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Multiple barriers are usually installed to effectively mitigate large-volume debris flows. Existing multiple-barrier design recommendations ignore the effects of solid–fluid interaction and may cause uncertainties in estimating the flow impact force on subsequent barriers. In this study, a fully coupled, two-layer, two-phase material point method with an incompressible fluid phase is implemented and validated using the experimental results of dry sand, water and sand–water mixture flows impacting on rigid barriers. Numerical parametric study is carried out using the validated model to investigate the effects of Froude number (Fr) and barrier spacing on second barrier impact force. A debris flow volume of 500 m3 is modelled, with the Fr ranging from 2 to 6; these are values relevant to the gentle and steep terrains in Hong Kong. Simulation results show the importance of changes in fluidisation ratio, which is the ratio of basal pore fluid pressure and total stress. The debris flow, after impacting the first barrier, overflows and lands on the slope between the two barriers. The fluidisation ratio of debris flow after landing increases by up to 30%, leading to an increase of impact velocity at the second barrier by up to 80%. Consequently, the impact force of debris flows on the second barrier is underestimated by up to 50% compared with existing design guidelines. This implies that neglecting the fluidisation ratio may lead to non-conservative design of multiple barriers. [ABSTRACT FROM AUTHOR]

It is well recognised that the rheology of an interstitial fluid has profound effects on debris flow dynamics. Existing design guidelines for multiple resisting barriers, however, do not consider the rheological behaviour of debris flows explicitly while estimating barrier spacing. A modified overflow equation is proposed, considering an improved overflow trajectory and a new yield stress-based velocity attenuation model, to estimate the overflow distance in two-phase flows. This study experimentally investigates the effects of yield stress of an interstitial fluid on the impact behaviour of two-phase flows with similar Froude numbers against dual-rigid barriers. The flow composition is varied to model a wide range of natural flows based on dimensionless yield stress. The results reveal that the hydrodynamic impact coefficient increases with increasing dimensionless yield stress and exceeds the existing international design guidelines by more than 13%. The existing guidelines underestimate the overflow distance by up to 115%. The modified formulation is verified and conservatively predicts overflow distance for water floods to debris flows. It is recommended that the dimensionless yield stress of interstitial fluid together with Froude number should be used to characterise the impact and overflow dynamics of two-phase flow for a conservative design of dual barriers. [ABSTRACT FROM AUTHOR]

An air-entraining vortex begins to form when the submergence of an intake is not adequate and less than the critical value known as critical submergence. In the present study, critical submergence for a laterally placed single rectangular intake under a uniform approach flow in an open channel was investigated experimentally. Analysis of the data collected in the present study reveals that critical submergence is significantly influenced by intake size, intake aspect ratios, approach Froude number, intake Froude number, intake Reynolds number, and Weber number. However, intake Froude number and intake aspect ratio were found to be the most sensitive parameters that affect critical submergence. An empirical relationship for critical submergence has been developed using collected data used to compute the critical submergence within an error of ±20%. The findings of this investigation is advantageous for hydraulic engineers when designing lateral rectangular intakes to prevent the formation of an air-entraining vortex. Practical Applications: Insufficient water cover over the hydraulic intakes causes an air-entraining vortex formation in the vicinity of the intake. The formation of such an air-entraining vortex results in significant hydraulic issues, structural damages, etc. Ensuring enough submergence for the intake during its operational period is necessary to evade such problems. The submergence at which the air-core tail of the surface vortex reaches the intake initiating air-entrainment is called critical submergence. Critical submergence is an important parameter for the design of intakes and is widely used as a parameter to determine an incipient state for which no air is entrained by intake vortices. This paper discusses the experimental investigation of critical submergence for single lateral rectangular intakes concerning significant geometrical parameters, such as intake aspect ratio, approach Froude number, intake Froude number, etc. The proposed empirical equations in this study are helpful to hydraulic engineers when computing critical submergence to fix the invert level of a lateral rectangular intake. [ABSTRACT FROM AUTHOR]

We perform the so‐called rigid lid limit on different shallow water models such as the abcd Bousssinesq systems or the Green–Naghdi equations. To do so, we consider an appropriate nondimensionalization of these models where two small parameters are involved: the shallowness parameter μ$\mu$ and a parameter ε$\epsilon$ which can be interpreted as a Froude number. When the parameter ε$\epsilon$ tends to zero, the surface deformation formally goes to the rest state, hence the name rigid lid limit. We carefully study this limit for different topologies. We also provide rates of convergence with respect to ε$\epsilon$ and careful attention is given to the dependence on the shallowness parameter μ$\mu$. [ABSTRACT FROM AUTHOR]

Urban pluvial floods can be produced or exacerbated by an insufficient density of inlets or by their poor hydraulic efficiency. Therefore, proper consideration of the hydraulic performance of inlets is essential to guarantee the correct functioning of urban drainage systems during heavy storm events. Recent advances in computational analysis in the field of hydrodynamics modelling allow the use of the well-known concept of dual drainage for design and planning purposes by simulating flow transfers between the surface layer (streets) and underground layers (sewers) through a proper hydraulic characterisation of inlet efficiency. Powerful commercial software packages allow simulations of flow transfer and use different approaches and formulas. Many of these approaches include the possibility of treating a sewer inlet as an orifice. In this context, this paper presents a methodology to obtain orifice discharge coefficients for three inlets previously tested at the hydraulics laboratory of the Technical University of Catalonia. Discharge coefficients of 0.18–0.58 were obtained for Froude numbers of 1.12–4.40, quite far from the usual recommended values. The proposed procedure can also be applied to non-tested grates. [ABSTRACT FROM AUTHOR]

Debris flows are considered one of the most hazardous types of mass movement. China has a long history of monitoring debris flows, which has enhanced the understanding of debris flows and the development of strategies for their prevention. This study reviewed case studies and outputs related to debris flow monitoring in China. The monitoring systems are set in seven catchments, with area between 2 and 40 km2, covering various types of debris flows in different climate conditions. This review also introduced the definitions and classifications adopted for debris flows in China for comparison with those used in Western literatures. A comprehensive analysis was conducted of debris flow parameters, including the grain size distribution, density, Froude number, velocity–depth relationship, volume–peak discharge relationship, volume–drainage area relationship, and velocity and peak discharge calculation methods. Additionally, the rainfall intensity–duration thresholds were compared. Accurate identification of such information is fundamental for enhancing comprehension of debris flow characteristics, facilitating monitoring, and the implementation of early warning and alarm systems. [ABSTRACT FROM AUTHOR]

