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Follett et al. (2020a, https://doi.org/10.1029/2020gl089346) developed an analytical model to predict backwater rise by log jams, using the size and packing density of logs and the jam length, as well as river slope and bed roughness. We show that the model formulas can be rewritten using the Froude number instead of river slope and roughness, thus improving their applicability in engineering practice. The equation terms and results of Follett et al. (2020a, https://doi.org/10.1029/2020gl089346) are found to be similar to those of the empirically derived formula by Schalko et al. (2018, https://doi.org/10.1061/(asce)hy.1943‐7900.0001501). However, some differences are identified, calling for further study. Most notably, these distinctions pertain to the effect of accumulation porosity, with additional minor differences in the exponent of the Froude number. Lastly, model implications for some broader applications are explored, showing a methodology to calculate the representative log size for log mixtures, and the expected effect of log orientation on backwater rise. Plain Language Summary Accumulations of wood in rivers (log jams) can block the flow and thereby cause water level rise. Follett et al. (2020a, https://doi.org/10.1029/2020gl089346) developed a theoretical model to predict how this water level rise depends on log jam properties and local river conditions. For the local river conditions, they used the river slope and bottom roughness. In this comment, we show that the Froude number can be used instead, with exactly the same result. The Froude number is a dimensionless number that depends directly on the local river conditions, making the adapted formula easier to apply in practice. The resulting formula shows good agreement with an earlier one based on experimental work by Schalko et al. (2018, https://doi.org/10.1061/(asce)hy.1943‐7900.0001501). Still, some differences were found that raise questions. Most notably, the formulas differ for the effect of accumulation porosity. This becomes especially clear when logs are packed closely together. Next, model implications for slightly different settings than those studied by Follett et al. (2020a, https://doi.org/10.1029/2020gl089346) were explored. This showed how to determine the average log size for a mixture of logs with different sizes, and how the expected water level rise changes with log orientation. Key Points Follett et al. (2020a, https://doi.org/10.1029/2020gl089346) predicted backwater rise by log jams using river slope and roughness. We show the Froude number can be used instead By using the Froude number, the link to the local river conditions becomes stronger, improving formula applicability in engineering practice The resulting formula is shown to be similar to earlier empirical work. But differences in jam porosity effects call for further study

The transition from moderate to weak turbulence regimes remains a grand challenge for stable boundary layer parameterizations in weather and climate models. In this study, a critical horizontal Froude number (≈0.28) is proposed to characterize such a transition, which corresponds to the development of quasi two‐dimensional pancake vortices. Traditionally defined stability parameters corresponding to the critical horizontal Froude number are estimated and are consistent with values in the literature. The critical horizontal Froude number can recover previously used height‐ and site‐dependent mean wind speed thresholds. These findings offer a way to constrain the validity range of Monin‐Obukhov similarity theory in numerical models for weather and pollutants dispersion. Plain Language Summary The transition from moderate to weak turbulence regimes in stable atmospheric boundary layers presents a grand challenge for numerical models. Our results show that such a transition occurs when the horizontal Froude number is equal to a critical value of about 0.28, which is physically connected to the development of quasi two‐dimensional pancake vortices. These findings can help improve turbulence parameterizations in numerical models for weather and pollutants dispersion. Key Points A critical horizontal Froude number (≈0.28) is proposed to characterize the transition from moderate to weak turbulence regimes The critical horizontal Froude number corresponds to the development of pancake vortices Previously used height‐ and site‐dependent mean wind speed thresholds can be recovered from the critical horizontal Froude number

In this paper, the scour downstream of a trapezoidal Piano key weir (PKW) is investigated under free and submerged flow conditions. For this purpose, an experimental model was used in a laboratory channel with a length of 10 m, width of 0.75 m, and height of 0.8 m at various discharges and tailwater depths. The results showed an increase and decrease in the maximum scour depth with an increase in the discharge and submergence ratio, respectively. In addition, increasing the particle Froude number enhanced the geometric features of the scour hole downstream of the PKW. The rate of bed changes slowed down over time. The average values of maximum scour depth, the distance of the maximum scour depth from the weir toe, maximum scour hole length and weir toe scour depth increased in the free flow compared to the submerged flow. The scour hole volume and scour hole area in the submerged flow were less compared to the free flow. The average maximum level of the sedimentary ridge in the free flow is less than the submerged flow. New equations for calculating the geometric characteristics of the scour hole downstream of the trapezoidal PKW are presented with acceptable accuracy.

