Water Depth Ratio Research Articles

Exploring coupling effects of rainfall and surface roughness on the sheet flow velocity

Accurately describing the path of sheet flow (SF) is crucial in soil erosion. Raindrop impact and underlying surface conditions can affect the SF velocity by changing the velocity profile. However, since this information is rarely known, the estimation of SF velocity is inaccurate. A series of upstream inflow and rainfall experiments were carried out on an impermeable flume to determine the coupling effects of rainfall and rough bed surfaces on the SF velocity and correction factor (α). The results showed that the roughness of the bed surface had a more pronounced effect on reducing the mean velocity compared to the surface velocity in both cases with and without raindrop impact. The raindrop impact notably reduced the flow velocity near the water surface, while the mean velocity slightly decreased or remained almost constant with increasing rainfall intensity. The reduction in SF velocity can be explained by the combined effects of the roughness reducing the mean velocity (up to 33.52%) and the raindrop impact reducing the surface velocity (up to 25.43%). In addition, α was not a constant when the SF was subjected to raindrop impact. The rainfall was found to increase α, while the roughness of the bed surface reduced α for all cases. Finally, a model was created to forecast α based on the ratio of water depth to roughness height, hydraulic slope, and rain Reynolds number. The results are valuable in soil erosion by providing accurate α for estimating the surface and mean velocities of SF.

Experimental study on the auto-parametric internal resonance of a frame structure excited by water vortex-induced vibration in the flume

A small external excitation can trigger a strong auto-parametric internal resonance response in underwater structure. Currently, research on auto-parametric internal resonance primarily relies on theoretical methods and experimental approaches involving the simulation of water flow forces using vibrators. To more realistically reflect the auto-parametric internal resonance of structures in water, this study investigates the phenomenon of auto-parametric internal resonance of a Γ-shaped frame structure induced by vortex-induced vibration in a laboratory flume. The results indicate that the auto-parametric internal resonance can be excited by water flow in the flume and the Γ-shaped frame structure is more prone to experience normal resonance than auto-parametric internal resonance. However, the vibration intensity caused by auto-parametric internal resonance is significantly greater than that of normal resonance. The range of h/L (the ratio of water depth to the length of the vertical beam) for auto-parametric internal resonance in both the clamped-pined joint system (CPJS) and the pined-pined joint system (PPJS) is 0.307–0.364, but the flow velocity range for auto-parametric internal resonance in CPJS is broader than that in PPJS. When h/L is 0.307, the reduced velocity Ur ranges for the auto-parametric internal resonance of CPJS and PPJS are 4.839–5.375 and 4.904–5.256, respectively. When h/L is 0.364, the Ur ranges for the auto-parametric internal resonance of CPJS and PPJS are 4.587–4.742 and 4.507–4.660, respectively.

Unsteady flow in a compound channel during flooding: Insights from a combined two-dimensional and three-dimensional numerical simulation

Natural channels often take the form of compound channels during flooding events. The unsteadiness of floods is crucial for flood management and river-floodplain ecosystems. However, the impact of unsteady flow on three-dimensional hydrodynamic processes within compound channels remains poorly understood. This study employed a validated two-dimensional/three-dimensional numerical model to examine how unsteady features influence key hydrodynamic indicators of compound channels, such as velocity distribution, turbulence characteristics, and discharge partitioning between the main channel and floodplain. A definitive positive correlation was found between water level fluctuation amplitudes and integrated discharge during unsteady events, as well as between mean water levels and mean discharges. The proportion of discharge conveyed by the main channel relative to the total was directly linked to the water depth ratio. The exchange at the main channel–floodplain interface exhibits a dual-layer flow pattern: surface waters spill into the floodplain, while deeper waters are siphoned into the main channel. Unsteady conditions principally modulate the intensity of these exchanges, altering hydraulic interactions and water transfer between areas. Pronounced wall shear stresses were detected at the main channel–floodplain interface due to swift channel flows and momentum exchange at the floodplain margin, with maxima adjacent to the floodplain edge correlating with peak flow velocities. Under deep conditions, cross-sectional flow across the compound channel's mixing layer was essentially two-dimensional. These findings elucidate the complex hydrodynamics inherent to unsteady overbank flows while holding implications for enhancing floodplain management and advancing the understanding of unsteady fluvial hydraulics.

