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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.

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 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.

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.

Sewer systems are usually built with a self-cleaning system that keeps the bottom of the channel free of sediment to lessen the effects of the constant buildup of sediment particles. Because of this, it is important to accurately predict the particle Froude number (Fr) when making sewer systems. For the prediction of Fr, five different sets of input variables were looked at. For the training and testing of the machine learning (ML) model, we used 10-fold cross-validation methodologies to prevent overfitting. M5Prime (M5P) model as a standalone and Bagging-M5P as a hybrid model were utilized, and the results were compared with the empirical equations proposed in the literature. Models perform best when all input variables are used for training and testing of models. The hybrid BA-M5P model performed better than the M5P model and empirical equations. We performed sensitivity analysis and compared the result based on MAE and MSE value, and we found sediment concentration (Svc) is the most important variable to predict the particle Froude number under non-deposition with deposited bed by best performing model BA-M5P. Hence, for the self-cleaning system, we prefer the BA-M5P ML model with Svc the most required variable.

This study presents a comparison of forcings between density gradient and tides in idealized funnel-shaped salt-plug estuaries. Three-dimensional numerical model results also examine longitudinal and lateral circulations. In salt-plug estuaries, a positive longitudinal estuarine circulation is observed landward of a salinity maximum zone or salt plug. Seaward of the salt plug, the estuary shows an inverse circulation cell. The longitudinal flows show a fortnightly variability inside the salt plug. Also, the salt plug is saltier in spring tides than in neap tidal cycles mainly owing to higher landward salt transport by tidal advection during the spring tides. The lateral circulation and divergence dv/dy have the influence of Coriolis acceleration. In the absence of Earth’s rotation, the tidally averaged lateral circulations have nearly the same directions within the positive and inverse cells. Directions of lateral flow reverse in the salt-plug area. Inside this area, the lateral circulation also shows clear neap–spring variability, including downwelling cells during spring tides and upwelling in neap tides. The salinity maximum zone exhibits a vertically homogeneous condition particularly in meso-tidal salt-plug estuaries. Finally, this study introduces the threshold of “ log(tidal Froude number)=3 ” (tidal forcing 3 orders of magnitude ≥ density gradients) for salt-plug estuaries as the condition under which the tidal forcing can overcome the density gradient, and consequently salinity inside the salt plug zone is reinforced by tides with a landward movement. This robust salinity maximum zone is also identified by a high Ekman number ( log(Ekman number)>0.25 ).

A series of laboratory experiments were conducted in a wave-current flume to investigate the scour evolution and scour morphology around tripod in combined waves and current. The tripod model was made using the 3D printing technology, and it was installed in seabed with three installation angles α = 0°, 90°and 180° respectively. In the present study, the scour evolution and scour characteristic were first analyzed. Then, the equilibrium scour depth Seq was investigated. Furthermore, a parametric study was carried out to study the effects of Froude number Fr and Euler number Eu on equilibrium scour depth Seq respectively. Finally, the effects of tripod’s structural elements on Seq were discussed. The results indicate that the maximum scour hole appeared underneath the main column for installation angle α = 0°, 90° and 180°. The Seq for α = 90° was greater than the case of α = 0° and α = 180°, implying the tripod suffered from more severe scour for α = 90°. When KC was fixed, the dimensionless time scale T* for α = 90° was slightly larger than the case of α = 0° and α = 180° and the T* was linearly correlated with Ucw in the range of 0.347 < Ucw < 0.739. The higher Fr and Eu both resulted in the greater scour depth for tripod in combined waves and current. The logarithmic formula can depict the general trend of Seq and Fr (Eu) for tripod in combined waves and current.