Spillway is a hydraulic structure designed to release of excess water, from the upstream to the downstream area of a dam. In the present study, a three-dimensional numerical model was employed using Flow-3D software. The accuracy of the model was verified through experimentation with a physical model scaled at 1:77. The objective was to analyze the flow characteristics of a distinctive type of morning glory spillway (MGS) in the Dokan Dam in Iraq. The study investigated various flow characteristics, including the discharge release, pressure and velocity distributions, and Froude number characteristics. The findings revealed that the relative error of flow rates was generally under 5%, indicating a good agreement between the numerical and physical models. Also, the discharge fluctuation was observed at low water levels and disappeared at higher water levels, due to continuous discharge at elevated water levels. Regarding pressure distribution, most discrepancies between the physical and numerical results were concentrated at specific points within the vertical shaft, and the highest pressure recorded at the bottom of the vertical shaft. Furthermore, the maximum and minimum recorded average velocities were 26.78 and 0.78 m/s, observed at Sects. 3 and 4 for water levels of 516 and 512 m, respectively. Finally, the analysis of Froude numbers showed that the downstream tunnel's flow regime transitioned from subcritical (Fr < 1) for lower water levels (512 and 513 m) to supercritical (Fr > 1) for higher water levels (514, 515, and 516 m) due to increased flow velocities. [ABSTRACT FROM AUTHOR]

Confluences are essential nodes in natural and artificial networks of open channels, where the merging of flows creates a complex flow and scour pattern. The present study is an experimental investigation on the zero-degree confluence of rigid and mobile bed channels. Excessive scouring at the confluence of the channels leads to the failure of the common wall and floor of the rigid channel. Experimental studies show that primarily two scour holes develop, one at the confluence point of the channels and a second downstream of the rigid (primary) channel. Results are presented for scour patterns and maximum scour depth for varied ratio of the discharge in the primary channel and total discharge and for varied tailwater depth. Experiments were also carried out for three length of the solid apron provided in the primary channel beyond the divide wall to examine the effect of the apron on the flow and scour pattern. Scour holes formed downstream of the primary channel and at the confluence point decreases with an increase in tailwater depth and solid apron length but increases with an increase in the ratio of discharge in the primary channel and total discharge. One scour hole formed at the confluence of the two channels and another hole formed downstream of the primary channel. The scour hole formed at the confluence was extending in the secondary channel. Equations are developed to compute the maximum scour depths of the two scour holes and extension of the scour hole in the mobile (secondary) channel. Sensitivity analysis shows that the Densimetric Froude number of flow downstream of the confluence is the most sensitive parameter that affects maximum scour depth of the scour holes and extension of scour hole in the secondary channel. [ABSTRACT FROM AUTHOR]

The stability of bridge foundations is affected by local scour, and the formation of ice jams exacerbates local scour around bridge piers. These processes, particularly the evolution of ice jams and local scour around piers, are more complex in curved sections than in straight sections. This study, based on experiments in an S-shaped channel, investigates how various factors—the flow Froude number, ice–water discharge rate, median particle diameter, pier spacing, and pier diameter—affect the maximum local scour depth around double piers in tandem and the distribution of ice jam thickness. The results indicate that under ice-jammed flow conditions, the maximum local scour depth around double piers in tandem is positively correlated with the ice–water discharge rate, pier spacing, and pier diameter and negatively correlated with median particle diameter. The maximum local scour depth is positively correlated with the flow Froude number when it ranges from 0.1 to 0.114, peaking at 0.114. Above this value, the correlation becomes negative. In curved channels, the arrangement of double piers in tandem substantially influences ice jam thickness distribution, with increases in pier diameter and spacing directly correlating with greater ice jam thickness at each cross-section. Furthermore, ice jam thickness is responsive to flow conditions, escalating with higher ice–water discharge rates and decreasing flow Froude numbers. [ABSTRACT FROM AUTHOR]

Seawater desalination is increasing due to the global water crisis, and velocity caps are widely used at intake entrances to protect marine life and facilitate the required flow. Despite various investigations of seawater intake, a lack of precise research on the discharge coefficient of these structures is evident. The discharge characteristics of seawater intake are investigated both analytically and experimentally. Results show that the circle velocity caps have higher capacity than square ones, about 2% to 3.5%. Also, the Froude number of approach flow and the area of the velocity caps are the two parameters with the greatest impact on discharge coefficients. However, the height of caps and the number of separator blades have the least effect. Furthermore, some equations of discharge coefficients are developed based on machine-learning techniques with appropriate accuracy. Additionally, the Taguchi method, evaluated as an economical approach, significantly reduces the number of tests while the accuracy of results decreases. [ABSTRACT FROM AUTHOR]

Due to the International Maritime Organization's (IMO) mandatory standards for Energy Efficiency Design Index (EEDI) and Energy Efficiency Existing Ship Index (EEXI) for new and existing ships, there is serious concern about lowering carbon emissions from ships in order to have a sustainable environment. A number of energy-saving technologies are used on ships to improve their efficiency and decrease fuel consumption. Hull vane is a fixed foil placed to the stern of a vessel to enhance local pressure by modifying the stern flow. This study examines the effects of retrofitting a hull vane to a high-speed displacement vessel at a 1:35 scale with various locations in X and Z directions from the transom of the vessel. The simulated resistance and trim values for the bare hull were validated with experimental results which are conducted in towing tank facility available in the Department of Ocean Engineering, Indian Institute of Technology Madras. The coefficient of residuary resistance value has been reduced by 21% at the HV5 location. Furthermore, the wave pattern behind the transom for the HV5 position was studied and reported at the operating Froude number. [ABSTRACT FROM AUTHOR]

In the present research, an attempt is made to use four machine learning technique techniques such as artificial neural network combined with particle swarm optimization (ANN-PSO), adaptive neuro-fuzzy inference system (ANFIS), multivariate adaptive regression splines (MARS), and M5Tree machine learning (ML) approaches to model the scour depth. A total of 534 live bed scouring (LBS) experimental and field datasets are collected for bridge pier scouring from the previously published literature, and a gamma test has been performed to identify the best input parameter combination. A total of 36 combinations were tested in the gamma test, five distinct input combinations such as pier width to flow depth (b/y), approach flow velocity to sediment incipient velocity (V/Vc), critical Froude number (Frc), pier width to median sediment size (b/d50), geometric standard deviation of bed material (σg) were selected based on the lowest gamma value and Vratio. The developed models have been validated using field datasets of Pearl River, Mississippi, USA, by Mueller and Wagner (2005) and Ganga River, Patna, India, by Kumar and Singh (2022) and compared with six other existing scour depth predictive models. Results indicate that the proposed M5Tree scour depth prediction model (R2 = 0.9196, RMSE = 0.0837) provided better accuracy for all combinations of input variables (b/y, V/Vc, Frc, b/ d50, σg) compared to other ML models. The developed M5Tree model was successfully applied to the field condition for Ganga River, Patna, India and Pearl River, Mississippi, USA, and the mean absolute percentage error (MAPE) value is found to be less than 12% and the coefficient of determination (R2) more than 0.98. [ABSTRACT FROM AUTHOR]

