Shear and Velocity Distribution in Shallow Channels

Lundgren, H.; Jonsson, Ivar G.

doi:10.1061/jyceaj.0000971

Cited by 46 publications

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“…The widening of straight channels until a stable cross section is attained has been simulated numerically by Pizzuto (), who applied the modified area procedure of Lundgren and Jonsson () to derive the cross‐sectional distribution of bed shear stresses. The channel bed topography was then derived according to the sediment flux balance equation and a heuristic bank failure law, based on exceeding the sediment repose angle.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium Cross Section of River Channels With Cohesive Erodible Banks

et al. 2020

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Predicting the equilibrium cross section of natural rivers has been widely investigated in Q1 Q2 Q3 fluvial morphology. Several approaches have been developed to meet this aim, starting from regime equations to the empirical formulations of Parker et al. (2007) and Wilkerson and Parker (2011), who Q4 proposed quasi-universal relations for describing bankfull conditions in sand and gravel bed rivers. Nevertheless, a general physics-based framework is still missing, and it remains an open issue to better clarify the basic mechanisms whereby a river selects its width. In this contribution we focus our attention on lowland rivers with cohesive banks, whose resistance to erosion is crucial to control the river width. In particular, we formulate a theoretical model that evaluates the equilibrium width of river cross sections modeling the interaction between the core flow in the central part of the section and the boundary layer that forms in the correspondence of the cohesive banks. The model computes the cross-section equilibrium configuration by which the shear stresses on the banks equal a critical threshold value. These stresses are computed by partitioning the total shear stress into an effective grain roughness component and a form component (Kean and Smith, 2006a). The model is applied to a large data set, concerning both sand and gravel bed rivers, and it is used to determine the relations expressing the channel width and the bankfull flow depth to the bankfull discharge, which appear to provide a unitary description of bankfull hydraulic geometry.

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Section: Introductionmentioning

confidence: 99%

Equilibrium Cross Section of River Channels With Cohesive Erodible Banks

et al. 2020

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“…However, for the almost vertical bank formed in the BS profile (e.g., Figure 3a), considering only the vertical profiles of the velocity leads to the underestimation of the bed shear stress on the vertical bank and hence the channel width. A more accurate momentum balance can be achieved using an orthogonal curvilinear coordinate system (e.g., Fagherazzi & Furbish, 2001; Lundgren & Jonsson, 1964; Pizzuto, 1990). We assume a specific friction formula (Equation ), an eddy viscosity closure assuming an identical turbulent transfer (Equation ), and a constant threshold shear stress (Equations and ).…”

Section: Discussionmentioning

confidence: 99%

“…The momentum balance described by Equation is valid for wide and shallow channels, where the lateral bed slope is small. Another commonly used version has been derived based on an orthogonal curvilinear coordinate system, in which the channel cross section is divided by normals perpendicular to the bed (e.g., D'Alpaos et al., 2006; Fagherazzi & Furbish, 2001; Lundgren & Jonsson, 1964; Pizzuto, 1990). The Cartesian coordinate system employed in this study facilitates the derivations of the theoretical forms.…”

Section: Methodsmentioning

confidence: 99%

Rationalizing the Differences Among Hydraulic Relationships Using a Process‐Based Model

Coco

Townend

et al. 2021

Water Resources Research

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An ancient Chinese proverb states: "Don't push the river, it flows by itself." Scientists and engineers have long struggled to fully translate the second part of the proverb into a mathematical description. Leopold and Maddock (1953) linked the time-varying measurements of instantaneous river width B, depth H and velocity U at a gauging station to the corresponding discharge Q using simple power functions, and termed such empirical relationships as at-a-station hydraulic geometry (denoted as "AHG" hereafter). At the same time, the authors created downstream hydraulic geometry (denoted as "DHG" hereafter) to describe the hydraulic relations with bankfull (or mean annual) B, H, U, and Q downstream along a river. The fundamental difference between these two relationships is that AHG deals with temporal variability while DHG focuses on spatial variability. In addition, the mean annual or bankfull parameters used in DHG generally have a longer returning period than the time-varying parameters of AHG. Despite their conceptual difference, both AHG and DHG were expressed by the same well-known functional forms:

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“…Leighly [3] proposed that the bed shear stress can be balanced by the downstream component of the weight of water contained within the bounding orthogonal. Lundgren and Jonsson [4] modified the logarithmic law to a parabolic cross-sectional open channel and suggested a method to estimate the velocity and shear stress distribution.…”

Section: Introductionmentioning

confidence: 99%

Entropy-Based Shear Stress Distribution in Open Channel for All Types of Flow Using Experimental Data

Choo

Jeon

Seo

2021

Entropy

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Korean river design standards set general design standards for rivers and river-related projects in Korea, which systematize the technologies and methods involved in river-related projects. This includes measurement methods for parts necessary for river design, but does not include information on shear stress. Shear stress is one of the factors necessary for river design and operation. Shear stress is one of the most important hydraulic factors used in the fields of water, especially for artificial channel design. Shear stress is calculated from the frictional force caused by viscosity and fluctuating fluid velocity. Current methods are based on past calculations, but factors such as boundary shear stress or energy gradient are difficult to actually measure or estimate. The point velocity throughout the entire cross-section is needed to calculate the velocity gradient. In other words, the current Korean river design standards use tractive force and critical tractive force instead of shear stress because it is more difficult to calculate the shear stress in the current method. However, it is difficult to calculate the exact value due to the limitations of the formula to obtain the river factor called the tractive force. In addition, tractive force has limitations that use an empirically identified base value for use in practice. This paper focuses on the modeling of shear-stress distribution in open channel turbulent flow using entropy theory. In addition, this study suggests a shear stress distribution formula, which can easily be used in practice after calculating the river-specific factor T. The tractive force and critical tractive force in the Korean river design standards should be modified by the shear stress obtained by the proposed shear stress distribution method. The present study therefore focuses on the modeling of shear stress distribution in an open channel turbulent flow using entropy theory. The shear stress distribution model is tested using a wide range of forty-two experimental runs collected from the literature. Then, an error analysis is performed to further evaluate the accuracy of the proposed model. The results reveal a correlation coefficient of approximately 0.95–0.99, indicating that the proposed method can estimate shear-stress distribution accurately. Based on this, the results of the distribution of shear stress after calculating the river-specific factors show a correlation coefficient of about 0.86 to 0.98, which suggests that the equation can be applied in practice.

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Shear and Velocity Distribution in Shallow Channels

Cited by 46 publications

References 0 publications

Equilibrium Cross Section of River Channels With Cohesive Erodible Banks

Equilibrium Cross Section of River Channels With Cohesive Erodible Banks

Rationalizing the Differences Among Hydraulic Relationships Using a Process‐Based Model

Entropy-Based Shear Stress Distribution in Open Channel for All Types of Flow Using Experimental Data

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