumer, B. M. , Chua, L. H. , Cheng, N. S. , and Fredsøe, J. , 2003, “ Influence of Turbulence on Bed Load Sediment Transport,” J. Hydraul. Eng., 129(8), pp. 585–596. [CrossRef]
Kline, S. J. , Reynolds, W. C. , Schraub, F. A. , and Runstadler, P. W. , 1967, “ The Structure of Turbulent Boundary Layers,” J. Fluid Mech., 30(4), pp. 741–773. [CrossRef]
Sutherland, A. J. , 1967, “ Proposed Mechanism for Sediment Entrainment by Turbulent Flows,” J. Geophys. Res., 72(24), pp. 6183–6194. [CrossRef]
Thorne, P. D. , Williams, J. J. , and Heathershaw, A. D. , 1989, “ In Situ Acoustic Measurements of Marine Gravel Threshold and Transport,” Sedimentology, 36(1), pp. 61–74. [CrossRef]
Best, J. I. M. , 1992, “ On the Entrainment of Sediment and Initiation of Bed Defects: Insights From Recent Developments Within Turbulent Boundary Layer Research,” Sedimentology, 39(5), pp. 797–811. [CrossRef]
Cao, Z. , 1997, “ Turbulent Bursting-Based Sediment Entrainment Function,” J. Hydraul. Eng., 123(3), pp. 233–236. [CrossRef]
Dwivedi, A. , Melville, B. , and Shamseldin, A. Y. , 2010, “ Hydrodynamic Forces Generated on a Spherical Sediment Particle During Entrainment,” J. Hydraul. Eng., 136(10), pp. 756–769. [CrossRef]
Heathershaw, A. D. , and Thorne, P. D. , 1985, “ Sea-Bed Noises Reveal Role of Turbulent Bursting Phenomenon in Sediment Transport by Tidal Currents,” Nature, 316(6026), pp. 339–342. [CrossRef]
Drake, T. G. , Shreve, R. L. , Dietrich, W. E. , Whiting, P. J. , and Leopold, L. B. , 1988, “ Bedload Transport of Fine Gravel Observed by Motion-Picture Photography,” J. Fluid Mech., 192(1), pp. 193–217. [CrossRef]
Song, T. , and Graf, W. H. , 1994, “ Non-Uniform Open-Channel Flow Over a Rough Bed,” J. Hydrosci. Hydraul. Eng., 12(1), pp. 1–25.
Bennett, S. J. , and Bridge, J. S. , 1995, “ The Geometry and Dynamics of Low-Relief Bed Forms in Heterogeneous Sediment in a Laboratory Channel, and Their Relationship to Water Flow and Sediment Transport,” J. Sediment. Res., 65(1), pp. 29–39.
Nikora, V. , and Goring, D. , 1999, “Effects of Bed Mobility on Turbulence Structure,” National Institute of Water and Atmospheric Research, Christchurch, New Zealand, NIWA Internal Report No. 48.
Nikora, V. , and Goring, D. , 2000, “ Flow Turbulence Over Fixed and Weakly Mobile Gravel Beds,” J. Hydraul. Eng., 126(9), pp. 679–690. [CrossRef]
Venditti, J. G. , Church, M. , and Bennett, S. J. , 2005, “ Morphodynamics of Small Scale Superimposed Sand Waves Over Migrating Dune Bed Forms,” Water Resour. Res., 41(10), p. W10423DOI.
Saber, A. , Lundström, T. S. , and Hellström, J. G. I. , 2016, “ Influence of Inertial Particles on Turbulence Characteristics in Outer and Near Wall Flow as Revealed With High Resolution Particle Image Velocimetry,” ASME J. Fluids Eng., 138(9), p. 091303. [CrossRef]
Rao, A. R. , Sreenivasulu, G. , and Kumar, B. , 2011, “ Geometry of Sand Bed Channels With Seepage,” Geomorphology, 128(3–4), pp. 171–177. [CrossRef]
Lu, Y. , Chiew, Y. M. , and Cheng, N. S. , 2008, “ Review of Seepage Effects on Turbulent Open-Channel Flow and Sediment Entrainment,” J. Hydraul. Res., 46(4), pp. 476–488. [CrossRef]
Cao, D. , and Chiew, Y. M. , 2014, “ Suction Effects on Sediment Transport in Closed-Conduit Flows,” J. Hydraul. Eng., 140(5), p. 04014008. [CrossRef]
Deshpande, V. , and Kumar, B. , 2016, “ Turbulent Flow Structures in Alluvial Channels With Curved Cross-Sections Under Conditions of Downward Seepage,” Earth Surf. Process. Landforms, 41(8), pp. 1073–1087. [CrossRef]
Singha, A. , Faruque, M. A. A. , and Balachandar, R. , 2012, “ Vortices and Large-Scale Structures in a Rough Open-Channel Flow Subjected to Bed Suction and Injection,” J. Eng. Mech., 138(5), pp. 491–501. [CrossRef]
Prinos, P. , 1995, “ Bed Suction Effects on Structure of Turbulent Open-Channel Flow,” J. Hydraul. Eng., 121(5), pp. 404–412. [CrossRef]
Sreenivasulu, G. , Kumar, B. , and Rao, A. R. , 2011, “ Variation of Stream Power With Seepage in Sand Bed Channels,” Water SA, 37(1), pp. 115–119. [CrossRef]
Lu, Y. , and Chiew, Y. M. , 2007, “ Seepage Effects on Dune Dimensions,” J. Hydraul. Eng., 133(5), pp. 560–563. [CrossRef]
