The backwater effect caused by tributary inflow can significantly elevate the water level profile upstream of a confluence point.However,the influence of mainstream and confluence discharges on the backwater effect in...The backwater effect caused by tributary inflow can significantly elevate the water level profile upstream of a confluence point.However,the influence of mainstream and confluence discharges on the backwater effect in a river reach remains unclear.In this study,various hydrological data collected from the Jingjiang Reach of the Yangtze River in China were statistically analyzed to determine the backwater degree and range with three representative mainstream discharges.The results indicated that the backwater degree increased with mainstream discharge,and a positive relationship was observed between the runoff ratio and backwater degree at specific representative mainstream discharges.Following the operation of the Three Gorges Project,the backwater effect in the Jingjiang Reach diminished.For instance,mean backwater degrees for low,moderate,and high mainstream discharges were recorded as 0.83 m,1.61 m,and 2.41 m during the period from 1990 to 2002,whereas these values decreased to 0.30 m,0.95 m,and 2.08 m from 2009 to 2020.The backwater range extended upstream as mainstream discharge increased from 7000 m3/s to 30000 m3/s.Moreover,a random forest-based machine learning model was used to quantify the backwater effect with varying mainstream and confluence discharges,accounting for the impacts of mainstream discharge,confluence discharge,and channel degradation in the Jingjiang Reach.At the Jianli Hydrological Station,a decrease in mainstream discharge during flood seasons resulted in a 7%–15%increase in monthly mean backwater degree,while an increase in mainstream discharge during dry seasons led to a 1%–15%decrease in monthly mean backwater degree.Furthermore,increasing confluence discharge from Dongting Lake during June to July and September to November resulted in an 11%–42%increase in monthly mean backwater degree.Continuous channel degradation in the Jingjiang Reach contributed to a 6%–19%decrease in monthly mean backwater degree.Under the influence of these factors,the monthly mean backwater degree in 2017 varied from a decrease of 53%to an increase of 37%compared to corresponding values in 1991.展开更多
Flotation indexes gradually decrease with the increase of cycle time of the backwater in bauxite floatation,and discharge of backwater brings environmental risk.In this study,methods such as Fenton-oxidation,adsorptio...Flotation indexes gradually decrease with the increase of cycle time of the backwater in bauxite floatation,and discharge of backwater brings environmental risk.In this study,methods such as Fenton-oxidation,adsorption and coagulation were used in the treatment of backwater,the flotation indexes were checked after backwater treatments,and Box-Behnken design(BBD)was used in the optimization of the main operating parameters.The results reveal that flotation indexes are effectively improved after coagulation treatment by polyaluminum ferric chloride(PAFC).The optimum parameters predicted by BBD are pH 7.55,1.09 g/L PAFC dosage and temperature of 25℃.Under these optimum conditions,a maximum recovery of Al2O3 of 82.83%and a minimum A/S of 1.30 of tailings are gained,while the deviations are less than 3%from the predicted values.These findings encourage the application of BBD for the optimization of critical parameters in backwater treatment.展开更多
Owing to extensive construction of dams, the impact of backwater on flow may lead to navigation or flood control issues in curved channels. To date, the impact of backwater on the water surface profile in curved chann...Owing to extensive construction of dams, the impact of backwater on flow may lead to navigation or flood control issues in curved channels. To date, the impact of backwater on the water surface profile in curved channels remains unknown and requires investigation. In this study, experiments were conducted in a glass-walled recirculating flume with a length of 19.4 m, a width of 0.6 m, and a depth of 0.8 m, and the impact of backwater on the water surface profile in a 90° channel bend was investigated. The experimental results showed that the backwater degree had a significant impact on the transverse and longitudinal flow depth distributions in the bend. The transverse slope of the flow (Jr) increased linearly with an increase in the Froude number of the approach flow upstream of the bend. Jr increased with the longitudinal location parameter ξ when −0.2 < ξ < 0.5, and decreased with ξ when 0.5 < ξ < 1.2. Furthermore, the results showed that Jr asymptotically decreased to zero with an increase in the degree of backwater. An equation was formulated to estimate the transverse slope of the flow in a 90° bend in backwater zones.展开更多
Based on the characteristics of backflow, a two-dimensional mathematical model of sediment movement was established. The complexity of the watercourse boundary at the confluence of the main stream and the tributary wa...Based on the characteristics of backflow, a two-dimensional mathematical model of sediment movement was established. The complexity of the watercourse boundary at the confluence of the main stream and the tributary was dealt with using a boundary-fitting orthogonal coordinate system. The basic equation of the two-dimensional total sediment load model, the numerical calculation format, and key problems associated with using the orthogonal curvilinear coordinate system were discussed. Water and sediment flow in the Chongqing reach of the Yangtze River were simulated. The calculated water level, flow velocity distribution, amount of silting and scouring, and alluvial distribution are found to be in agreement with the measured data, which indicates that the numerical model and calculation method are reasonable. The model can be used for calculation of flow in a relatively complicated river network.展开更多
