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The east coast of India is highly prone to devastating winds, torrential rainfall, and storm surges caused by tropical cyclones. The storm surge is affected by ocean basin characteristics involving the width and slope of the continental shelf. The bed roughness plays a major role in surge formation. The east coast of India is characterized by a broader shelf in the north and a narrow shelf in the south. This paper uses a hybrid Finite Volume Method–Finite Element Method based Shallow water equation (SWE) solver to predict the storm surges during different cyclone events, and the roughness parameter Manning’s n is used in bed friction calculations. The bottom friction coefficient parameterization involving bed roughness is used to calibrate the resistance to flow in the numerical model. The calibration exercises are carried out with different values of n for each surge simulations for different cyclones to predict the surface elevation. Different statistical parameters against the measured values are used to analyze the impact of varying n values on predicted surge levels, and the most suitable n value is carefully chosen. The relationship between n and the bed slope is established as an expression, to replace the formulations involving Manning’s n , thereby minimizing the usual computational efforts. The performance of the novel bed friction formulation involving the physical parameter in bed slope is demonstrated through statistical evaluations.

Emergent vegetation in an open channel is a significant factor in flow resistance and has greater influence on flow characteristics. This paper aims to compare the significance of emergent vegetation under various flow conditions including sub and supercritical flow conditions. The methodology utilizes two types of flow condition (sub and supercritical flow), and each type was further considered on the basis of varying discharge and constant channel bed slope and vice versa. For example, under subcritical flow Froude number was defined as a (Fr (CD-VS) represent Froude number under constant discharge and varying channel bed slope) and (Fr (CS-VD) represent Froude number under constant channel bed slope and varying discharge). A similar flow condition was defined under supercritical flow conditions. Various parameters such as backwater rise, hydraulic jump, energy reduction, fluid force (RFI%) and moment index reduction (RMI%) as well as reduction of overflow volume (∆Q%) were investigated. The result has been explained in two phases such as sub and supercritical flow. Under sub-critical flow, an undulated hydraulic jump was observed on the downstream side of the vegetation and a maximum energy reduction was 28% in the case of (Fr (CS-VD) ) and 33.4% in the case (Fr (CD-VS) ). Moreover, in the case of (Fr (CS-VD) ) the maximum value of the RFI% and RMI% increased by increasing the values of (Fr (CS-VD) ). The maximum reduction of overflow volume observed was 72% in the case of (Fr (CS-VD) ). Under supercritical flow, an undulated hydraulic jump was observed on the upstream side of vegetation and energy reduction increases by increasing the values of (Fr (CS-VD) ). The maximum value of the RFI% and RMI% observed was 16.67% in the case of (Fr (CS-VD) ). These results contribute to understanding the complex interactions between vegetation and flow dynamics, with implications for managing and mitigating flood risks in vegetated environments.

Purpose This study aims to provide a review for scour in complex rivers and streams with coarser bed material, steep longitudinal bed slopes and dynamic environments, in the interest of the safety and the economy of hydraulic structures. The knowledge of scour in such geographical complexities is very crucial for a comprehensive understanding of scour failures and for establishing definitive criteria to bridge this major research gap. Design/methodology/approach The existing available literature shows significant work done in case of silt, sand and small sized coarser bed material but any substantial work for bed material of gravel size or above is lacking, resulting in a wide gap. Though some researchers have attempted to explore possibilities of refining the existing models by adding pier size, shape, sediment non-uniformity and armouring effects, which otherwise have been given a miss by the various researchers, including the pioneer in the field Lacey–Inglis (1930). But still, a rational model for scour estimation in such complex conditions for global use is yet to come. This is because all the parameters governing the scour have not been studied properly till date as is evident from the globally available literature and is witnessed in the field too, in recurrent failure of hydraulic structures especially bridges. Findings The researchers presume that the finer materials move only as a result of erosion. However, in actual field conditions, it has been observed that the large-sized stones also roll down and cause huge erosion along the river bed and damage the hydraulic structures, especially in the steep river/stream beds along hilly slopes. This fact has been overlooked in the models available globally and has been highlighted only in the current work in an attempt to recognize this major research gap. A study carried out on a number of streams globally and in Jammu and Kashmir, India also, has shown that in steep river and stream beds with bed material consisting of gravel size or greater than gravel, large scour holes ranging from 1 m to 5 m were created by furious floods, and due to other unknown forces along the channel path and near foundations of hydraulic structures. Originality/value To the best of the authors’ knowledge, this work is purely original.