In this paper, the results of numerical simulations of open-channel flow through boulder arrays at varying Froude numbers are reported. The simulations aim at clarifying the role of the Froude number on flow, turbulence, and hyporheic exchange. At low and intermediate Fr, the boulder top is above the water surface, and time-averaged streamwise flow velocity, Reynolds shear stresses, and the turbulent kinetic energy (TKE) are relatively low in the wake of boulders. Conversely, at high Fr values, the boulders are submerged, hence the flow separates at the boulder crest, creates vertical recirculation, and reattaches on the bed downstream, resulting in an area of elevated Reynolds shear stresses and TKE downstream of the boulders. Two dominant turbulence structures are observed: (i) flapping of boulder wakes with a characteristic length of 2.1 times the boulder diameter (D) at low and intermediate Fr and (ii) an upstream oriented hairpin vortex with a length scale of 1.0 D at high Fr. These turbulence structures influence hyporheic exchange downstream of boulders within a limited region of x / D < 2.0. In other locations, hyporheic flow is driven by downwelling flow immediately upstream of boulders with a wavelength larger than 2.9 D. Finally, the normalized time-averaged hyporheic flux increases with increasing Fr, but it decreases at higher Fr values once the overtopping flow disrupts the formation of the boulder wake. [ABSTRACT FROM AUTHOR]

One of the complex challenges in ventilated cavitating flow studies is analyzing hysteresis behavior and the formation air entrainment coefficient ( C q f ) under different conditions. This study explores the formation and collapse processes of the supercavity using experimental observations, numerical simulations, and machine learning (ML) models to reveal the hysteresis behavior of air entrainment at different flow conditions. Initially, the research focused on studying air entrainment hysteresis for a disk-shaped cavitator under different Froude numbers (Fr) through experimental and numerical methods. The study identified two key air entrainment coefficients in the hysteresis curves, which are important for gas generator design. In the ML section, hyperparameter optimization for the random forest (RF) model is performed using genetic algorithm (GA) and particle swarm optimization (PSO). The results demonstrate that the GA-RF model is more accurate than the PSO-RF model in predicting experimental data. The GA-RF findings show that, for a fixed cavitator diameter, C q f increases with Fr, reaching a maximum value (Max C q f ) before decreasing as Fr continues to rise. Additionally, with an increase in the cavitator diameter, Max C q f increases and Fr belonging to this ventilation coefficient (F r MaxCq f ) decreases. [ABSTRACT FROM AUTHOR]

We move forward the important topic of water entry by documenting splash dynamics arising from the impact of hydrophilic spheres with buoyant millimetric microplastics, mimicked in our study by polystyrene beads. Collision with small, buoyant beads is yet another means to manipulate splash dynamics. In this experimental study, we investigate the fluid–structure interactions between beads and hydrophilic spheres for Froude numbers in the range of 20 − 100. Generally, hydrophilic spheres entering a liquid bath below the critical velocity of 8 m/s produce minimal fluid displacement and no cavity formation. The presence of proximally adjacent beads atop the fluid with respect to impacting spheres promote flow separation and compound cavities for sufficiently large Froude numbers, while suppressing the growth of splash crowns. Compound cavities consist of a shallow, quasi-static first cavity that seals near the water line, and a second, deeper cavity produced in the wake of descending spheres. A vertically protruding Worthington jet follows cavity collapse. The resulting splash metrics differ from those of hydrophobic spheres with respect to the properties of impacted beads. We find impactors traversing a deep liquid pool layered with beads experience drag reduction when compared to entry into a clean pool due to the drag-reducing benefits of flow separation while not offering a high inertial penalty. Our study unravels the physics behind the widely encountered interaction of solid projectiles impacting passively floating particles, and our results translate to the entry dynamics of water-diving creatures and projectiles into water bodies polluted by floating millimetric microplastics. [ABSTRACT FROM AUTHOR]

The topography of Madagascar and the strength of the Mozambique Channel Trough (MCT) modulate summer rainfall over southern Africa. A strong MCT hinders the penetration of moisture bearing easterlies from the South Indian Ocean into the mainland, thus reducing rainfall there and vice versa for weak MCT summers. Given the link between the MCT and rainfall, it is important to analyse how climate models represent the trough. Here, output from 20 models within the CMIP6 ensemble of Coupled General Circulation Models (CGCMs) are analyzed to investigate how state-of-the-art CGCMs represent the MCT and its link to southern African rainfall. Overall, the ensemble mean insignificantly underestimates the observed MCT. There is a large spread among the models, with the strength of the MCT significantly correlated with the Froude number based on the mountain height over Madagascar. In models, the vorticity tendency in the MCT area is dominated by the stretching and friction terms, whereas the vertical advection, tilting and residual terms dominate in the ERA5 reanalysis. The link between MCT and rainfall in the southern African subcontinent is missing in the models. Large rainfall biases are depicted over mainland even in models with a very strong MCT. It is found that the impacts of the MCT in the models could be masked by a complex mix of processes such as the strength of the Angola low, moisture fluxes from the Indian and South Atlantic Oceans as well as overestimated convection in the Mozambique Channel area. [ABSTRACT FROM AUTHOR]

Using an asymptotic method, this article deals with flexural-gravity wave scattering with undulating bottom topography, including the effect of uniform currents. The interest in this problem lies in developing second-order solutions using the Fourier transform, which minimises the error gap between first and second-order solutions. The present method allows the physical processes involved in the sea-bed topography, uniform current, plate-covered surface, and wave interaction to be studied. Specifically, we observe Bragg resonance between the flexural-gravity waves and the bottom ripples, which are associated with the reflection of incident wave energy. We examine the effects of wave current and emphasise how crucial the asymptotic expansion method is to the emergence of the current response. We demonstrate that bottom topography dominates the effects of Bragg resonance for depth Froude numbers valued at 0.8 or less. Further, most reflected wave components have their frequencies shifted by the current, and wave action conservation causes reflected wave energy to be enhanced for following currents. Using the Joint North Sea Wave Observation Project spectrum and the discrete Fourier transform, the theory derived in the frequency domain is shown in the time domain to analyse wave propagation through the whole system. • A mathematical model to study flexural-gravity wave scattering with undulating bottom in the presence of uniform current. • The problem is studied using an asymptotic approach under linear water wave theory. • Develop the second-order solutions using the Fourier transform technique. • Identify the existence of Bragg resonance between the flexural-gravity waves and the bottom ripples. • The frequency domain analysis is illustrated in the time domain using JONSWAP. [ABSTRACT FROM AUTHOR]

This study experimentally investigated the temporal evolution of the scour parameters downstream of a trapezoidal piano key weir. The densimetric Froude number (Frd50) in the range of 0.39–0.57 and the relative vertical distance of the sediment bed level to the weir toe (Δz/P) in the range of 0.025–0.5 were taken into consideration. In general, with an increase in Frd50, the scouring rate, maximum scour depth, scour hole area and scour hole volume enhanced over time. The increases in the scour parameters were greater at the initial stages of the tests. About 87, 80, 65 and 70% of the maximum scour depth, weir toe scour, scour hole area and scour hole volume occurred within the first 20% of the durations of the tests, respectively. Any increase in Frd50 and Δz/P augmented the scour depth at the weir toe. The results also indicated that the distance of maximum scour depth from the weir increased for greater values of Δz/P and Frd50. The amounts of scour downstream of the outlet keys were greater than those downstream of the inlet keys. The trend of variations of the longitudinal bed profiles remained nearly unchanged over time. New equations were developed to predict the temporal variations of scour parameters, with acceptable accuracy. [ABSTRACT FROM AUTHOR]