Experimental study on the influence of water depth and bed slope variations on dam-break flood wave propagation

Damage to dam structures frequently results in catastrophic consequences. Consequently, understanding of the characteristics of the movement of dam-break flow along the sloping wet bed can assist in the issuance of timely flood warnings and risk mitigation. In this study, a series of large-scale flume experiments was conducted with the objective of investigating the effects of upstream and downstream water depth and bed slope on the propagation of dam-break waves. The water level is measured and processed to calculate the wavefront velocity. Results show that the wave propagation behavior can be classified as bore and undular waves through the global Froude numbers (Frx) and local Froude numbers (Frl). When Frx < 1.225 or Frl < 1.475, the dam-break wave propagates as the undular wave. In the undular wave state, the wavefront velocity (U) decreases with increasing water depth ratio α. Additionally, the U with Frx shows a similar trend, where the experimental value surpasses the analytical solution. The dimensionless maximum wave height (ΔHmax) increases with Frx and then decreases. The deviation from the analytical solution ranges between 67.22% and 127.38%. When Frx > 1.225 or Frl > 1.475, the dam-break wave propagates as the bore wave. In the bore wave state, the U increases slightly with the water depth ratio α, while the change rule of U with Frx is similar to it. The dimensionless maximum wave height (ΔHmax) remains relatively constant as Frx increases, showing a high degree of consistency with the analytical solution. The presence of bed slope results in increased wavefront velocity and wave heights, while an increase in α results in the emergence of more pronounced undular wave phenomena. Furthermore, the experimental results are compared with existing analytical solutions, and the validity of the analytical solutions and their limitations are discussed.

Enhanced Removal of River‐Borne Nitrate in Bioturbated Hyporheic Zone

AbstractThe influence of bioturbation induced by bottom‐dwelling macrozoobenthos on nitrogen dynamics in lotic stream sediments remains unclear. In this work, we advance the understanding of faunal bioturbation in lotic environments by developing a fully‐coupled flow and multicomponent reactive transport model and investigate the influence of sediment reworking and burrow ventilation processes on nitrogenous transformations. The model results indicate that sediment reworking and burrow ventilation significantly increase nitrate (NO3−) influx, penetration depth, and reaction rates in the streambed. Denitrification rates were observed up to three times higher in beds with U‐shaped burrows compared to flatbeds. The ratio of mound height to stream water depth ratio (h/H0) is a dominant control on determining the relative importance of the sediment reworking and burrow ventilation processes in modulating nitrogenous reactions. A power‐law scaling framework is ultimately proposed to predict NO3− removal efficiency based on the Damköhler number in bioturbated lotic streambeds.

A Study on the Scour Surrounding the Fixed Foundation of an Offshore Wind Turbine under Complex Waves, Tidal Currents, and Pile Vibration Conditions

Scouring around the fixed foundations of offshore wind turbines (OWTs) remains a pressing concern within the offshore wind industry, significantly jeopardizing OWT safety. Despite previous efforts, the current understanding of this phenomenon remains incomplete, as various factors related to offshore wind farms and OWT operations can exert intricate influences. To further explore this matter, this paper undertakes a new study to further understand the interplay between monopile vibrations, tidal currents, and sea waves, elucidating their combined impact on scour surrounding an OWT’s foundation. It was found that, besides pile vibration amplitude and frequency, the pile vibration direction can also notably influence the scour around the monopile. Specifically, the most pronounced scour mostly transpires when the monopile undergoes vibrations along the 135° direction relative to the inflow direction. The mildest scour mostly occurs when the pile vibrates along the 90° direction. Additionally, this study reveals that different types of waves, indicated by the ratio of water depth, H, to wavelength, L, also engender varying scour around the monopile. The influence of waves on scour increases with the decrease in the H/L ratio, implying that OWT foundations are more threatened by shallow water waves than by deep water waves.