This paper studies the flow structure and the bedload transport regime in backwater flows, to provide a theoretical support for solving the sediment transport and bed scour problems in rivers or reservoirs with backwa...This paper studies the flow structure and the bedload transport regime in backwater flows, to provide a theoretical support for solving the sediment transport and bed scour problems in rivers or reservoirs with backwater. The bedload transport rates under different conditions are analyzed first on the basis of theoretical analysis, measurement comparison and flume experiment, and it is pointed out that the existing formulas for the bedload transport rate are not applicable for the bedload transport rate in backwater flows. Next, the flow structure in a non-uniform flow is observed by flume experiments, and by introducing the backwater degree index, the quantitative relation between the relative bed shear stress and the backwater degree is obtained. Finally, the formula for the bedload transport rate applicable for the reservoir channel segment with backwater flows is obtained through measurements and flume experiments.展开更多
Floodplain lakes are important water storage areas in lowland regions that often undergo geomorphologic evolution,and timely topographic data are generally unavailable.In this study,to assess the impacts of lakebed de...Floodplain lakes are important water storage areas in lowland regions that often undergo geomorphologic evolution,and timely topographic data are generally unavailable.In this study,to assess the impacts of lakebed deformation on hydraulic performance in Dongting Lake,a set of semi-empirical methods was proposed to establish performance graphs(PGs)using only hydrological data.These methods were used to evaluate the changes in water level,storage capacity,and flood detention ability in Dongting Lake caused by topographic adjustment after the Three Gorges Reservoir impoundment.These methods showed that PGs can effectively simulate the water level and outflow processes of Dongting Lake with Nash-Sutcliffe efficiency coefficients(NSEs)above 0.9.A comparison of the estimated water level and discharge using PGs from different periods suggested that bed erosion in Dongting Lake caused water level decreases of 0.18 m and 0.32 m during the flood and dry seasons,respectively.Because the magnitude of erosion at high elevations in the lake is small,the impacts of bed adjustment on the storage capacity and flood detention ability are not currently significant.This study showed that the hydraulic performance of a floodplain lake can be evaluated independently of topographic data under the condition of no reverse flows or negative watersurface slopes.展开更多
The Sulige gas field is a typical low-pressure low-permeability tight sandstone gas reservoir. The reservoir has poor seepage capacity, strong heterogeneity, high mineralization of formation water and extremely scarce...The Sulige gas field is a typical low-pressure low-permeability tight sandstone gas reservoir. The reservoir has poor seepage capacity, strong heterogeneity, high mineralization of formation water and extremely scarce water resources on the site. These unfavorable factors have brought great difficulties to the on-site mining process. Now, a nano-composite green environmental protection slick water fracturing fluid system CQFR can be quickly dissolved because of the larger specific surface area, and the small molecular size makes the damage to the reservoir less than 5%, and the average drag reduction effect can reach more than 73%. It can quickly and well dissolve and maintain performance under high salinity conditions and fracturing flowback fluids. It responds well to the complex reservoir conditions on the construction site and makes the flowback fluid recyable, which greatly reduces the consumption of water resources on the construction site and effectively improves the construction efficiency and economic benefits.展开更多
By introducing a water depth connecting formula, the hydraulic equations in the dividing channel system were coupled and the relation of discharge distribution between the branches of the dividing channels can be yiel...By introducing a water depth connecting formula, the hydraulic equations in the dividing channel system were coupled and the relation of discharge distribution between the branches of the dividing channels can be yielded. In this manner, a numerical model for the confluent channels was established to study the variation of backwater effects with the parameters in the channel junction. The meeting of flood peaks in the mainstream and tributary can be analyzed with this model.The flood peak meeting is found to be a major factor for the extremely high water level in the mainstream during the 1998 Yangtze River flood. Subsequently the variations of discharge distribution and water level with channel parameters between each branch in this system were studied as well. As a result, flood evolution caused by Jingjiang River shortcut and sediment deposition in the entrance of dividing channels of the Yangtze River may be qualitatively elucidated.It is suggested to be an effective measure for flood mitigation to enhance regulation capability of reservoirs available upstream of the tributaries and harness branch entrance channels.展开更多
