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Momentum transfer across an open-channel, turbulent flow

Published online by Cambridge University Press:  23 February 2024

Predrag Popović Open the ORCID record for Predrag Popović [Opens in a new window] ,
Olivier Devauchelle Open the ORCID record for Olivier Devauchelle [Opens in a new window]  and
Eric Lajeunesse Open the ORCID record for Eric Lajeunesse [Opens in a new window]
Predrag Popović*
Affiliation:
Institut de Physique du Globe de Paris, F-75238 Paris, France Faculty of Physics, University of Belgrade, POB 44, 11001 Belgrade, Serbia
Olivier Devauchelle
Affiliation:
Institut de Physique du Globe de Paris, F-75238 Paris, France
Eric Lajeunesse
Affiliation:
Institut de Physique du Globe de Paris, F-75238 Paris, France
*
†Email address for correspondence: arpedjo@gmail.com
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Abstract

The distribution of stress generated by a turbulent flow matters for many natural phenomena, of which rivers are a prime example. Here, we use dimensional analysis to derive a linear, second-order ordinary differential equation for the distribution of stress across a straight, open channel, with an arbitrary cross-sectional shape. We show that this equation is a generic first-order correction to the shallow-water theory in a channel of large aspect ratio. It has two adjustable parameters – the dimensionless diffusion parameter, $\chi$, and a local-shape parameter, $\alpha$. By assuming that the momentum is carried across the stream primarily by eddies and recirculation cells with a size comparable to the flow depth, we estimate $\chi$ to be of the order of the inverse square root of the friction coefficient, $\chi \sim C_f^{-1/2}$, and predict that $\alpha$ vanishes when the flow is highly turbulent. We examine the properties of this equation in detail and confirm its applicability by comparing it with flume experiments and field measurements from the literature. This theory can be a basis for finding the equilibrium shape of turbulent rivers that carry sediment.

JFM classification

Waves/Free-surface Flows: Channel flow Turbulent Flows: Turbulence modelling Geophysical and Geological Flows: River dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 981 , 25 February 2024 , A24
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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