Predicting discharge coefficient of weir–orifice in closed conduit using a neuro-fuzzy model improved by multi-phase PSOGSA

This study investigates the viability of a strong algorithm (PSOGSA) merging particle swarm optimization (PSO) and gravity search algorithm (GSA) in tuning adaptive neuro-fuzzy system (ANFIS) parameters for modeling dimensionless experimental discharge of combined weir–orifices. The results are compared with the standard ANFIS and two hybrid models ANFIS tuned with PSO and GSA. The models are assessed by applying several dimensionless input parameters, consisting h/D (the ratio of upstream water depth to channel diameter), W/D (the ratio of orifice opening height to channel diameter), H/D (the ratio of plate height to channel diameter) and using comparison indices such as root-mean-square error and mean absolute error. The outcomes reveal that the new ANFIS-PSOGSA method provides superior accuracy in modeling dimensionless experimental discharge over the ANFIS-PSO, ANFIS-GSA and standard ANFIS method. Among the input parameters, the h/D was found to be the most effective input on modeling dimensionless experimental discharge while involving the H/D parameter deteriorated the models’ performances. The relative root-mean-square error differences between ANFIS-PSOGSA and ANFIS are found as 50% and 68.29% for pipe A and B, respectively. By implementing the ANFIS-PSOGSA, the accuracy of ANFIS-PSO and ANFIS-GSA is also improved in modeling dimensionless experimental discharge by 45.71% and 29.63% in pipe A and by 63.89% and 45.83% in pipe B with respect to root-mean-square error.

Influence of hydrological features on CO2 and CH4 concentrations in the surface water of lakes, Southwest China: A seasonal and mixing regime analysis

Due to the large spatiotemporal variability in the processes controlling carbon emissions from lakes, estimates of global lake carbon emission remain uncertain. Identifying the most reliable predictors of CO2 and CH4 concentrations across different hydrological features can enhance the accuracy of carbon emission estimates locally and globally. Here, we used data from 71 lakes in Southwest China varying in surface area (0.01‒702.4 km2), mean depth (< 1‒89.6 m), and climate to analyze differences in CO2 and CH4 concentrations and their driving mechanisms between the dry and rainy seasons and between different mixing regimes. The results showed that the average concentrations of CO2 and CH4 in the rainy season were 23.9 ± 18.8 μmol L−1 and 2.5 ± 4.9 μmol L−1, respectively, which were significantly higher than in the dry season (10.5 ± 10.3 μmol L−1 and 1.8 ± 4.2 μmol L−1, respectively). The average concentrations of CO2 and CH4 at the vertically mixed sites were 24.1 ± 21.8 μmol L−1 and 2.6 ± 5.4 μmol L−1, being higher than those at the stratified sites (14.8 ± 13.4 μmol L−1 and 1.7 ± 3.5 μmol L−1, respectively). Moreover, the environmental factors were divided into four categories, i.e., system productivity (represented by the contents of total nitrogen, total phosphorus, chlorophyll a and dissolved organic matter), physicochemical factors (water temperature, Secchi disk depth, dissolved oxygen and pH value), lake morphology (lake area, water depth and drainage ratio), and geoclimatic factors (altitude, wind speed, precipitation and land-use intensity). In addition to the regression and variance partitioning analyses between the concentrations of CO2 and CH4 and environmental factors, the cascading effects of environmental factors on CO2 and CH4 concentrations were further elucidated under four distinct hydrological scenarios, indicating the different driving mechanisms between the scenarios. Lake morphology and geoclimatic factors were the main direct drivers of the carbon concentrations during the rainy season, while they indirectly affected the carbon concentrations via influencing physicochemical factors and further system productivity during the dry season; although lake morphology and geoclimatic factors directly contributed to the carbon concentrations at the vertically mixed and stratified sites, the direct effect of system productivity was only observed at the stratified sites. Our results emphasize that, when estimating carbon emissions from lakes at broad spatial scales, it is essential to consider the influence of precipitation-related seasons and lake mixing regimes.