The accumulation of aquatic vegetation in open channels,such as leaves,weeds,and large wood,poses a threat to the safety of hydraulic structures and disrupts the normal operation of hydropower stations,resulting in su...The accumulation of aquatic vegetation in open channels,such as leaves,weeds,and large wood,poses a threat to the safety of hydraulic structures and disrupts the normal operation of hydropower stations,resulting in substantial economic losses.Studying the hydraulic characteristics with vegetation accumulation is a prerequisite for solving this engineering challenge.The effects of vegetation accumulation on the hydraulic characteristics with three types of vegetation were investigated using experimental and numerical simulation methods.The results indicate both backwater rise and head loss increase exponentially with blockage ratio.Furthermore,vegetation accumulation results in an uneven vertical distribution of streamwise velocity,leading to the formation of low-velocity regions and backflow vortexes in the upper water layer.For all cases,the bottom gap velocity increases markedly,forming a high-velocity jet region.The maximum jet velocity remains constant in the near wake region and the decay rate in the far wake region is positively correlated with the blockage ratio.Bed shear stresses in the corresponding region are 1-6 times higher than before vegetation accumulation,increasing the potential for riverbed erosion.This study extends the existing knowledge of vegetation accumulation hydrodynamics to provide a basis for the safe operation of hydraulic structures and river management.展开更多
River-dominated lacustrine deltas typically consist of multiple lobes due to autogenic lobe switching that occurs over short time scales.However,the switching patterns of multiple lobes in these deltas remain poorly u...River-dominated lacustrine deltas typically consist of multiple lobes due to autogenic lobe switching that occurs over short time scales.However,the switching patterns of multiple lobes in these deltas remain poorly understood,and the architectural features attributed to lobe switching are also lacking.By integrating Delft3D simulations,flume experiments,and modern deposit analysis,we proposed that autogenic lobe switching follows a cyclic pattern.Autocyclicity begins with the formation of an offshore lobe and concludes after a series of longshore lobe growth events,marked by longshore avulsions occurring along the sides of offshore distributary channels.Longshore avulsions follow a sequence that usually occurs earlier distally than proximally and subsequently occurs on one longshore side and then on the other side.Each lobe begins with rapid growth,which gradually slows and then stops once a channel avulsion is influenced by the backwater effect that triggers lobe switching.Three signals indicate lobe switching:a decrease in progradation rate,foreset slope steepening coupled with topset slope gentling,and the deposition of mud-dominated sediments.The number of autocyclic events never exceeds seven.The first two autocyclicities contribute to more than 55%of delta length and 70%of delta area.The lobes are separated by 1-6 stages of mud-dominated accretion beds that exhibit a downstream-inclined shape and convexup or lateral overlapping pattern.This study conducts a coupled growth-geometric assessment to establish an architectural pattern for river-dominated lacustrine deltas.This architectural pattern offers valuable insights into predicting sandy lobe distribution in river-dominated lacustrine delta reservoirs,and the architecture of muddy accretion beds aids in predicting the rule of oil-water movement and distribution of remaining oil.展开更多
A coastal forest combined with a backward-facing step is an efficient facility to reduce tsunami damage to residential areas behind sea embankments.This study establishes a generalized model,and experimentally explore...A coastal forest combined with a backward-facing step is an efficient facility to reduce tsunami damage to residential areas behind sea embankments.This study establishes a generalized model,and experimentally explores the water level changes upstream of the vegetation-step mitigation model as well as its energy dissipation effect under different initial Froude numbers,step heights,and vegetation conditions.The results show that the relative backwater rise increases with the growth of vegetation density,patch length and initial Froude number,representing a slowing down of the tsunami inundation.As for energy dissipation,it is mainly caused by the additional resistance of the vegetation and the hydraulic jump.And the vegetation condition not only affects the energy dissipation due to stem-scale turbulence within the patch,but also changes the hydraulic jump process of water falling from the step in cooperation with the step height.As a result,the energy dissipation efficiency always increases with the growth of vegetation density,vegetation patch length and step height.With the criterion that the energy dissipation efficiency and its growth rate can hardly change with vegetation parameters,this study innovatively defines the threshold slope and gives the principle of judging the most cost-effective vegetation conditions at different step heights.These results are expected to provide an important reference for the design of composite tsunami mitigation facilities.展开更多
基金supported by the National Key Research and Development Program of China(Grant No.2023YFC3209504)the National Natural Science Foundation of China(Grants No.U2040215 and 52479075)the Natural Science Foundation of Hubei Province(Grant No.2021CFA029).
