Environmental Fluid Mechanics

, Volume 7, Issue 2, pp 159–172 | Cite as

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

  • V. Nikora
  • R. Nokes
  • W. Veale
  • M. Davidson
  • G. H. Jirka
Original Article


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.


Shallow free-surface flows Velocity structure functions Velocity spectra Correlation functions Two-dimensional turbulence Inverse energy cascade 



Particle Tracking Velocimetry


Charge-coupled device


TM-6710 progressive scan digital camera


Gravity acceleration


Flow depth


Bed slope


Longitudinal velocity component


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


Vertically-averaged longitudinal velocity


Spatially- and time-averaged near-surface longitudinal velocity


Transverse velocity component


Fluid density

τ o

Bed shear stress


Froude number, Fr = U a /(gH)0.5


Reynolds number, Re = U a H


Friction factor, f = 8(u * /U a )2


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • V. Nikora
    • 1
  • R. Nokes
    • 2
  • W. Veale
    • 2
  • M. Davidson
    • 2
  • G. H. Jirka
    • 3
  1. 1.Department of EngineeringUniversity of AberdeenAberdeen, ScotlandUK
  2. 2.Department of Civil EngineeringUniversity of CanterburyChristchurchNew Zealand
  3. 3.Institute of HydromechanicsUniversity of KarlsruheKarlsruheGermany

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