Environmental Fluid Mechanics

, Volume 9, Issue 2, pp 125–142

Turbulent air–water flows in hydraulic structures: dynamic similarity and scale effects

Original Article

DOI: 10.1007/s10652-008-9078-3

Cite this article as:
Chanson, H. Environ Fluid Mech (2009) 9: 125. doi:10.1007/s10652-008-9078-3


In hydraulic structures, free-surface aeration is commonly observed: i.e., the white waters. The air bubble entrainment may be localised (hydraulic jumps, plunging jets) or continuous along an interface (water jets, chutes). Despite recent advances, there are some basic concerns about the extrapolation of laboratory results to large size prototype structures. Herein the basic air bubble entrainment processes are reviewed and the relevant dynamic similarities are discussed. Traditionally, physical studies are conducted using a Froude similitude which implies drastically smaller laboratory Reynolds numbers than in the corresponding prototype flows. Basic dimensional analyses are developed for both singular and interfacial aeration processes. The results are discussed in the light of systematic investigations and they show that the notion of scale effects is closely linked with the selection of relevant characteristic air–water flow properties. Recent studies of local air–water flow properties highlight that turbulence levels, entrained bubble sizes and interfacial areas are improperly scaled based upon a Froude similitude even in large-size models operating with the so defined Reynolds numbers ρw × qw/μw up to 5 E+5. In laboratory models, the dimensionless turbulence levels, air–water interfacial areas and mass transfer rates are drastically underestimated.


Air–water flows Air bubble entrainment Turbulence Hydraulic engineering Dynamic similarity Scale effects Froude similitude Plunging jets Hydraulic jumps Spillway chutes Stepped spillways High-velocity water jets 

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Division of Civil EngineeringThe University of QueenslandBrisbaneAustralia

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