Sedimentation in storm sewers strongly depends on velocity at limit of deposition. This study provides application of a novel stochastic-based model to predict the densimetric Froude number in sewer pipes. In this way, the generalized likelihood uncertainty estimation (GLUE) is used to develop two parametric equations, called GLUE-based four-parameter and GLUE-based two-parameter (GBTP) models to enhance the prediction accuracy of the velocity at the limit of deposition. A number of performance indices are calculated in training and testing phases to compare the developed models with the conventional regression-based equations available in the literature. Based on the obtained performance indices and some graphical techniques, the research findings confirm that a significant enhancement in prediction performance is achieved through the proposed GBTP compared with the previously developed formulas in the literature. To make a quantified comparison between the established and literature models, an index, called improvement index (IM), is computed. This index is a resultant of all the selected indices, and this indicator demonstrates that GBTP is capable of providing the most performance improvement in both training () and testing () phases, comparing with a well-known formula in this context.

In this study, numerical simulations have been carried out to evaluate the influence of internal Froude number (Fr) on the wake characteristics of a sphere in linearly stratified flow. Five models with different levels of Fr (Fr = 0.05, 0.2,0.25,0.5 and 1) at a Reynolds number of Re = 3700 have been selected for comparative study. UDF (User Defined Function) is employed to establish linear density stratification. The influences of stratification on wake characteristics are studied by analyzing the wake patterns, vortical structures, velocity distributions, and lee waves. The results of the study demonstrate that reduced Fr values lead to heightened vertical suppression of the near wake, while increased stratification prompts a transformation of the wake's three-dimensional coherent structures towards quasi-two-dimensionality. Furthermore, the presence of stratification notably impacts the length and amplitude of the lee wave.

The understanding of how the sediment deposit thickness influences the incipient motion characteristic is still lacking in the literature. Hence, the current study aims to determine the effect of sediment deposition thickness on the critical velocity for incipient motion. An incipient motion experiment was conducted in a rigid boundary rectangular flume of 0.6 m width with varying sediment deposition thickness. Findings from the experiment revealed that the densimetric Froude number has a logarithmic relationship with both the thickness ratios ts/d and ts/y0 (ts: sediment deposit thickness; d: grain size; y0: normal flow depth). Multiple linear regression analysis was performed using the data from the current study to develop a new critical velocity equation by incorporating thickness ratios into the equation. The new equation can be used to predict critical velocity for incipient motion for both loose and rigid boundary conditions. The new critical velocity equation is an attempt toward unifying the equations for both rigid and loose boundary conditions.

Hydraulic jumps are commonly employed as energy dissipators to guarantee long-term operation of hydraulic structures. A comprehensive and in-depth understanding of their main features is therefore fundamental. In this context, the current study focused on hydraulic jumps with low Froude numbers, i.e. Fr 1 = 2.1 and 2.4, at relatively high Reynolds number: Re ~2 × 10 5 . Experimental tests employed a combination of dual-tip phase-detection probes and ultra-high-speed video camera to provide a comprehensive characterisation of the main air-water flow properties of the hydraulic jump, including surface flow features, void fraction, bubble count rate and interfacial velocities. The current research also focused on the transverse distributions of air-water flow properties, i.e. across the channel width, with the results revealing lower values of void fraction and bubble count rate next to the sidewalls compared to the channel centreline data. Such a spatial variability in the transverse direction questions whether data near the side walls may be truly representative of the behaviour in the bulk of the flow, raising the issue of sidewall effects in image-based techniques. Overall, these findings provide new information to both researchers and practitioners for a better understanding of the physical processes inside the hydraulic jump with low Froude numbers, leading to an optimised design of hydraulic structures. Article Highlights Experimental investigation of air-water flow properties in hydraulic jumps with low Froude numbers Detailed description of the main air-water surface features on the breaking roller Transversal distribution of the air-water flow properties across the channel width and comparison between centreline and sidewall.