Performance Characteristics of a Submerged Semicircular Breakwater Exposed to Regular Waves: An Experimental Study

Many mangrove replanting programs fail due to the drifting of the mangrove sapling by waves and coastal currents soon after the replanting. Hence, adequate wave protection for the mangrove planting site is required to enhance the survivability rates of the newly planted saplings. A small scaled modular submerged semicircular breakwater (SBW) is perceived to be a viable option to provide the required level of wave protection to mangroves. The study is set to investigate wave transmission, reflection, and energy loss by a SBW subjected to different immersion depths under a regular wave environment via physical modelling. The SBW model was tested in a wave flume and was subjected to relative immersion depth, i.e., a ratio of water depth to the height of the SBW, of 1.00 and 1.33, and wave steepness ranging from 0.02 to 0.06. The alternatively submerged SBW was found to be an effective breakwater design to provide the required level of wave tranquility to various coastal applications.

Analysis of discharge characteristics of a symmetrical stepped labyrinth side weir based on global sensitivity

Abstract In this paper, the discharge coefficient prediction model for this structure in a subcritical flow regime is first established by extreme learning machine (ELM) and Bayesian network, and the model's performance is analyzed and verified in detail. In addition, the global sensitivity analysis method is introduced to the optimal prediction model to analyze the sensitivity for the dimensionless parameters affecting the discharge coefficient. The results show that the Bayesian extreme learning machine (BELM) can effectively predict the discharge coefficients of the symmetric stepped labyrinth side weir. The range of 95% confidence interval [−0.055,0.040] is also significantly smaller than that of the ELM ([−0.089,0.076]) and the Kernel extreme learning machine (KELM) ([−0.091,0.081]) at the testing stage. The dimensionless parameter ratio of upstream water depth of stepped labyrinth side weir p/y1 has the greatest effect on the discharge coefficient Cd, accounting for 55.57 and 54.17% under single action and other parameter interactions, respectively. Dimensionless step number bs/L has little effect on Cd, which can be ignored. Meanwhile, when the number of steps is less (N = 4) and the internal head angle is smaller (θ = 45°), a larger discharge coefficient value can be obtained.

A Simplified Approach for Predicting Bend Radius in HDPE Pipelines during Offshore Installation

Traditionally, subsea pipelines designed for the transportation of oil, gas, and water are constructed using carbon steel due to its strength, toughness, and ability to operate at temperatures up to 427 °C. However, polyethylene (PE), especially its high-density variant (HDPE), presents advantages such as reduced installation costs, diminished water leakage, and superior corrosion resistance. As research endeavours to enhance PE properties, its adoption for subsea applications is anticipated to rise. This study first delineates the mechanical behaviour of HDPE pipelines for offshore installation, identifying pulling tension, dimension ratio, water depth, and air fill ratio as the paramount lay parameters. Subsequently, a theoretical bend radius equation was derived from pipelaying mechanics using a purely geometric approach. Within this equation, two determinants, parameter X and parameter Y, dictate the sagbend bend radius. Regression analysis elucidated the relationships of lay parameters with both X and Y, yielding a general equation for X in terms of pull tension, water depth, and air fill ratio and another for Y as a function of water depth. Together, these geometric determinants underpin the sagbend bend radius estimation model. For overbend bend radius prediction, a lay index (IL) was fashioned from the aforementioned three parameters. Correlation assessments between the lay index and overbend bend radius revealed R2 values of 0.940, 0.836, and 0.712 for pipes with diameters of 2.0, 2.5, and 3.0 metres, respectively. This underscores the model’s proficiency in predicting the bend radius, albeit with decreasing precision for larger-diameter pipelines.

