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Large-scale turbulent structure of uniform shallow free-surface flows

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Abstract

The hydrodynamics of super- and sub-critical shallow uniform free-surface flows are assessed using laboratory experiments aimed at identifying and quantifying flow structure at scales larger than the flow depth. In particular, we provide information on probability distributions of horizontal velocity components, their correlation functions, velocity spectra, and structure functions for the near-water-surface flow region. The data suggest that for the high Froude number flows the structure of the near-surface layer resembles that of two-dimensional turbulence with an inverse energy cascade. In contrast, although large-scale velocity fluctuations were also present in low Froude number flow its behaviour was different, with a direct energy cascade. Based on our results and some published data we suggest a physical explanation for the observed behaviours. The experiments support Jirka’s [Jirka GH (2001) J Hydraul Res 39(6):567–573] hypothesis that secondary instabilities of the base flow may generate large-scale two-dimensional eddies, even in the absence of transverse gradients in the time-averaged flow properties.

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Abbreviations

PTV:

Particle Tracking Velocimetry

CCD:

Charge-coupled device

PULNiXTM :

TM-6710 progressive scan digital camera

g :

Gravity acceleration

H :

Flow depth

S :

Bed slope

u :

Longitudinal velocity component

u * :

Shear velocity, u * = (τ o /ρ)0.5 = (gHS)0.5

U a :

Vertically-averaged longitudinal velocity

U s :

Spatially- and time-averaged near-surface longitudinal velocity

v :

Transverse velocity component

ρ:

Fluid density

τ o :

Bed shear stress

Fr :

Froude number, Fr = U a /(gH)0.5

Re :

Reynolds number, Re = U a H/ν

f :

Friction factor, f = 8(u * /U a )2

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Authors and Affiliations

  1. Department of Engineering, University of Aberdeen, Fraser Noble Building, Kings College, Aberdeen, Scotland, AB24 3UE, UK

    V. Nikora

  2. Department of Civil Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8020, New Zealand

    R. Nokes, W. Veale & M. Davidson

  3. Institute of Hydromechanics, University of Karlsruhe, Kaiserstr. 12, 76128, Karlsruhe, Germany

    G. H. Jirka

Authors
  1. V. Nikora
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  2. R. Nokes
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  3. W. Veale
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  4. M. Davidson
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  5. G. H. Jirka
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Correspondence to V. Nikora.

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Nikora, V., Nokes, R., Veale, W. et al. Large-scale turbulent structure of uniform shallow free-surface flows. Environ Fluid Mech 7, 159–172 (2007). https://doi.org/10.1007/s10652-007-9021-z

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