A mixing length model for estimating channel conveyance

Horritt, M. S.; Wright, Nigel

doi:10.1680/wama.11.00066

Proceedings of the Institution of Civil Engineers - Water Manag

2013

DOI: 10.1680/wama.11.00066

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A mixing length model for estimating channel conveyance

M. S. Horritt¹,

Nigel Wright²

Abstract: This paper describes a simple, physically based mixing length model that explains the functional form of Manning's equation for mean velocity in open channels. Manning's equation has been used to describe mean velocity for over 100 years and is essentially an empirical result rather than being based on an understanding of physical processes.The model described in this paper uses Prandtl's mixing length hypothesis, with mixing length modelled at each point within the cross-section being proportional to the dist… Show more

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Cited by 2 publications

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“…and 'why is the power two-thirds?' The first paper, by Horritt and Wright (2013), describes the use of a mixing length model for estimating channel conveyance and shows that this simple, physically based model explains the functional form of Manning's equation and the Colebrook-White formula. The model applies Prandtl's mixing length hypothesis, with the mixing length at each point in a river cross-section being proportional to the distance to the nearest solid boundary.…”

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Spencer¹

2013

Proceedings of the Institution of Civil Engineers - Water Manag

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Although the papers in this issue have no core theme, they cover some interesting applications over a range of topics.Manning's empirical equation has been used for over 100 years to describe the mean velocity in open channels. The form of the equation raises questions such as 'why does the velocity depend on the hydraulic radius?' and 'why is the power two-thirds?' The first paper, by Horritt and Wright (2013), describes the use of a mixing length model for estimating channel conveyance and shows that this simple, physically based model explains the functional form of Manning's equation and the Colebrook-White formula. The model applies Prandtl's mixing length hypothesis, with the mixing length at each point in a river cross-section being proportional to the distance to the nearest solid boundary. The model is applied to three different geometries (planar beds and circular conduits, rectangular channels, and arbitrary cross-sections) and different numerical solution methods (one-dimensional Runge-Kutta and the Jacobi method) are used for each geometry. The results show that the mixing length model reproduces some of the well-known hydraulic behaviours of open channel flows, and how essentially empirical results such as Colebrook-White and Manning's arise from open channel hydraulic processes. It also reproduces the dependence of mean velocity on channel geometry, and produces further information such as velocity profiles and bed shear. The authors suggest that the method may have further usefulness in such aspects as modelling complex geometries, interactions between regions of flow, turbulence modelling, head loss through structures, and scour and sediment transport.Marine outfall discharges of wastewater effluents typically contain contaminants even after treatment. The paper by Liu and Li (2013) addresses the question 'To what extent is the receiving environment being exposed to effluents?' by describing a particle-tracking model of outfall flumes in a tidal channel. In the model, effluents are represented by a large number of particles, whose trajectories are tracked under various conditions of flow and density stratification. The technique is particularly useful for examining the undesirable scenario of effluents rising to the surface or coming into contact with the seabed. The method takes into account advection, non-Fickian horizontal diffusion and vertical diffusion. The paper describes an application of the technique to an outfall discharge in British Columbia, Canada, where it successfully captured the detailed structures of outfall plumes. Based on the technique, the paper details a number of important conclusions for modelling these conditions. The paper by Pagliara and Carnacina (2013) addresses the effect debris collected on bridge piers has on the scour pattern. This can be a significant contributor to bridge failure. Previous work has shown that scour hole dimensions generally increase with debris accumulation and roughness. The paper describes a series of experimental runs in a hydraulic labora...

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Predictive model for stage-discharge curve in compound channels with vegetated floodplains

Liu

Yang

2014

Appl. Math. Mech.-Engl. Ed.

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A mixing length model for estimating channel conveyance

Cited by 2 publications

References 15 publications

Editorial

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Predictive model for stage-discharge curve in compound channels with vegetated floodplains

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