The dependence of wave height probability distributions on physical parameters from measurements near Sakhalin Island

The data of long-term surface waves measurements with bottom sensors near Sakhalin Island were used to build instrumental probability distributions for exceedance of wave heights. Waves with heights exceeding the significant wave height by more than three times were recorded. Specific features of the observations conducted during the periods of open and ice-covered sea surfaces are discussed. The subsets of statistically homogeneous data are arranged through selection considering the natural physical dimensionless parameters of the task, that control the effects of finite depth and nonlinearity (namely, the wave steepness, the wave amplitude to water depth ratio, the Ursell parameter). The manifestation of these and composite parameters in theoretical probability distributions of wave heights is discussed. The effects of nonlinearity and the measurement point depth on probability distributions are estimated with a focus on abnormally high waves. In particular, it is shown that for the place of registration an increase in the wave amplitude to water depth ratio parameter leads to a decrease in the probability of abnormally high waves. This behavior is consistent with the Glukhovsky theoretical distribution. The waves characterized by relatively large dimensionless depth parameter exhibit a higher probability of substantial exceedance of the significant height and are better described by the Rayleigh distribution.

The Secchi disk depth to water depth ratio affects morphological traits of submerged macrophytes: Development patterns and ecological implications

Water clarity, represented by Secchi disk depth (SD), and water depth (WD) alter bottom light availability, and SD/WD is critical for morphological trait development of submerged macrophytes in freshwater ecosystems. However, the underlying mechanism and trait development patterns of submerged macrophytes to a decreasing SD/WD gradient remains largely unknown. Here, we performed a 42-day mesocosm experiment with the erect type submerged macrophyte, Hydrilla verticillata, along a decreasing SD/WD gradient to study the relationship of morphological trait development with light availability, to determine the critical SD/WD at which changes in the development of morphological traits occur, and to gain insights into the potential mechanism involved. The results indicate that most of the morphological traits, including biomass, relative growth rate, number of clonal propagules, and the root/shoot ratio decreased with a decrease in the SD/WD ratio. Conversely, plant height and shoot increment rate increased with a decrease in the SD/WD ratio. Principal component analysis indicated that the SD/WD ratio is critical in determining the growth, stability, and reproduction of H. verticillata, and that only SD/WD ratios ≥ 0.45 and ≥0.55 ensured growth ability and stability, respectively. Possible development patterns of functional traits in relation to SD/WD reduction were investigated, and patterns of key traits of H. verticillata were distinct from those of Vallisneria natans, indicating different strategies for the adaptation to conditions of decreasing light availability. These results highlight the role of adaptive changes in morphology, resource allocation and life strategies for the maintenance of growth, stability and resilience of submerged macrophytes in low light conditions. Our present study provides a basis from which we could enhance our understanding of the critical transition mechanisms involved in morphological trait development in response to bottom light availability.

Dominant factors responsible for wave modulation in the macro-tidal Gyeonggi Bay of the Yellow Sea

Surface gravity waves, crucial for sediment transport in coastal regions, undergo wave modulation owing to local hydrodynamic conditions. However, the cause of the spatial and temporal distribution of the dominant factors in wave modulation remains vague. This study was aimed at identifying the causes of tidal modulation of waves in Gyeonggi Bay, which exhibits shallow water and macro-tidal environment, and estimating site-specific dominant factors using numerical modeling. The results indicated that tides significantly impact wave dynamics at semidiurnal tidal frequencies, with spatiotemporal variability. The most dominant factor in wave modulation in the nearshore region is the depth change caused by tides, and the most notable impact was found in tidal flats. Depth dependence is mainly evident in surf zones, with a clear distinction at locations where the wave height to water depth ratio reaches 0.2. While idealized studies highlight the significant role of wind in governing incoming waves, it is not the primary cause of modulation. Nevertheless, stronger tidal strength can lead to more pronounced modulation, which is further amplified when accompanied by strong wind conditions. This finding indicates that the spatiotemporal distribution of wave modulation in macro-tidal regions may have a significant impact on various estuarine dynamics including sediment transport.