Debris jams contribute to bridge pier failures. Previous investigations showed that a debris jam can constrict the flow cross section, enhance flow intensity, and result in significant scour. Physical modeling was conducted to investigate the influence of debris jams on scour depth. Instead of using a static block to represent a debris jam, dynamic debris jams composed of real tree seedlings were investigated to represent jams forming of woody debris with roots and branches. The dynamic jam was achieved by continuously releasing individual seedlings from upstream. The resulting seedling jams had a typical half-cone shape and generally grew continuously over time, with observed scour increasing with the size of the debris jam. The scour in the presence of a dynamic debris jam could have depth up to twice and volume up to eight times that of a pier without a debris jam. In addition, the dynamic debris jam also induced additional hydraulic head across the cylinder pier, which correlated with the size of debris jam and Froude number. Practical Applications: Scour around a bridge pier is the removal of sediment from the pier foundation by the surrounding flow. This can destabilize the bridge infrastructure, leading to potential failure. The accumulation of wood debris on a bridge pier leads to the formation of a debris jam that can increase scour. Most previous studies measured scour induced by a fixed debris jam geometry of constant size, with no temporal variation. However, in real situations, debris will gradually and often rapidly, especially during floods, accumulate over time around a bridge pier, and the associated scour increases as the debris jam increases in size. This paper presents an experimental study of the temporal evolution of debris accumulation on the model of a bridge pier and the associated progress of scour as a debris jam develops. In contrast to most previous studies that used wooden dowels, the debris is modeled using real seedling trees, which have roughness characteristics more akin to real-world debris. The resulting debris jams are relatively stable due to the interlocking of debris pieces. It was found that the instantaneous scour depth increased in the presence of the developing debris jam and that it was proportional to how much the debris jam blocked the flow. Interestingly, the plan area of the scour hole increased more than that occurring in the absence of the debris; the scour hole volume is hence much greater when a debris jam is present. [ABSTRACT FROM AUTHOR]

Vertical water jets present significant challenges for hydraulic structures due to their potential to cause erosion and structural damage. This study aimed to predict the dimensionless pressure coefficient (Cp) of vertical water jets by examining the relationships between experimental parameters, such as Froude number, slope, and the ratio of waterfall height over the product of the Froude number and diameter, referred to as α, using machine learning models. Two hundred forty controlled experiments were conducted, with pressure data collected. To address the problem's non-linearity, six machine learning models were tested: linear regression, K-nearest neighbors, decision tree, support vector regression, random forest, and XGBoost. The XGBoost model outperformed others, achieving an R-squared of 0.953 and a Root Mean Squared Error (RMSE) of 0.191. Residual analysis validated its better performance, demonstrating that it delivered the most accurate predictions with minimal bias. Feature importance analysis revealed the Froude number was the most significant predictor, followed by slope and diameter. This study emphasizes the importance of the Froude number in predicting jet behavior and shows the efficacy of advanced machine learning models in capturing complex fluid dynamics, providing valuable insights for optimizing engineering applications such as water jet cutting and cooling systems. [ABSTRACT FROM AUTHOR]

The hydraulic characteristics (such as velocity profiles, near-bed velocity profile, bed shear stress, and resistance coefficients) of shallow flows over rough surfaces were investigated using numerical simulations. A novel method is presented to simulate shallow flows over rough surfaces in a two-dimensional (2D) numerical domain, where the physical numerical domain represents bed topography. Results reveal that the model can accurately predict spatially averaged velocity profiles, turbulence characteristics, shear stresses, and uniform flow depths. The analysis identified two distinct flow regions based on mean and turbulent flow profiles. Results show that the turbulent shear stress profiles provide a more accurate estimation of the bed shear stresses. Resistance coefficients (friction factor or Manning's roughness coefficient) vary with Froude number and submergence ratio (depth divided by roughness height). [ABSTRACT FROM AUTHOR]

A new approach to predicting the geometrical characteristics of the mixing behavior of an inclined dense jet for angles ranging from 15° to 85° is proposed in this study. This approach is called the group method of data handling (GMDH) and is based on the artificial neural network (ANN) technique. The proposed model was trained and tested using existing experimental data reported in the literature. The model was then evaluated using statistical indices, as well as being compared with analytical models from previous studies. The results of the coefficient of determination (R2) indicate the high accuracy of the proposed model, with values of 0.9719 and 0.9513 for training and testing for the dimensionless distance from the nozzle to the return point x r / D and 0.9454 and 0.9565 for training and testing for the dimensionless terminal rise height y t / D . Moreover, four previous analytical models were used to evaluate the GMDH model. The results showed the superiority of the proposed model in predicting the geometrical characteristics of the inclined dense jet for all tested angles. Finally, the standard error of the estimate (SEE) was applied to demonstrate which model performed the best in terms of approaching the actual data. The results illustrate that all fitting lines of the GMDH model performed very well for all geometrical parameter predictions and it was the best model, with an approximately 10% error, which was the lowest error value among the models. Therefore, this study confirms that the GMDH model can be used to predict the geometrical properties of the inclined negatively buoyant jet with high performance and accuracy. [ABSTRACT FROM AUTHOR]

This study explores how the ice cover on water surfaces affects the deformation of the channel bed around non-submerged spur dikes. Laboratory experiments have been conducted by using two types of model ice cover with different roughness coefficients and three sands with different median grain sizes. The effects of various layout angles of non-submerged spur dikes on the maximum scour depth and scour patterns around spur dikes have been evaluated. Results showed that the dike orientation angle is the critical factor influencing the maximum scour depth. The presence of an ice cover and its roughness coefficient dramatically affect the channel bed deformation around spur dikes. The combined effect of the dike orientation angle, ice cover roughness, and flow Froude number resulted in different scour patterns. For instance, the upstream length of scour holes decreases by approximately 60% when the dike angle changes from 90º to 60º, while an increase in flow rate by about 50% leads to a 20% increase in the downstream length of scour holes. Equations have been derived to determine the maximum scour depth around spur dikes, considering the effects of ice cover, bed material and the dike layout angles. [ABSTRACT FROM AUTHOR]

Abutment scour is a major cause of bridge failures worldwide, leading to disruptions, economic losses, and loss of life. The present experimental study examines countermeasures against abutment scour using hooked-collar protections on vertical-wall and wing-wall abutments (at 45° and 60°) under different flow conditions. All 60 experiments were performed under sub-critical flow conditions by investigating scour around an abutment 20 cm long, 20 cm wide, and 25 cm tall. Two distinct values of the Froude number, 0.154 and 0.179, and a sediment particle diameter (d50) of 0.88 mm were used throughout the experimental phase. The resulting equilibrium scour around the abutments was compared to those with collar and hooked-collar protections. It was determined that the maximum abutment scour depth reduction was 83.89% when hooked collars were placed on vertical wall abutments beneath the bed surface level, and for wing-wall abutments at 45° and 60°, it was 74.2% and 73.5%, respectively, at the bed surface level. Regression analysis was conducted to assess the non-dimensional scour depth (Ds/Yf) and scour reduction (RDs/Yf), with a high enough coefficient of determination (R2 values of 0.96 and 0.93, respectively), indicating high confidence in the analysis. The sensitivity analysis findings demonstrate that the width of the collar (Wc) and La are the most influencing factors affecting Ds/Yf and RDs/Yf. [ABSTRACT FROM AUTHOR]

