Experiments in Fluids

, Volume 49, Issue 6, pp 1325–1338 | Cite as

Experiments on turbulence beneath a free surface in a stationary field generated by a Crump weir: free-surface characteristics and the relevant scales

  • Sandro LongoEmail author
Research Article


This work concerns the analysis of experimental instantaneous fluid levels and three-component fluid velocity measurements in a stationary flow field generated by a Crump weir in a laboratory flume using an ultrasonic distance sensor and a three-probe arrangement of an ultrasonic Doppler velocity profiler. The tests are characterised by different and increasing Froude numbers (Fr = 0.10–0.38), with the free surface of the fluid ranging from flat (low Froude number) to almost aerated (high Froude number). The statistics of the free surface are computed, and the relevant length and velocity scales are measured. A free-surface boundary layer was detected having a thickness proportional to the root mean square of the free-surface height series and with a velocity scale that related well to the free-surface elevation time gradient. The mean velocity profiles are presented. There are many indicators that a specific regime occurs with an optimal tuning between free surface and turbulence. In this regime, the length scales are raised.


Free Surface Flow Field Particle Image Velocimetry Froude Number Peregrine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

\( \langle \ldots \rangle \)

Space average operator

\( \overline{ \ldots } \)

Time average operator

\( \widetilde{ \ldots } \)

Phasic average operator


Thickness of the viscous sub-layer


Volume fraction or concentration for the j phase


Integral length scale in the vertical computed on using the vertical fluctuation velocity


Mass density


Surface tension


Kinematic fluid viscosity


Abscissa in the beam axis reference system




Weighting function

A, B

Matrix for reference transformation

a_umrms, a_dmrms

Root mean square of the up-midlevel amplitude (crests) and of the down-midlevel amplitude (troughs)


Celerity of propagation of ultrasound


Head over the weir crest


Water depth upstream


Direct numerical simulation


Cut-off frequency


Frequency of the carrier


Froude number based on free-surface scales

Frupstream, Fr

Froude number in the upstream section, in the section of measurement


Full scale

H, Hrms

Wave height, root mean square wave height

H1/3, H1/10, …

Mean value of the first third, of the first tenth, …

h, hmeas, hwave

Instantaneous filtered value, measured value, value due to potential flow




Distance of the target


Probability density function


Particle image velocimetry


Volume discharge

Re, Res

Reynolds number, based on surface scales


Coefficient of determination


Signal to noise ratio




Period of the waves, period of time average

Tmean, T1/3, …

Period of the waves, mean value, mean value of the first third, …


Time between two subsequent pulses




Ultrasonic Doppler velocity profiler

u, v, w

Streamwise, spanwise, vertical fluid velocity

u′, v′, w′

Streamwise, spanwise, vertical fluctuating fluid velocity

u′rms, v′rms, w′rms

Streamwise, spanwise, vertical root mean square value of the fluctuating fluid velocity


Velocity component along the i beam axis


Velocity scale

uupstream, ums

Mean fluid velocity in the upstream section, in the section of measurement


Volume of integration


Velocity of the surface


Weber number, based on surface scales

x, y, z, xi

Spatial co-ordinates

x, s

Space vector


Phasic function for the j phase


Instantaneous level of the free surface



Support from FIL 2008 is acknowledged. The paper was completed and revised during my sabbatic leaving in CEAMA, Grupo de Dinámica de Flujos Ambientales, University of Granada, Spain, where I was kindly hosted by Miguel A. Losada.


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of ParmaParmaItaly

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