Patel, M. , Deshpande, V. , and Kumar, B. , 2015, “ Turbulent Characteristics and Evolution of Sheet Flow in an Alluvial Channel With Downward Seepage,” Geomorphology, 248, pp. 161–171. [CrossRef]
Devi, T. B. , Sharma, A. , and Kumar, B. , 2016, “ Turbulence Characteristics of Vegetated Channel With Downward Seepage,” ASME J. Fluids Eng., 138(12), p. 121102. [CrossRef]
Devi, T. B. , Daga, R. , Mahto, S. K. , and Kumar, B. , 2016, “ Drag and Turbulent Characteristics of Mobile Bed Channel With Mixed Vegetation Densities Under Downward Seepage,” ASME J. Fluids Eng., 138(7), p. 071104. [CrossRef]
Qian, J. , 1998, “ Scaling Exponents of the Second Order Structure Function of Turbulence,” J. Phys. A: Math. Gen., 31(14), p. 3193. [CrossRef]
Davidson, P. A. , Nickels, T. B. , and Krogstad, P. Å. , 2006, “ The Logarithmic Structure Function Law in Wall-Layer Turbulence,” J. Fluid Mech., 550(1), pp. 51–60. [CrossRef]
Huang, Y. X. , Schmitt, F. G. , Lu, Z. M. , Fougairolles, P. , Gagne, Y. , and Liu, Y. L. , 2010, “ Second Order Structure Function in Fully Developed Turbulence,” Phys. Rev. E, 82(2), p. 026319. [CrossRef]
Meneveau, C. , and Marusic, I. , 2013, “ Generalized Logarithmic Law for High-Order Moments in Turbulent Boundary Layers,” J. Fluid Mech., 719, p. R1.
de Silva, C. M. , Marusic, I. , Woodcock, J. D. , and Meneveau, C. , 2015, “ Scaling of Second-and Higher-Order Structure Functions in Turbulent Boundary Layers,” J. Fluid Mech., 769, pp. 654–686. [CrossRef]
Wu, W. , Wang, S. S. , and Jia, Y. , 2000, “ Non-Uniform Sediment Transport in Alluvial Rivers,” J. Hydraul. Res., 38(6), pp. 427–434. [CrossRef]
Sharma, A. , and Kumar, B. , 2016, “ Probability Distribution of Turbulence in Curvilinear Cross Section Mobile Bed Channel,” Water Sci. Technol., 73(6), pp. 1472–1482. [CrossRef] [PubMed]
Sharma, A. , and Kumar, B. , 2016, “ Probability Distribution Functions of Turbulence in Seepage-Affected Alluvial Channel,” Fluid Dyn. Res., 49(1), p. 015508. [CrossRef]
Marsh, N. A. , Western, A. W. , and Grayson, R. B. , 2004, “ Comparison of Methods for Predicting Incipient Motion for Sand Beds,” J. Hydraul. Eng., 130(7), pp. 616–621. [CrossRef]
Goring, D. G. , and Nikora, V. I. , 2002, “ Despiking Acoustic Doppler Velocimeter Data,” J. Hydraul. Eng., 128(1), pp. 117–126. [CrossRef]
Lacey, R. W. , and Roy, A. G. , 2008, “ Fine-Scale Characterization of the Turbulent Shear Layer of an Instream Pebble Cluster,” J. Hydraul. Eng., 134(7), pp. 925–936. [CrossRef]
Smith, J. D. , and McLean, S. R. , 1977, “ Spatially Averaged Flow Over a Wavy Surface,” J. Geophys. Res., 82(12), pp. 1735–1746. [CrossRef]
Sharma, A. , and Kumar, B. , 2017, “ Structure of Turbulence Over Non Uniform Sand Bed Channel With Downward Seepage,” Eur. J. Mech./B Fluids, 65, pp. 530–541. [CrossRef]
Prandtl, L. , 1925, “ Bericht Uber Untersuchungen Zur Ausgebildeten Turbulenz,” Z. Angew. Math. Mech., 5(2), pp. 136–139.
Von Kármán, T. , 1930, “ Mechanische Änlichkeit Und Turbulenz. Nachrichten Von Der Gesellschaft Der Wissenschaften Zu Göttingen,” Math.-Phys. Kl., pp. 58–76.
Smits, A. J. , McKeon, B. J. , and Marusic, I. , 2011, “ High Reynolds Number Wall Turbulence,” Annu. Rev. Fluid Mech., 43(1), pp. 353–375. [CrossRef]
Jiménez, J. , 2012, “ Cascades in Wall-Bounded Turbulence,” Annu. Rev. Fluid Mech., 44(1), pp. 27–45. [CrossRef]
Nezu, I. , 1977, “Turbulent Structure in Open-Channel Flows,” Ph.D. thesis, Kyoto University, Kyoto, Japan.
Marusic, I. , and Kunkel, G. J. , 2003, “ Streamwise Turbulence Intensity Formulation for Flat-Plate Boundary Layers,” Phys. Fluids, 15(8), pp. 2461–2464. [CrossRef]
Hultmark, M. , Vallikivi, M. , Bailey, S. C. C. , and Smits, A. J. , 2012, “ Turbulent Pipe Flow at Extreme Reynolds Numbers,” Phys. Rev. Lett., 108(9), p. 094501. [CrossRef] [PubMed]
Marusic, I. , Monty, J. P. , Hultmark, M. , and Smits, A. J. , 2013, “ On the Logarithmic Region in Wall Turbulence,” J. Fluid Mech., 716, p. R3. [CrossRef]
Fernholz, H. H. , and Finleyt, P. J. , 1996, “ The Incompressible Zero-Pressure-Gradient Turbulent Boundary Layer: An Assessment of the Data,” Prog. Aerosp. Sci., 32(4), pp. 245–311. [CrossRef]