This investigation explores the interactions of different shaped debris with an array of obstacles under subcritical flow conditions, representative of a flood associated with a storm surge or tsunami. Panels, blocks and cylinders were used in a flow channel, as analogues for house panels, cars/containers and trees respectively, whilst some tests used a mix of debris. The backwater effect due to the blockage caused by the obstacles was most (least) significant for panels (cylinders). There was some evidence that smaller key log types and higher flow rates led to smaller dams. It was also evident that key logs formed at different depths depending on debris shape; debris shape also determined the vertical shape of the dam. Capture efficiency had a broadly negative (positive) correlation with the Froude number (permeability). Also, from video footage there were examples of the debris moving more quickly through partial dams. Finally, the drag force, deduced from only the water depths and the flow discharge, showed a clear relationship between drag force and Froude number, and a dependency of drag force on debris shape. There are some implications for the layout of building footprints in the inundation zones and the use of large, break‐away panels. [ABSTRACT FROM AUTHOR]

Large amplitude and unexpected waves are a regular source of natural disasters. Among them, impulse waves generated by landslides can represent a significant threat. Therefore, predicting and measuring the generation of such waves is essential. In this study, the phenomenon is modeled by a 2D‐experimental setup using a steady non‐uniform granular flow along a slope as a forcing wave generator. The present device provides a continuous supply of grains to avoid finite volume effects, as the part of the landslide actually involved in the wave generation strongly depends on the configuration and is not necessarily available in geophysical events. This system consists of an energy transfer between the granular flow and the wave generation which is characterized by a Froude number. It is found that the latter cannot be defined only based on the dry flow properties to characterize the wave. In particular, the dynamics underwater influence wave generation during a finite time. Accordingly, the present study shows that the wave maximum amplitude is governed by a newly defined Froude number, based on both dry and underwater granular flow properties. Moreover, it is shown that the granular deposit, specifically its runout, can be thought as a proxy of the immersed granular dynamics as long as the impact properties are still considered. Plain Language Summary: Landslides can cause huge waves if they impact the surface of an ocean, a lake or a sea. The properties of the landslide as well as the wave formation are complex features. In this study, an attempt to model this phenomenon experimentally at the laboratory scale is made, using a controlled granular flow impacting water in a 2D wave channel. The rapid evolution of this system requires a camera in order to extract the dynamics of both the wave and the granular material, simultaneously. From these measurements, it is shown that the wave and the granular flow are strongly linked at early stages. Moreover, after the maximum wave amplitude is reached, the wave propagates freely and may influence the granular deposit. This study proposes to link these processes and the wave characteristics to a single dimensionless parameter, which is a combination of Froude numbers. Key Points: A detailed analysis of new impulse wave experiments using a continuous granular supply is presented to highlight the wave‐granular couplingThe wave maximum amplitude is shown to evolve non‐monotonically with the deposit runoutConsidering wave‐granular interaction, a newly defined Froude number allows to accurately predict the wave characteristics [ABSTRACT FROM AUTHOR]

We develop a multilayer model to study roll waves in mudflow of Herschel–Bulkley fluids initiated by periodic and localized disturbance. Simulations are conducted of the temporal development of periodic roll waves and spatial development of wave packets due to localized disturbance. The results of the temporal development are expressed in terms of the power-law index, the relative plug-layer thickness, the Froude number, and the perturbation wavelength. Our simulation for the spatial development shows the roll waves led by a dominant front runner and followed by a quiescent tail, closely reproducing a well-known river-clogging phenomenon of the natural mudflow observed in the mountain rivers on mild slopes. The leading wave of the roll-wave packet, i.e., the front runner, grows in depth, velocity, celerity, and wavelength with distance from the localized disturbance. The front-runner wave amplitude depends on the distance from the localized disturbance, the power law index, the plug-layer thickness, and the Froude number. We calculated the front-runner's wave amplitude due to a line source of disturbance in a 1D unidirectional development and the roll waves' 2D development due to a point source. The initial nonlinear growth in the 2D front runner is a fraction of the 1D waves, but the increase in the wave amplitude with distance follows the same trend. We have also conducted a mesh refinement study to determine the convergence and accuracy. The present simulations using 64 layers have attained an accuracy within a 2% error. [ABSTRACT FROM AUTHOR]

Dissolved oxygen (DO) concentration in water is one of the most important water quality parameters in rivers, lakes, and reservoirs. The most effective way to increase DO concentration in water is aeration. Conduits with high aeration performance are predicted to significantly increase aeration efficiency. Based on this prediction, the physical parameters affecting the aeration efficiency (E20) of the conduit aeration system were experimentally investigated. The effect of different jet plunge angles, flow rates, hydrostatic levels, Froude numbers, and gate opening rates was investigated to optimize the system for the best ventilation efficiency. As a result, the aeration efficiency (E20) improves with increasing air intake performance at low gate openings, high Froude numbers, and hydrostatic levels. The increase in jet plunge angles and hydrostatic level directly increases the aeration efficiency. The study showed that conduit systems can be an important alternative for pond aeration due to initial investment and operating costs, low energy cost, and high aeration efficiency. [ABSTRACT FROM AUTHOR]

An inviscid vortex shedding model is numerically extended to simulate falling flat plates. The body and vortices separated from the edge of the body are described by vortex sheets. The vortex shedding model has computational limitations when the angle of incidence is small and the free vortex sheet approaches the body closely. These problems are overcome by using numerical procedures such as a method for a near-singular integral and the suppression of vortex shedding at the plate edge. The model is applied to a falling plate of flow regimes of various Froude numbers. For Fr = 0.5 , the plate develops large-scale side-to-side oscillations. In the case of Fr = 1 , the plate motion is a combination of side-to-side oscillations and tumbling and is identified as a chaotic type. For Fr = 1.5 , the plate develops to autorotating motion. Comparisons with previous experimental results show good agreement for the falling pattern. The dependence of change in the vortex structure on the Froude number and its relation with the plate motion is also examined. [ABSTRACT FROM AUTHOR]

Urban pumping stations often adopt the design of lateral-intake multiple forebays to accommodate multiple pump units in a limited space and to reduce interaction between the operating units. However, a full understanding of the undesired flows and hydraulic characteristics of lateral-intake multiple forebays remains limited, resulting in the design of flow-regulating measures relying on trial and error. This study numerically investigated the undesired flows in lateral-intake multiple forebays and their hydraulic implications, using Asia's largest urban water supply pumping station as a case study. The results show that the undesired flows, including flow recirculation, helical mainstream and vortex strip, are the main reasons for the deterioration of hydraulic characteristics in the forebays. The undesired flows are more pronounced at higher inflow Froude numbers or for the forebay closer to the diversion channel inlet, resulting in lower flow uniformity and higher hydraulic loss. Further discussion shows that the flow-regulating measures improve the hydraulic characteristics by limiting the generation and development of undesired flows within the forebays. This provides references for the design of flow-regulating measures for similar forebays to reduce the cost of trial and error, which is of general value for the lateral-intake multiple forebays required for urban pumping stations. [ABSTRACT FROM AUTHOR]