Assessing ecosystem health of floodplain lakes using an Integrated Bioassessment Index

Lakes within river-floodplain ecosystems are key biodiversity refuges majorly threatened by eutrophication and hydrologic river-lake fragmentation. However, an integrative index, specifically designed to comprehensively assess the health of floodplain lakes, considering multiple biological taxa and major stressors, remains unavailable. Based on biological data collected from 68 isolated lakes in the eastern plain lake region of China, we constructed a reliable index for assessing floodplain lake ecosystem health: Integrated Bioassessment Index (L-IBAI). The L-IBAI consists of components of overall health and species diversity, eutrophication, and hydrological connectivity and water level regimes. To construct the L-IBAI, we firstly used the observed species (SO)-area (A) model to predict the expected species richness (SE), and then developed observed to expected indices by calculating the SO/SE ratio for fish (F-O/E-SA) and benthos (B-O/E-SA). The health level thresholds for the other four indices, namely the ratio of Secchi depth and water depth (ZSD/ZM), chlorophyll a in phytoplankton (Chl a), the percent of rheophile fish species, and emergent macrophytes coverage, were determined using cumulative frequency curves. The final L-IBAI score was obtained by summing the weighted values of the three components mentioned earlier. The L-IBAI can significantly discriminate rural from urban lakes, and is a reliable index for assessing lake ecosystem health. Moreover, we developed three simplified three-index integrated bioassessment indices, which consists of three indices belonging to the three elements are also effective. The developed L-IBAI is flexible to be extended and applied to other floodplain lakes, and outcomes of health assessments for the eastern plain lakes in China helped to identify conservation and restoration priorities.

Scour hole reduction at a diversion channel junction using different entrance edge shapes

In the current study, the effect of the entrance edge shape on the scour hole in the diversion junction region was experimentally investigated. The investigation has considered three entrance models-rounded edge shapes on one or both sides of the diversion channel entrance-with five different inlet edge radius ratios (rr) of 25%, 37.5%, 50%, 62.5%, and 75% and five different diversion discharge ratios (Qr) of 7.5%, 12.5%, 17.5%, 22.5%, and 30%. The results have found the direct relation between Qr and the scour depth to the diversion channel water depth ratio (ds/yb). Moreover, the use of a rounded edge shape on one or both sides of the diversion channel entrance instead of a sharp shape results in a reduction in scour depth to diversion channel water depth ratio (ds/yb) when the Qr is greater than 20%. The results also indicated that the largest decrease in the scour coefficient (Kds) for the model with a rounded downstream edge compared with the sharp edge diversion channel entrance shape was 22% at a discharge ratio of 22.5% and an edge radius ratio of 37.5%. In addition, the entrance shape model with a rounded edge at the upstream outperformed other models in scour reduction with an average of all experiments of 5.77%. Finally, empirical relations for estimating scour depth for different rounded edge models in terms of the effective dimensionless parameters were established with coefficients of determination (R2) of not less than 0.853.

Breaking Undular and Breaking Surges Advancing in Still Water

The propagation of secondary surges can lead to unexpected interaction events with navigation ships and downstream hydraulic structures; hence, they may cause navigation accidents and structural damage. In the present study, physical experiments were performed in a long water wave tank to study the evolution of breaking undular and breaking surges advancing in still water. Both free-surface and velocity measurements were conducted. It was observed that the transition from a breaking undular surge to a breaking surge occurred as the ratio of the mean water depth behind the surge to the still water depth equal to 1.68–1.71. Empirical expressions based on the experimental data were proposed to predict the wave amplitude and wave steepness of breaking undular surges. The unsteady flow results demonstrated that the normalized longitudinal velocity component beneath the surge front was governed mainly by the normalized free-surface elevation, independently of the surge type. Moreover, the maximum vertical velocity component during the surge front passage had a linear dependence on the vertical location. The present result provided new quantitative information on breaking undular and breaking surges advancing in still water.