The application of models capable of estimating sediment transport in sewers has been a frequent practice in the past years. Considering the fact that predicting sediment transport within the sewer is a complex phenomenon, the existing equations used for predicting densimetric Froude number do not present similar results. Using Adaptive Neural Fuzzy Inference System (ANFIS) this article studies sediment transport in sewers. For this purpose, five different dimensionless groups including motion, transport, sediment, transport mode and flow resistance are introduced first and then the effects of various parameters in different groups on the estimation of the densimetric Froude number in the motion group are presented as six different models. To present the models, two states of grid partitioning and sub-clustering were used in Fuzzy Inference System (FIS) generation. Moreover, the training algorithms applied in this article include back propagation and hybrid. The results of the proposed models are compared with the experimental data and the existing equations. The results show that ANFIS models have greater accuracy than the existing sediment transport equations.

Accurate prediction of scour depth downstream of water conveyance structures such as culverts and sluices is critical for ensuring infrastructure safety and for mitigating environmentally damaging bed degradation, sediment mobilization, and habitat disturbance. Although these structures share similar hydraulic and geometric characteristics, previous studies have typically analyzed them separately, often leading to inconsistent conclusions regarding the most effective predictive models and dominant parameters. This study presents a unified framework that evaluates multiple machine learning (ML) models—Random Forest (RF), Artificial Neural Network (ANN), Group Method of Data Handling (GMDH), and Support Vector Regression (SVR)—for predicting maximum scour depth downstream of both sluices and culverts. A Model-based Sensitivity Analysis (MBSA) approach is introduced to quantify the relative importance of input parameters without model retraining. Results show that RF significantly outperforms other ML models and empirical equations in terms of predictive accuracy, confirmed by statistical testing across 100 independent trials. Furthermore, the MBSA consistently identifies the densimetric Froude number (Fd) as the most influential parameter governing scour development. These findings demonstrate RF’s robustness for scour depth prediction and highlight MBSA as a reliable, physically interpretable tool for understanding parameter influence in hydraulic systems with direct implications for environmentally resilient river management and design.

Side weirs are utilized to regulate water surface and to control discharge and water elevation in rivers and channels. Here, the discharge coefficient for trapezoidal sharp-crested side weirs (TSCSW) and their affecting parameters are numerically investigated. To simulate the hydraulic and geometric characteristics of TSCSWs, three weir crest lengths of 15 cm, 20 cm and 30 cm with lengths of 20 cm, 30 cm and 40 cm and with two different sidewall slopes are utilized. The results show that for constant P/B (P: weir height, B: main channel width), the depth of flow along the channel and weir decreases as the crest length increases. Also, with increasing P/y1 ratio (P: weir height, y1: upstream flow depth), the discharge coefficient decreases for small crest lengths and increases for large crest lengths. The results show that for constant T/L ratio (T: passing flow width, L: side weir crest length), increasing the length, height and sidewall slope of a side weir will increase the discharge coefficient. It is observed that as the upstream Froude number increases for side weirs with longer crest lengths, the intensity of deviating flow and kinetic energy over the TSCSW will increase. Finally, some relations with high correlation factors are proposed for obtaining discharge coefficients using the dimensionless parameters of P/y1, T/L and Fr1. Based on proposed relations and sensitivity analysis, it is shown that T/L and P/y1 are the most effective parameters for reducing the discharge coefficient reduction.