Vortex flow characteristics in a reservoir and horizontal water intake have been predicted by using regression models in this numerical research. In this paper, three standalone machine learning models - Random Forest (RF), K-nearest neighbours (KNN), Gradient Boosting (GB) - and a proposed hybrid model based on Lévy Jaya Algorithm (LJA) and GB (LJA-GB) are employed to estimate the effect of trash racks on flow properties at power intakes. The experimental data which are prepared for the proposed study in this paper were obtained through a rectangular laboratory tank 8.3m³ with various submergence depths and Froude numbers on nine trash racks with 63.7%-84.1% opening, made out of 2, 2.5, 4, and 6 mm thick copper wire. The outcomes revealed that the proposed LJA-GB model shows the best overall performance among the four models used for estimation. Thus, the LJA-GB model has the lowest mean absolute error (MAE) (0.3344), mean squared error (MSE) (0.1784), and root mean squared error (RMSE) (0.4223) values and highest R-squared (R²) (0.9899) and Willmott's index (WI) values (0.9508) in the testing stage metrics for Vxy/Vi estimation and MAE (0.0061), MSE (0.0001), RMSE (0.0073), R² (0.9971), WI (0.9727) for Nt estimation. Whereas the RF and KNN models exhibited poor performance in both stages of estimation. [ABSTRACT FROM AUTHOR]

Large eddy simulations of an open channel bend are performed at a variety of water depths and flow rates. The results at several cross sections are decomposed into sub-cells of secondary circulation using clusters of instantaneous vortices. The strength and position of the sub-cells are then modelled using decision trees, multiple linear regression, multi-layer perceptrons, and adaptive neuro-fuzzy inference systems to obtain parametric models of secondary circulation development in a channel bend. The development of individual cells and total circulation is shown for an arbitrary flow condition using the model, as well as the dependence of all the circulation output variables on the input parameters of aspect ratio and Froude number. The positions of the sub-cells (but not their circulations) are largely independent of the Froude number, and the cross-stream position of the centre cell is found to behave linearly. The model with the best performance across all predicted variables is the ANFIS model without classification. [ABSTRACT FROM AUTHOR]

The experimental evaluation of the performance of a corrugated apron under free flow subcritical and submerged conditions was conducted, with a focus on scour patterns over the apron. Comparative analysis with a smooth rigid apron revealed an increase in scour depth upon the application of the corrugated apron under free and submerged jet flow conditions. The implementation of a corrugated apron resulted in a considerable reduction in scour depth and length compared to a smooth rigid apron. The maximum reduction in scour depth and length amounted to 79% and 83%, respectively, while the minimum reduction observed was 13% in scour depth and 11% in scour length. Additionally, investigations into velocity and turbulence characteristics over both smooth and corrugated aprons were conducted. It was observed that the rate of turbulence intensity increase within the scour hole due to the presence of a smooth apron surpassed that of the corrugated apron. Scour downstream of the corrugated apron exhibited distinct delineations, including regions of jet diffusion, transition, acceleration, and a recirculating zone near the bed of the scour hole. [ABSTRACT FROM AUTHOR]

The phenomenon of hydraulic jumps has been widely studied in laboratory flumes. However, few studies have been made to bridge the discrepancy encountered in the formulation of relations ascribing hydraulic jumps based on laboratory model studies and that occur in natural conditions. Most of the predictive formulae for sequent depth ratio and length of jump proposed in the literature have not been verified in the field. The present study attempts to link the field investigation data of hydraulic jump in a weir with laboratory channel flume observation for similar flow conditions. The hydraulic jump parameters were collected in the field using feasible technologies in the study weir. The weir selected for this study has geometric, kinematic and Froude similarities with the laboratory model. The comparison of laboratory model data and field measurements showed inconsistency. It is observed that the sequent depth ratio and length of the jump are inaccurately predicted by the laboratory relation compared to the field observations by the laboratory relation. A fieldvalidated-based relationship is suggested for the calculation of sequent depth and length of jump in a smooth rectangular channel for Froude numbers ranging from 4 to 10. [ABSTRACT FROM AUTHOR]

Gated conduits involve high-velocity air–water flow. When studies on gated conduits are examined, it is determined that the air-demand ratio changes according to the hydraulic and geometric parameters. However, no study has investigated the effect of the cross-sectional geometry of high-head conduits with a sluice gate on the air-demand ratio. In this study, the effect of conduit cross-sectional geometry on the air-demand ratio is examined. Results indicate that a conduit's cross-sectional geometry has an important effect on the air-demand ratio, especially at 10% and 15% gate opening rates. It is seen that the effect of the conduit geometry on the air-demand ratio decreases at 20%, and for greater gate opening rates. Moreover, a formula for estimated the air-demand ratio is presented, relating the air-demand ratio to the gate opening rate, Froude number, hydraulic radius and conduit length. [ABSTRACT FROM AUTHOR]

The formation conditions of maximum- and minimum-wave jumps were experimentally investigated. A total of 110 wave-type jump experiments were carried out for several discharges, supercritical upstream and subcritical downstream water depths and drop heights. The experimental results revealed that the influential parameters on wave-type jumps are the upstream Froude number and the relative drop height. As the classical hydraulic jump equation is not sufficient to define conjugate depths of wave-type flow, empirical equations were developed for defining the conjugate depths of maximum-wave jumps and minimum-wave jumps (for which insufficient experimental data are available in the literature). The agreement between calculated and measured conjugate depths was good. It was also found that the value of the lower limit for the upstream Froude number is not constant for the formation of a maximum-wave jump – it depends on the relative drop height. Furthermore, the experimental results showed that the energy-dissipation ratios of maximum- and minimum-wave jumps are equal to or larger than those of classical hydraulic jumps. For this reason, wave-type jumps may be preferred at stilling basins with drops along with A-jumps. [ABSTRACT FROM AUTHOR]

This paper studies the characteristics of internal waves induced by the motion of a submerged body through a combination of experimental and numerical methods. First, by deploying an array of conductivity probes in an experiment, the temporal evolution of the internal wave at the plane of the conductivity probe array is obtained and compared with numerical simulation results based on the Navier–Stokes equations, thereby validating the accuracy of the Computational Fluid Dynamics (CFD) model. Subsequently, utilizing CFD calculations, further exploration is conducted on the spatiotemporal distribution characteristics of the internal wave, encompassing its generation and evolution, velocity field distribution, wake angle, and wave profile features. Finally, the variation of the internal wave with the Froude number (Fr) is investigated, revealing that it varies apparently with Fr, including the wave component, wave mode, wake length, wake angle, wave amplitude, and so on. It is found that when Fr is large, the internal wave converges toward the centerline behind the body, until forming a line. The wave magnitude changes with Fr in four stages, i.e., increasing with Fr from zero in the first stage, reaching a peak and decreasing thereafter in the second stage, then changing little in the third stage, and finally increasing approximately linearly in the fourth stage. [ABSTRACT FROM AUTHOR]