Wave interaction with a rigid porous structure under the combined effect of refraction–diffraction

Water wave scattering, trapping, and generation by a thin porous structure placed on an uneven bottom are studied approximately. The classical eigenfunction expansion method is employed for the uniform bottom, whereas the Galerkin-Eigenfunction expansion method is employed for the uneven bottom. The solution is derived in the form of a system of algebraic equations through matching procedure. Wave reflection, transmission, and wave-induced forces on the porous structure and backwall are investigated under the combined refraction–diffraction effect. In the scattering problem with periodic bottom, Bragg resonance is minimized at the Bragg frequency, whereas the porous structure at other frequencies maximizes wave reflection. Consequently, wave transmission is very low for all wave frequencies in this situation. In the wave trapping problem, forces on the porous structure and the backwall are reduced substantially when the water depth ratio decreases. Feasible locations of the porous structure are shown at which wave reflection and forces on it and backwall are optimized. In the wave generation problem, the comparison of results for flat and uneven bottoms reveals that waves have a smaller amplitude at infinity as uniform bottom levels become farther for relatively small values of the reciprocal of the wave-effect parameter (C).

Prediction of Reservoir Bank Collapse Based on the Limit Equilibrium Theory

The prediction of reservoir bank collapse width is a unique problem encountered in the construction of hydropower projects. Existing empirical graphic methods are based on the final state of bank collapse and can be used to predict only bank collapse width, and they thus do not adequately reflect the characteristics of the bank collapse process. To solve this problem, a prediction model for bank collapse width based on the limit equilibrium theory was established, and the key parameters and bank collapse process of the model were analyzed. The results reveal the necessity of selecting a reasonable underwater accumulation rate when predicting the bank collapse width using the limit equilibrium theory. At a constant ratio of water depth to bank slope height, the underwater accumulation rate increases with increasing bank slope height, with a linear relationship between them. In contrast, the bank slope angle has little impact on bank collapse width. Specifically, it mainly affects the width of the first bank collapse but has little effect on the width of subsequent bank collapses. With an increase in the bank slope angle, the bank collapse width fluctuates and rises. The prediction model of bank collapse width based on the limit equilibrium theory can better explain the time-dependent behavior of bank collapse. The research results are of high significance for the prediction of loess bank collapse.

Attenuation in hydroelastic response of floating-elastic-plate by porous membrane in two-layer fluid with bottom undulation

The prime intention of this article is to study the effects of bottom undulation and a porous membrane barrier on the hydroelastic response of an elastic plate floating in a two-layer fluid with changing bottom topography assuming the small amplitude waves and potential flow theory. Finite and semi-infinite plates coupled with porous membrane barriers are considered in this study. As a mathematical technique, the eigenfunction expansion method along with an approximation method mild-slope are adopted for the uniform bottom and variable bottom topographies, respectively. In the variable bottom topography, a system of differential equations is solved. By using matching and jump conditions, the solution is expressed as a linear algebraic system, from which the unknown constants of interest are computed. The effects of fluid density ratio, water depth ratio, bottom topography, and porous membrane on the bending moment, shear force, and deflection of the elastic plate are studied. It is found that when the density ratio becomes closer to one, the bending moments and shear forces acting on the elastic plates tend to diminish. The variations in the bending moments, shear forces, and plate deflection with respect to changing density ratios are found to be in opposite trends caused by surface and interfacial waves, respectively. With higher tension and a less porous membrane, the bending moment, shear forces, and pate deflection are reduced. Concave-up bottoms reflect more surface wave energy, whereas concave-down bottoms reflect more interfacial wave energy. The observations made in this article may help in analyzing the response of very-large floating structures in the presence of an undulating seabed.