The quality of groundwater resources in coastal aquifers is affected by saltwater intrusion. Over-abstraction of groundwater and seawater level rise due to climate change accelerate the intrusion process. This paper investigates the effects of aquifer bed slope and seaside slope on saltwater intrusion. The possible impacts of increasing seawater head due to sea level rise and decreasing groundwater level due to over-pumping and reduction in recharge are also investigated. A numerical model (SEAWAT) is applied to well-known Henry problem to assess the movement of the dispersion zone under different settings of bed and seaside slopes. The results showed that increasing seaside slope increased the intrusion of saltwater by 53.2% and 117% for slopes of 1:1 and 2:1, respectively. Increasing the bed slope toward the land decreased the intrusion length by 2% and 4.8%, respectively. On the other hand, increasing the bed slope toward the seaside increased the intrusion length by 3.6% and 6.4% for bed slopes of 20:1 and 10:1, respectively. The impacts of reducing the groundwater level at the land side and increasing the seawater level at the shoreline by 5% and 10% considering different slopes are studied. The intrusion length increased under both conditions. Unlike Henry problem, the current investigation considers inclined beds and sea boundaries and, hence, provides a better representation of the field conditions.

【Background】Most irrigation districts in northern China are flatten and water in their channels is muddy. Existing facilities for measuring water flow in channels could cause backward water flow in their upstream and are prone to sediment deposition. Horizontal plate is a new and simply structured facility to measure water flow and can alleviate sediment deposition. While the impact of the discharge and other factors such as plate deflection angle, water depth in both upstream and downstream, and plate profile on performance of the plate method has been well documented, how bed slope of a channel affects hydraulic characteristics of the plate remains poorly understood. 【Objective】The purpose of this paper is to plug this knowledge gap, systematically investigating the effects of bed slope on reliability and accuracy of the horizontal plate for measuring water flow. 【Method】U-shaped channel commonly used in irrigation areas in northern China was taken to test the method, and the volume of the horizontal plate with optimal contraction ratio of cross-section (0.439) was selected as the test object. With a total of 18 combinations, which included three bed slope ranging from 0.000 2 to 0.001 with each associated with 4 7 flow rates ranging from 10 to 44 L/s, variation of the water-surface line and the plate deflection angles in each combination were measured, from which we analyzed the impact of the bed slope on water-surface line, relative water head loss, energy conversion coefficient, plate deflection angle and comprehensive flow coefficient. Using the formula of sluice flooding discharge, a semi-empirical flow formula with the bed slope as independent variable was used to fit the data. 【Result】Under the same water flow rate, the hydraulic jump length behind the plate, the energy conversion coefficient and the comprehensive flow coefficient all increased as the bed slope became steeper; in contrast, the water-surface line, the relative water head loss and the plate deflection angle all decreased as the bed slope increased. For all tested flow rates, the average relative error of the fitting formula for water flow rate was 2.6%, with a maximum of 6.5%, meeting the requirement for water flow in irrigated areas. 【Conclusion】The bed slope of channel has a significant influence on accuracy of the horizontal plate for measuring water flow in U-shaped channels, and a formula considering the bed slope was proposed to calculate water flow in U-shaped channels.

This study aimed at investigating the effect of grain roughness and bed-load transport on erodible beds friction coefficient (f) in a laboratory flume of 8 m long and 25.5 cm wide. Experiments were carried out at slopes 2, 3 and 5% for an erodible bed consisting of uniform grains with the median diameter of 1.7, 3.3 and 8.2 mm. The maximum dimensionless discharge of the bed-load transport was obtained equal to 0.30. Conducting the experiments in uniform bed material and with the use of empirical relations, friction factor caused by bed roughness (fc) was obtained and the resistance coefficient caused by the bed-load transport (fm) was calculated using the linear theory. By analyzing 130 data from the experimental results of this research and experimental data gathered by Recking et al. (J Hydraul Eng 134(9):1302–1310, 2008) it was realized that at the slopes 5% or more, the frictional resistance caused by the bed-load transport (fm) had more contribution on the total friction resistance f. Also the resistance friction caused by the grains roughness had more contribution at small slope so that in the range of fc/f > 0.6, about 90% of the data was placed at slopes 2–3%, while in the range of fc/f< 0.3, about 90% of the data was placed at slopes of 5–9%. By dimensional analysis, non-dimensional parameters influencing fm were identified and an empirical equation was proposed for fm and validated by experimental results of the previous studies. The accuracy of the relation proposed for prediction of fm was acceptable. The sensitivity analysis of the effective parameters in the proposed equation showed that the Froude number and slope had the greatest effect on the frictional resistance caused by the bed erosion (fm), respectively.