To understand the stratification of the smoke layer in a road tunnel, numerical simulations are employed to model tunnel fires with varying heat release rates. The different simulations cases are carried out with FDS (Fire dynamic simulations). These simulations are conducted to examine the influence of tunnel slope and longitudinal airflow on the smoke stratification along the downstream side of tunnel. The aim is to explore the relationship between longitudinal airflow and temperature ratio taking into account the tunnel slope. As a result, a quantitative analysis, based on Newman's theory, is conducted to assess the clarity of the smoke layer stratification, a Froude number (Fr = 0.63) is obtained. The slopes in tunnels can have a substantial impact on smoke flow during a fire, primarily driven by thermal buoyancy and the stack effect. With a slope less than 1.5°, the stratification improves. Similarly, clear stratification occurs when the longitudinal airflow is less than 1 m/s. However, a balance between inertia force and buoyancy force is crucial for maintaining clear stratification. Increasing both the longitudinal airflow and the tunnel slope serves to disturb the stratification of the smoke layer. [ABSTRACT FROM AUTHOR]

To reduce the resistance of high-speed displacement ships with Froude numbers (Fr) between 0.4 and 0.5, this paper proposes the installation of hydrofoils at the bow and stern of the ship. Firstly, starting from the bow wave, this paper proposes the installation of a flat plate appendage at the free surface of the ship's bow to suppress the height of the bow wave and thus reduce the hull resistance. Taking the DTMB 5415 ship model as the research object, CFD calculation results show that installing a flat plate appendage at the free surface of the ship's bow can effectively suppress the height of the bow wave, and the total resistance reduction ratio can reach 6.49% when Fr = 0.45. Then, the flat plate appendage was improved to a hydrofoil appendage, further reducing the hull resistance. As a result, the total resistance reduction rate can reach 9.15% at Fr = 0.45. Following this, hydrofoil appendages were installed simultaneously at the bow and stern. The drag reduction effect and mechanism were studied, and the results show that the hydrofoils at the bow and stern have a good drag reduction effect. Suppressing the bow and stern waves and improving the flow field are the main reasons for the drag reduction. Finally, the drag reduction effect of the hydrofoil appendages was verified through experiments, demonstrating its excellent drag reduction effect when Fr = 0.4–0.5 and a maximum total resistance reduction ratio of 14.552%. [ABSTRACT FROM AUTHOR]

Rock weirs, typically created by the placement of loose rocks, are eco-friendly hydraulic structures used for raising the upstream water level, which has benefits for irrigation, shipping, and grade control. Although rock weirs are frequently submerged in rivers, few studies have systematically investigated their impacts on the upstream water level under submerged conditions. A series of flume experiments regarding this topic were conducted. Different flow discharges, tail-water depths, and void ratios were adopted in the experiments. The results show that (1) the submerged rock weirs primarily function to raise the upstream water level, while having a limited impact on the tail-water level; (2) for a given tail-water depth and void ratio, the upstream water level rise increases with increased discharge, although this response becomes insignificant as tail-water depth increases; (3) as void ratio increases, the upstream water level rise is expected to decrease for a given tail-water depth and discharge; and (4) based on the data and observations, a predictor including the effects of Froude number, submergence, and void ratio is proposed for estimating the upstream water level rise of submerged rock weirs. These results contribute to further understanding the hydraulic properties of rock weirs and are important for river training practices using rock weirs. [ABSTRACT FROM AUTHOR]

As urbanization progresses and city populations grow, river-crossing tunnels assume a crucial role in transportation networks, with the maximum scour depth constituting a critical parameter influencing tunnel safety. Using Line 6 of the Nanning Metro in Guangxi, China as a case study, a two-dimensional hydrosediment mathematical model was employed to investigate variations in maximum bedrock scouring. This study introduces the concept of critical frequency floods and compares it with urban flood control standards to determine the appropriate flood frequency for calculating maximum bedrock scour depth. The impact of bed sediment particle size on maximum scour depth is quantified, revealing a decrease in scour depth of 0.3 to 0.6 m for every 1 mm increase in particle size. The relationship between bed sedimentation and the Froude number demonstrates an upward-opening parabolic symmetry: lower Froude numbers correspond to relatively stable beds, while higher numbers correlate with an increased amplitude of bed erosion or deposition. The curve's nadir identifies the critical threshold of the Froude number, facilitating calculation of the channel's critical water depth. In practical engineering applications, a bed under conditions of critical water depth tends to be more stable, thereby favoring the selection of sites for river-crossing tunnels. [ABSTRACT FROM AUTHOR]

The characteristics of grain-size distribution on the surface of gravel bars have important implications for riverbed development and fish spawning. In this study, an unmanned aerial vehicle was used to sample 204 sites on the surface of a gravel bar in the upper reaches of the Yangtze River, China. Photogrammetry was used to generate digital elevation model data for the bar. Based on the calculation results of a two-dimensional river hydrodynamic model, clear distribution maps of the flow and grain-size fields were obtained. In addition, the correlation between the hydrodynamic and grain-size indicators was discussed, and a relational equation between the Froude number and median grain size was derived. Finally, the effect of topographic changes on the grain-size distribution was analyzed. The results showed that the grain size at the head of the gravel bar was larger than that at the tail, influenced by the scouring of the flow; coarsening of the gravel at the edge of the bar bend was also evident. A positive correlation was found between , flow velocity, and the Froude number. The sorting coefficient, , exhibited a negative correlation with the flow velocity and Froude number. A positive correlation was found between grain size variability indicator and topographic variability indicator . The variability in the grain-size distribution was the highest near areas with more drastic topographic variations. The bar surfaces exhibited a pattern of coarse-grained tops and fine-grained pools. The results of this study contribute to further understanding the geomorphology of gravel bars and may help investigate the spawning sites of organisms on the bar surface sensitive to bottom particle size. [ABSTRACT FROM AUTHOR]

The Improved Delayed Detached Eddy Simulation (IDDES), VOF (Volume of Fluid) multiphase flow model, and overlapping grid technology were adopted in this paper. The results show that the interaction between the high-speed regions and the low-speed flow increases, as the Kelvin–Helmholtz instability phenomenon occurs in the mixing fluid during traveling underwater. Under the effect of the inertial force, the tail bubble expands successively, resulting in an increase in cavity volume and a decrease in pressure. In addition, the wake vortex is composed of the main vortex and secondary vortex, which is a cone of the major influencing factors causing the disturbance of the flow field. As the vehicle continuously passes through the free surface, the buoyancy center of the vehicle successively moves downward, resulting in a change in the direction of buoyancy moment and aggravating the deflection amplitude of the vehicle. [ABSTRACT FROM AUTHOR]