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Fig. 1

Schematic diagram of large tilting flume

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Fig. 2

Particle size distribution of sediment mixture used in the experiments

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Fig. 3

Velocity power spectra before and after spike removal with Kolmogorov's −5/3 law in the inertial sub range at z = 5 mm for streamwise velocities of flow subjected to NS, 10% seepage (10% S), and 15% seepage (15% S)

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Fig. 4

(a) Vertical profiles of normalized time average streamwise velocity (=u/ufs, where ufs is the free stream velocity) and (b) vertical profiles of Reynolds shear stress for flow subjected to NS, 10% seepage (10% S), and 15% seepage (15% S)

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Fig. 5

Variance of streamwise velocity in turbulent boundary layers for flow subjected to NS, 10% seepage (10% S), and 15% seepage (15% S)

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Fig. 6

Premultiplied PDF of normalized velocity fluctuations u+2p P(u+) for flow subjected to NS, 10% seepage (10% S), and 15% seepage (15% S) at a height of z/h = 0.07. Different moments are represented as (a) 2p = 2, (b) 2p = 4, and (c) 2p = 6.

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Fig. 7

Moments of order 2p = 6 of streamwise velocity as a function of wall-normal distance, for flow subjected to NS, 10% seepage (10% S), and 15% seepage (15% S)

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Fig. 8

Moments of different orders of streamwise velocity fluctuation as a function of wall-normal distance for flow subjected to NS, 10% seepage (10% S), and 15% seepage (15% S)

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Fig. 9

Coefficients Ap in logarithmic law for moments as a function of moment order 2p for no seepage (•), 10% seepage (▪), and 15% seepage runs (▲). The crosses and dashed lineshow the results expected for Gaussian statistics, Ap=A1[(2p−1)!!]1/p.

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Fig. 10

Flatness factor F4 as a function of wall distance, for flow subjected to NS, 10% seepage (10% S), and 15% seepage (15% S)



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