文摘The backwater effect caused by tributary inflow can significantly elevate the water level profile upstream of a confluence point.However,the influence of mainstream and confluence discharges on the backwater effect in a river reach remains unclear.In this study,various hydrological data collected from the Jingjiang Reach of the Yangtze River in China were statistically analyzed to determine the backwater degree and range with three representative mainstream discharges.The results indicated that the backwater degree increased with mainstream discharge,and a positive relationship was observed between the runoff ratio and backwater degree at specific representative mainstream discharges.Following the operation of the Three Gorges Project,the backwater effect in the Jingjiang Reach diminished.For instance,mean backwater degrees for low,moderate,and high mainstream discharges were recorded as 0.83 m,1.61 m,and 2.41 m during the period from 1990 to 2002,whereas these values decreased to 0.30 m,0.95 m,and 2.08 m from 2009 to 2020.The backwater range extended upstream as mainstream discharge increased from 7000 m3/s to 30000 m3/s.Moreover,a random forest-based machine learning model was used to quantify the backwater effect with varying mainstream and confluence discharges,accounting for the impacts of mainstream discharge,confluence discharge,and channel degradation in the Jingjiang Reach.At the Jianli Hydrological Station,a decrease in mainstream discharge during flood seasons resulted in a 7%–15%increase in monthly mean backwater degree,while an increase in mainstream discharge during dry seasons led to a 1%–15%decrease in monthly mean backwater degree.Furthermore,increasing confluence discharge from Dongting Lake during June to July and September to November resulted in an 11%–42%increase in monthly mean backwater degree.Continuous channel degradation in the Jingjiang Reach contributed to a 6%–19%decrease in monthly mean backwater degree.Under the influence of these factors,the monthly mean backwater degree in 2017 varied from a decrease of 53%to an increase of 37%compared to corresponding values in 1991.
基金Project(1053320170205)supported by the Research and Innovation Project of Graduate Students of Central South University,ChinaProject(502211704)supported by the Fundamental Research Funds for the Central Universities,China+3 种基金Project(SKL-SPM-201809)supported by the State Key Laboratory of Advanced Technologies for Comprehensive Utilization of Platinum Metals,ChinaProject(SKLAM005-2016)supported by the State Key Laboratory of Applied Microbiology Southern ChinaProjects(51320105006,51504106,51871250)supported by the National Natural Science Foundation of ChinaProject(2015FB204)supported by the Science and Technology Project of Yunnan Province,China
文摘Flotation indexes gradually decrease with the increase of cycle time of the backwater in bauxite floatation,and discharge of backwater brings environmental risk.In this study,methods such as Fenton-oxidation,adsorption and coagulation were used in the treatment of backwater,the flotation indexes were checked after backwater treatments,and Box-Behnken design(BBD)was used in the optimization of the main operating parameters.The results reveal that flotation indexes are effectively improved after coagulation treatment by polyaluminum ferric chloride(PAFC).The optimum parameters predicted by BBD are pH 7.55,1.09 g/L PAFC dosage and temperature of 25℃.Under these optimum conditions,a maximum recovery of Al2O3 of 82.83%and a minimum A/S of 1.30 of tailings are gained,while the deviations are less than 3%from the predicted values.These findings encourage the application of BBD for the optimization of critical parameters in backwater treatment.