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Hydrogen is an ideal energy source and plays an important role in increasingly global energy issues and environmental problems. Liquid hydrogen (LH2) has many advantages over other storage methods, especially in terms of energy density. However, it may cause enormous harm once it leaks accidently. LH2 leakage is a complex multiphase process involving evaporation, condensation, transfer of mass and heat, and dispersion. In order to study LH2 transportation and storage systems safety, a research project has been carried out to develop a 3D numerical model using an open-source CFD code, OpenFoam, for investigating LH2 accidental release scenarios. Since the release of LH2 is a very complex process, our strategy is to study it step by step. Therefore, in this paper we present our research work at the first stage, a dispersion process of room-temperature gaseous hydrogen without multiphase flow. A small-scale hydrogen release conducted by Sandia National Laboratories is simulated. In this experiment, room-temperature gaseous hydrogen is injected upwards into the air from a small hole with a 1.91 mm diameter. The situations of Froude (Fr) number = 99, 152, and 268 are studied, respectively. The behavior of hydrogen at different Fr numbers is discussed. When high-speed hydrogen enters the air, the speed and concentration of hydrogen decrease rapidly. In addition, the greater the speed, the faster it decays. The result shows a close range of hydrogen reach. Details about the numerical model are introduced. The simulation results are used to verify the validity of the developing numerical model for dispersion and mixing of multi-species. The simulated concentrations and velocity distribution are analyzed and compared with experimental data. The simulation shows a good agreement with the data of Sandia National Laboratories. The agreement between experiments and simulations is measured using the Pearson correlation coefficient (>0.98), which indicates excellent consistency. In the next step, we will integrate the multiphase flow and phase change into the current model. The phase change of liquid hydrogen and air will be simulated to study the release of liquid hydrogen. • Using the open-source CFD code OpenFOAM for simulation of hydrogen jet. • A good agreement between the simulations results and experimental data has been found in this paper. • When high-speed hydrogen is injected into the air, both velocity and concentration drop rapidly. • Final concentration is not sensitive to different injection velocity. [ABSTRACT FROM AUTHOR]

In our previous work dedicated to the strongly stratified Boussinesq system, we obtained for the first time a limit system (when the froude number ε goes to zero) that depends on the thermal diffusivity ν ′ (other works obtained a limit system only depending on the visosity ν). To reach those richer asymptotics we had to consider an unusual initial data which is the sum of a function depending on the full space variable and a function only depending on the vertical coordinate, and we studied the convergence of the weak Leray-type solutions. In the present article we extend these results to the strong Fujita-Kato-type solutions. In this setting, and compared to the case of weak solutions, we obtain far better convergence rates (in ε) for ill-prepared initial data with very large oscillating part of size some negative power of the small parameter ε. The main difficulties come from the anisotropy induced by the presence of x3-depending functions. [ABSTRACT FROM AUTHOR]

This study aims to develop and assess seven machine learning (ML) models, including an Artificial Neural Network (ANN), Gradient Boosting (GB), Extra Trees (ET), Lasso Regression (LASSO), Least Angle Regression (Lars), Random Forest (RF), and Adaptive Boosting (Adaboost), that are effective and simple in forecasting the roller length of a hydraulic jump in a rectangular horizontal canal. This study also proposes a novel approach for applying the Buckingham Pi theorem to ascertain four model inputs and one output, corresponding to five dimensionless Pi terms that have not previously been explored. The impact of channel surface roughness, fluid viscosity, channel geometry, and gravity on the hydraulic jump's roller length was considered to improve the model's performance. Furthermore, the importance of input features was determined, resulting in two model input scenarios. The scenario with four inputs containing the inflow Reynolds number Re1* surpasses the three-input scenario. Because of their high accuracy and efficiency, six ML models outperformed three empirical equations. The GB, ANN, and ET models showed the best performance in both validation and testing phases, whereas LASSO, Lars, RF, and Adaboost performed with lower precision, in descending order. Regarding the ANN model, the best has two hidden layers of sixteen neurons each. In the validation and testing phases, this model achieves the highest Nash–Sutcliffe efficiency of 0.992 and 0.933, respectively. As a result, this study recommends using the GB, ANN, and ET models to forecast the roller length of the hydraulic jump instead of empirical equations when the inflow Froude number, Fr1, varies between 2.4 and 15.9. [ABSTRACT FROM AUTHOR]

In the design and optimisation of marine wireless communication and navigation systems, a thorough investigation of radio wave propagation characteristics under atmospheric ducting conditions is essential. The authors aim to enhance the efficiency of radio wave propagation loss prediction in marine atmospheric ducting environments, proposing a prediction model based on Fast Reordered‐Alternate Direction Decomposition (FR‐ADD). By approximating the diffraction term into three independent components, exploiting the commutative properties of the Fourier transform to reduce the spatial dimensions, and incorporating a rapid algorithm for the parabolic equation, the model optimises the stepping process and significantly improves computational efficiency. Simulation experiments demonstrate that, in the long‐distance and complex marine ducting environments, the model not only maintains prediction accuracy but also substantially reduces computational load and prediction time, effectively realising over‐the‐horizon propagation prediction. In the experiment of radio wave propagation characteristics in the Yellow and Bohai Seas, the simulation data from the FR‐ADD model showed significant correlation with actual measurements and simulations from the AREPS software, confirming the method's efficiency and practicality. [ABSTRACT FROM AUTHOR]

This study experimentally investigates the hydrodynamic forces acting on wood debris accumulations. Tests were performed under steady subcritical flow conditions by letting debris elements accumulate against an obstacle. We analyze the influence of a variety of variables involved in the problem, namely the Froude number, the blockage ratio, the geometric parameters of the dam, its porosity, and the debris type. Resulting forces are expressed through a typical drag coefficient formula, where the coefficient depends on the Froude number and the blockage ratio, but is independent of the geometric characteristics of the debris accumulation. The model is validated against literature data, providing both best-fit and safe-side predictors. Practical Applications: Wood debris can build up on bridge piers and decks, which increase the water's force on these structures. In this paper, we offer a straightforward method to estimate these forces. We have calibrated an empirical model using data from laboratory experiments and checked its accuracy against information from existing studies. With this model, one can input the basic characteristics of the flowing water (such as its depth, width, and speed) and the size of the debris pile facing the flow. The model then provides the drag coefficient, which, in turn, allows determining the drag force acting on the debris pile. [ABSTRACT FROM AUTHOR]

This study conducted experiments to investigate the impact of bottom obstacles, specifically broad-crest weir-type and cylindrical obstacles, on the flow within a sewer pipe. It was observed that these two types of obstacles, when possessing the same cross-sectional area and length, exhibited nearly equivalent hydraulic responses for both supercritical and subcritical flows. The obstacle height was found to be the primary factor responsible for choking and the transition between different flow regimes. The results of the one-dimensional analysis show that the threshold value of obstacle height depends on the approaching flow conditions, including the Froude number and the filling ratio that is defined as the flow depth to the pipe diameter. In the context of a partially blocked sewer, the relationships established by using the one-dimensional model between the size of the bottom obstacle and the inflow characteristics enable the identification of flow regimes, assessment of reduced hydraulic capacity, and evaluation of local energy loss. The findings of this study elucidate the hydraulic behavior of obstructed sewers, contributing to the development of more effective strategies for the identification of obstructions through monitoring data. [ABSTRACT FROM AUTHOR]