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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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Figures

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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. 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. 2

Particle size distribution of sediment mixture used in the experiments

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Fig. 1

Schematic diagram of large tilting flume

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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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