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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

Abstract

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.

Keywords

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

δv

Thickness of the viscous sub-layer

Φj

Volume fraction or concentration for the j phase

Λzz

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

ρ

Mass density

σ

Surface tension

ν

Kinematic fluid viscosity

ζ0

Abscissa in the beam axis reference system

Θ

Temperature

a

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)

c

Celerity of propagation of ultrasound

d′

Head over the weir crest

d

Water depth upstream

DNS

Direct numerical simulation

fco

Cut-off frequency

fe

Frequency of the carrier

Frs

Froude number based on free-surface scales

Frupstream, Fr

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

FS

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

k

Coefficient

L0

Distance of the target

PDF

Probability density function

PIV

Particle image velocimetry

Q

Volume discharge

Re, Res

Reynolds number, based on surface scales

R2

Coefficient of determination

S/N

Signal to noise ratio

t

Time

T

Period of the waves, period of time average

Tmean, T1/3, …

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

tprf

Time between two subsequent pulses

US

Ultrasound

UVP

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

ui

Velocity component along the i beam axis

us

Velocity scale

uupstream, ums

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

V

Volume of integration

Vs

Velocity of the surface

Wes

Weber number, based on surface scales

x, y, z, xi

Spatial co-ordinates

x, s

Space vector

Xj

Phasic function for the j phase

zs

Instantaneous level of the free surface

Notes

Acknowledgments

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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