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Coupling between free-surface fluctuations, velocity fluctuations and turbulent Reynolds stresses during the upstream propagation of positive surges, bores and compression waves

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Abstract

In open channel, canals and rivers, a rapid increase in flow depth will induce a positive surge, also called bore or compression wave. The positive surge is a translating hydraulic jump. Herein new experiments were conducted in a large-size rectangular channel to characterise the unsteady turbulent properties, including the coupling between free-surface and velocity fluctuations. Experiments were repeated 25 times and the data analyses yielded the instantaneous median and instantaneous fluctuations of free-surface elevation, velocities and turbulent Reynolds stresses. The passage of the surge front was associated with large free-surface fluctuations, comparable to those observed in stationary hydraulic jumps, coupled with large instantaneous velocity fluctuations. The bore propagation was associated with large turbulent Reynolds stresses and instantaneous shear stress fluctuations, during the passage of the surge. A broad range of shear stress levels was observed underneath the bore front, with the probability density of the tangential stresses distributed normally and the normal stresses distributed in a skewed single-mode fashion. Maxima in normal and tangential stresses were observed shortly after the passage of a breaking bore roller toe. The maximum Reynolds stresses occurred after the occurrence of the maximum free-surface fluctuations, and this time lag implied some interaction between the free-surface fluctuations and shear stress fluctuations beneath the surge front, and possibly some causal effect.

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Acknowledgments

The authors thank Dr Carlo Gualtieri (University of Napoli “Federico II”, Italy), and Professor Shin-ichi Aoki (Osaka University, Japan) for their valuable comments. They also thank Professor Pierre Lubin (University of Bordeaux, France) for his contribution. The authors acknowledge the technical assistance of Jason Van Der Gevel and Stewart Matthews (The University of Queensland). The financial support through the Australian Research Council (Grant DP120100481) is acknowledged.

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Authors and Affiliations

  1. School of Civil Engineering, The University of Queensland, Brisbane, QLD, 4072, Australia

    Xinqian Leng & Hubert Chanson

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  1. Xinqian Leng
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  2. Hubert Chanson
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Corresponding author

Correspondence to Hubert Chanson.

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Appendix 1. Maximum reynolds stresses and corresponding time lag Δt in positive surges

Appendix 1. Maximum reynolds stresses and corresponding time lag Δt in positive surges

During the present study, the maximum Reynolds stresses and associated time lag ΔT between the occurrences of the maximum stress and bore front arrival were carefully documented. The experimental results are reported below.

So

Q (m3/s)

d1

(m)

Fr1

z/d1

Bore type

(vxvx)max

(m2/s2)

Time lag ΔTxx

(s)

(vxvy)max

(m2/s2)

Time lag ΔTxy

(s)

(vyvy)max

(m2/s2)

Time lag ΔTyy

(s)

(vyvz)max

(m2/s2)

Time lag ΔTyz

(s)

(vzvz)max

(m2/s2)

Time lag ΔTzz

(s)

(vxvz)max

(m2/s2)

Time lag ΔTxz

(s)

0.0075

0.102

0.099

2.2

0.1

Breaking

0.095

1.05

0.039

0.945

0.017

2.60

0.005

3.215

0.057

0.88

0.073

1.03

0.0075

0.102

0.099

2.2

0.4

Breaking

0.074

1.665

0.033

2.155

0.023

2.465

−0.011

2.44

0.052

1.41

−0.017

1.71

0.0075

0.102

0.1

2.2

0.8

Breaking

0.077

1.795

0.012

2.015

0.019

2.6

−0.021

1.14

0.543

0.57

0.05

0.565

0.0005

0.055

0.074

1.5

0.1

Breaking

0.038

1.21

0.007

1.13

0.009

2.09

−0.007

1.46

0.039

1.50

−0.004

1.28

0.0005

0.055

0.074

1.5

0.4

Breaking

0.026

1.57

0.004

1.44

0.006

3.07

−0.006

1.76

0.024

3.51

−0.011

2.88

0.0005

0.055

0.074

1.5

0.8

Breaking

0.017

5.36

0.023

5.09

0.004

4.89

−0.01

1.83

0.297

1.31

0.027

1.30

0

0.101

0.175

1.5

0.1

Breaking

0.011

1.33

−0.001

1.22

N/A

N/A

N/A

N/A

0.013

1.33

−0.006

1.19

0

0.102

0.181

1.5

0.4

Breaking

0.016

0.52

−0.001

1.21

0.003

1.95

−0.004

1.95

0.011

0.46

−0.005

0.56

0

0.102

0.175

1.5

0.8

Breaking

0.008

1.43

0.001

1.44

0.003

1.35

0.002

1.35

0.015

1.38

−0.005

1.62

0

0.102

0.205

1.2

0.1

Undular

0.009

1.025

0.001

1.065

N/A

N/A

N/A

N/A

0.015

1.51

−0.005

0.64

0

0.102

0.204

1.2

0.4

Undular

0.006

1.495

−0.001

0.35

N/A

N/A

N/A

N/A

N/A

N/A

0.002

1.48

0

0.102

0.203

1.2

0.8

Undular

0.006

0.88

−0.001

0.865

N/A

N/A

−0.001

1.42

0.028

1.82

−0.003

1.19

0

0.056

0.196

1.2

0.1

Undular

0.007

2.665

N/A

N/A

N/A

N/A

N/A

N/A

N/A

N/A

−0.003

0.42

0

0.056

0.197

1.2

0.4

Undular

0.006

0.79

N/A

N/A

N/A

N/A

−0.002

1.18

0.103

2.285

N/A

N/A

0

0.056

0.198

1.2

0.8

Undular

0.007

0.925

−0.001

0.955

0.0008

0.925

−0.002

1.565

0.033

2.395

−0.003

0.805

  1. Italic data unusual although likely meaningful data; Bold Italic data suspicious data

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Leng, X., Chanson, H. Coupling between free-surface fluctuations, velocity fluctuations and turbulent Reynolds stresses during the upstream propagation of positive surges, bores and compression waves. Environ Fluid Mech 16, 695–719 (2016). https://doi.org/10.1007/s10652-015-9438-8

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