Rebuttal on “A mathematical model on depth-averaged β-factor in open-channel turbulent flow” Environmental Earth Sciences 77:253 (2018)

Absi, Rafik

doi:10.1007/s12665-020-8849-0

Cited by 5 publications

(11 citation statements)

References 13 publications

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“…Te results are enlisted in Table 1. Te coefcients in (21) are calibrated locally based on diferent water depths. Te values of vertical time-averaged velocity coefcients calibrated at 0.4 h, 0.6 h, and 0.8 h are 0.18, 0.31, and 0.44, respectively.…”

Section: Discussionmentioning

confidence: 99%

“…According to the vertical relative distribution of the sediment concentration calculated by Rouse, assuming m � 0, the estimated relative sediment concentration theoretical value is on the lower side, ignoring the infuence of the vertical velocity on the sediment movement. In addition, the distribution of suspended sediment in (21) is slightly diferent for diferent values of the vertical time-averaged velocity coefcient. [17,[38][39][40].…”

Section: Verification Of Thementioning

confidence: 92%

“…Te higher the value of δ in the sediment concentration vertical distribution (21), the greater the infuence of the vertical velocity on the sediment concentration vertical distribution. Furthermore, to separately analyze the infuence of diferent vertical velocity assumptions on the calculation of sediment concentration, the theoretical distribution of δ can be drawn as shown in (22).…”

Section: Verification Of Thementioning

confidence: 99%

“…As highlighted in Figure 3, when Z * � 1, the relative distribution of the vertical sediment concentration under four assumptions is drawn using equations ( 1)-( 4) in combination with (21). According to the vertical relative distribution of the sediment concentration calculated by Rouse, assuming m � 0, the estimated relative sediment concentration theoretical value is on the lower side, ignoring the infuence of the vertical velocity on the sediment movement.…”

Section: Verification Of Thementioning

confidence: 99%

“…Chien and Wang fgured out that this improvement was only for the derivation of the formula and could not refect the law of sediment transport on the bed surface, making it difcult to conclude [14]. In recent years, Zhang [15], Zheng et al [16], Li et al [17], Boudreau et al [18], and Baronas et al [19] have improvised the Rouse equation from various aspects and made some remarkable achievements [9,[20][21][22][23]. Among them, Li et al derived the vertical distribution of velocity based on the power function of velocity and friction velocity.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The Influence of Vertical Velocity Distribution on the Calculation of Suspended Sediment Concentration

Quan

et al. 2022

Discrete Dynamics in Nature and Society

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Based on the advection-diffusion equation of suspended sediment, a general formula of vertical distribution of suspended sediment concentration was derived by considering the influence of vertical velocity. The new formula was tested against over 3000 sets of field data and obtained a reasonable agreement. Comparing with the Rouse equation of concentration, the accuracy of the new formula increases significantly, and the shortcoming of the underestimation of the Rouse profile in practical application is revised. Through the analysis of the new formula with different vertical time-averaged velocity coefficients m , it was found that vertical velocity does have an impact on the accurate estimation of sediment concentration, and the extent of which is related to the value of sediment concentration. Utilizing the regression analysis, it was found the vertical time-averaged velocity coefficient m increases with the height above the bed.

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Section: Discussionmentioning

confidence: 99%

Section: Verification Of Thementioning

confidence: 92%

Section: Verification Of Thementioning

confidence: 99%

Section: Verification Of Thementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Influence of Vertical Velocity Distribution on the Calculation of Suspended Sediment Concentration

Quan

et al. 2022

Discrete Dynamics in Nature and Society

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Analytical Eddy Viscosity Model for Velocity Profiles in the Outer Part of Closed- and Open-Channel Flows

Absi

2021

Fluid Dyn

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Suspended Sediments in Environmental Flows: Interpretation of Concentration Profiles Shapes

Absi

2022

Hydrology

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In environmental flows, field and laboratory measurements of suspended sediments show two kinds of concentration profiles. For coarse sediments, a near-bed upward convex profile is observed beneath the main upward concave profile. In this study, we consider two 1-DV models, namely, the classical advection–diffusion equation (ADE) based on the gradient diffusion model, and the kinetic model. Both need sediment diffusivity, which is related to the eddy viscosity, and an y-dependent β-function (i.e., the inverse of the turbulent Schmidt number). Our study shows that the kinetic model reverts to the classical ADE with an “apparent” settling velocity or sediment diffusivity. For the numerical resolution of the ADE, simple and accurate tools are provided for both the sediment diffusivity and hindered settling. The results for the concentration profiles show good agreement with the experimental data. An interpretation of the concentration profiles is provided by two “criteria” for shapes. The main for steady open-channel flows shows that the shape of the concentration profiles in the Cartesian coordinate depends on the vertical distribution of the derivative of R (the ratio between the sediment diffusivity and the settling velocity of the sediments): dR/dy > −1 for the upward concave concentration profile while dR/dy < −1 for the near-bed upward convex profile. A generalization is proposed for oscillatory flows over sand ripples, where the time-averaged concentration profiles in the semi-log plots are interpreted by a relation between the second derivative of the logarithm of the concentration and the derivative of the product between the sediment diffusivity and an additional parameter related to the convective sediment entrainment process.

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Rebuttal on “A mathematical model on depth-averaged β-factor in open-channel turbulent flow” Environmental Earth Sciences 77:253 (2018)

Cited by 5 publications

References 13 publications

The Influence of Vertical Velocity Distribution on the Calculation of Suspended Sediment Concentration

The Influence of Vertical Velocity Distribution on the Calculation of Suspended Sediment Concentration

Analytical Eddy Viscosity Model for Velocity Profiles in the Outer Part of Closed- and Open-Channel Flows

Suspended Sediments in Environmental Flows: Interpretation of Concentration Profiles Shapes

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