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2018 | OriginalPaper | Chapter

8. Local Scours

Author : Aronne Armanini

Published in: Principles of River Hydraulics

Publisher: Springer International Publishing

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Abstract

The suspended sediment and bedload transport in a turbulent channel flow are basically governed by the turbulence generated by the bed (wall turbulence). However, there are situations where the bed experiences the effects of free turbulence phenomena, such as boundary layer separation and secondary circulations induced by hydraulic structures inserted in the channel.

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previous chapter Mathematical Models of Riverbed Evolution

In the literature, especially that developed at the University of Auckland (Raudkivi and Ettema 1977; Raudkivi and Sutherland 1981; Melville 1992) but also by Graf and Altinakar (1998), the flow velocity is not directly included among the parameters which determine the maximum scour depth. In fact, the parameters identified by these authors are:

$$\begin{aligned} f_3(y_{sm}, h_o, u_* (\text {or} \,\,\tau _o), \rho _s, \rho , \nu , g, D_p, Sf_p, d, \sigma _g)=0 \end{aligned}$$

(8.27)

The dimensional analysis allows Eq. (8.24) with eleven parameters to move to the relation with the following seven dimensionless groups:

$$\begin{aligned} f_4\left( {y_{sm} \over D_p},\; {u_*^2 \over g\varDelta d},\; {u_* \; d \over \nu },\; {h_o\over D_p},\; {d\over D_p},\; \displaystyle {\rho _s-\rho \over \rho },\; Sf_p,\; \sigma _g \right) =0 \end{aligned}$$

(8.24)

Here, we consider the hypothesis of the uniform flow upstream of the pier, and thus, we assume that the ratio ($U{/}u_*$) is assigned a priori and is equal to the dimensionless friction coefficient, for instance, ($U = u_* \chi /\sqrt{g}$), being $\chi =\textit{func}(\theta , d/h_o, R_*)$ the Chézy friction coefficient. The Froude number, instead, appears in Eq. (8.23) and is replaced by a combination of other parameters to obtain the reduced relative density of the material or vice versa, e.g.,

$$\begin{aligned} \varDelta {u_*^2\over g\varDelta d} \ {d \over h_o} \left( {U\over u_*} \right) ^2 ={U^2\over gh}=F_r^2 \end{aligned}$$

(8.25)

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Title: Local Scours
Author: Aronne Armanini
Publisher: Springer International Publishing
Book: Principles of River Hydraulics
Print ISBN: 978-3-319-68099-6

Electronic ISBN: 978-3-319-68101-6

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-68101-6_8

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