The aim of the study was to assess the possibility of using the empirical formulas to determine the roughness coefficient in gravel-bed streams, the bed slopes of which range from 0.006 to 0.047. Another aim was to determine the impact of taking into account the conditions of non-uniform flow on the application of these formulas and to develop the correlation relationships between the roughness coefficient and water surface slope and also between the roughness coefficient and friction slope in order to estimate the roughness coefficient in gravel-bed streams. The studies were conducted in eight measuring sections of streams located in the Kraków-Częstochowa Upland, southern Poland. The roughness coefficient for these sections was calculated from the transformed Bernoulli equation based on the results of surveys and hydrometric measurements. The values of were compared with the calculation results obtained from fourteen empirical formulas presenting the roughness coefficient as a function of slope. The Lacey, Riggs, Bray and Sauer formulas were found to provide an approximate estimate of the value, while the best roughness coefficient estimation results were obtained using the Riggs formula. It was also found that taking into account the non-uniform flow and using the friction slope in the formulas instead of the bed slope or water surface slope did not improve the estimated values of the roughness coefficient using the tested formulas. It was shown that the lack of differences in the RMSE and MAE error values calculated for the developed correlation equations between the roughness coefficient and the friction slope or with the water surface slope also indicate no influence of the assumed friction slope or water surface slope on the value of the estimated roughness coefficient.

Velocity distribution plays a fundamental role in understanding the hydrodynamics of open-channel flow. Among a multitude of approaches, the entropy-based approach holds great promise in achieving a reasonable characterisation of the velocity distribution. In entropy-based methods, the distribution depends on a key parameter, known as the entropy parameter (a function of the time-averaged mean velocity and maximum velocity), that relates to channel characteristics, such as channel roughness and channel bed slopes. The entropy parameter was regarded as constant for lack of experimental evidence, which would otherwise demonstrate if it had any correlation with channel properties. A series of experiments were conducted to collect velocity data in the laboratory flume for seven different values of the channel bed slope. The experimental data analysis revealed dissimilar fluctuations in entropy parameter values with varying bed slopes, with the lowest coefficient of variation in Renyi's (∼0.5%) and the highest in Shannon's case (∼10%). Performance evaluation of the predicted results substantiated good accuracy for all three entropies with the best results of Renyi entropy and lent strong support for using a constant (overall average) value of the entropy parameter for a specific channel cross-section rather than separate values for each channel bed slope.

Understanding flow dynamics in open-channel node systems is crucial for designing effective hydraulic engineering solutions and minimizing energy losses. This study investigates how junction geometry—specifically the lateral inflow angle (α = 45° and 60°) and the longitudinal bed slope (I = 0.0011 to 0.0051)—influences the water velocity distribution and hydraulic losses in a rigid-bed Y-shaped open-channel junction. Experiments were performed in a 0.3 m wide and 0.5 m deep rectangular flume, with controlled inflow conditions simulating steady-state discharge scenarios. Flow velocity measurements were obtained using a PEMS 30 electromagnetic velocity probe, which is capable of recording three-dimensional velocity components at a high spatial resolution, and electromagnetic flow meters for discharge control. The results show that a lateral inflow angle of 45° induces stronger flow disturbances and higher local loss coefficients, especially under steeper slope conditions. In contrast, an angle of 60° generates more symmetric velocity fields and reduces energy dissipation at the junction. These findings align with the existing literature and highlight the significance of junction design in hydraulic structures, particularly under high-flow conditions. The experimental data may be used for calibrating one-dimensional hydrodynamic models and optimizing the hydraulic performance of engineered channel outlets, such as those found in hydropower discharge systems or irrigation networks.

The operational measurement of discharge in medium and large rivers is mostly based on indirect approaches by converting water stages into discharge on the basis of steady-flow rating curves. Unfortunately, under unsteady flow conditions, this approach does not guarantee accurate estimation of the discharge due, on the one hand, to the underlying steady state assumptions and, on the other hand, to the required extrapolation of the rating curve beyond the range of actual measurements used for its derivation. Historically, several formulae were proposed to correct the steady-state discharge value and to approximate the unsteady-flow stage-discharge relationship. In the majority of these methods, the correction is made on the basis of water level measurements taken at a single cross section where a steady state rating curve is available, while other methods explicitly account for the water surface slope using stage measurements in two reference sections. However, most of the formulae available in literature are either over-simplified or based on approximations that prevent their generalisation. Moreover they have been rarely tested on cases where their use becomes essential, namely under unsteady-flow conditions characterised by wide loop rating curves. In the present work, an original approach, based on simultaneous stage measurements at two adjacent cross sections, is introduced and compared to the approaches described in the literature. The most relevant feature is that the proposed procedure allows for the application of the full dynamic flow equations without restrictive hypotheses. The comparison has been carried out on channels with constant or spatially variable geometry under a wide range of flood wave and river bed slope conditions. The results clearly show the improvement in the discharge estimation and the reduction of estimation errors obtainable using the proposed approach.