基金supported by the National Key Research and Development Program of China(Grant No.2019YFC1510701)the National Natural Science Foundation of China(Grant No.U20A20319).
文摘Owing to extensive construction of dams, the impact of backwater on flow may lead to navigation or flood control issues in curved channels. To date, the impact of backwater on the water surface profile in curved channels remains unknown and requires investigation. In this study, experiments were conducted in a glass-walled recirculating flume with a length of 19.4 m, a width of 0.6 m, and a depth of 0.8 m, and the impact of backwater on the water surface profile in a 90° channel bend was investigated. The experimental results showed that the backwater degree had a significant impact on the transverse and longitudinal flow depth distributions in the bend. The transverse slope of the flow (Jr) increased linearly with an increase in the Froude number of the approach flow upstream of the bend. Jr increased with the longitudinal location parameter ξ when −0.2 < ξ < 0.5, and decreased with ξ when 0.5 < ξ < 1.2. Furthermore, the results showed that Jr asymptotically decreased to zero with an increase in the degree of backwater. An equation was formulated to estimate the transverse slope of the flow in a 90° bend in backwater zones.
基金supported by the National Natural Science Foundation of China (Grant No. 50879006)
文摘Based on the characteristics of backflow, a two-dimensional mathematical model of sediment movement was established. The complexity of the watercourse boundary at the confluence of the main stream and the tributary was dealt with using a boundary-fitting orthogonal coordinate system. The basic equation of the two-dimensional total sediment load model, the numerical calculation format, and key problems associated with using the orthogonal curvilinear coordinate system were discussed. Water and sediment flow in the Chongqing reach of the Yangtze River were simulated. The calculated water level, flow velocity distribution, amount of silting and scouring, and alluvial distribution are found to be in agreement with the measured data, which indicates that the numerical model and calculation method are reasonable. The model can be used for calculation of flow in a relatively complicated river network.
基金supported by the National Natural Science Foun-dation of China(Grant Nos.51339001,51479009)
文摘This paper studies the flow structure and the bedload transport regime in backwater flows, to provide a theoretical support for solving the sediment transport and bed scour problems in rivers or reservoirs with backwater. The bedload transport rates under different conditions are analyzed first on the basis of theoretical analysis, measurement comparison and flume experiment, and it is pointed out that the existing formulas for the bedload transport rate are not applicable for the bedload transport rate in backwater flows. Next, the flow structure in a non-uniform flow is observed by flume experiments, and by introducing the backwater degree index, the quantitative relation between the relative bed shear stress and the backwater degree is obtained. Finally, the formula for the bedload transport rate applicable for the reservoir channel segment with backwater flows is obtained through measurements and flume experiments.
基金National Natural Science Foundation of China,No.51879198The Follow-up Research Program for the Three Gorges Project from the Ministry of Water Resources of China,No.12630100100020J005。
文摘Floodplain lakes are important water storage areas in lowland regions that often undergo geomorphologic evolution,and timely topographic data are generally unavailable.In this study,to assess the impacts of lakebed deformation on hydraulic performance in Dongting Lake,a set of semi-empirical methods was proposed to establish performance graphs(PGs)using only hydrological data.These methods were used to evaluate the changes in water level,storage capacity,and flood detention ability in Dongting Lake caused by topographic adjustment after the Three Gorges Reservoir impoundment.These methods showed that PGs can effectively simulate the water level and outflow processes of Dongting Lake with Nash-Sutcliffe efficiency coefficients(NSEs)above 0.9.A comparison of the estimated water level and discharge using PGs from different periods suggested that bed erosion in Dongting Lake caused water level decreases of 0.18 m and 0.32 m during the flood and dry seasons,respectively.Because the magnitude of erosion at high elevations in the lake is small,the impacts of bed adjustment on the storage capacity and flood detention ability are not currently significant.This study showed that the hydraulic performance of a floodplain lake can be evaluated independently of topographic data under the condition of no reverse flows or negative watersurface slopes.
文摘The Sulige gas field is a typical low-pressure low-permeability tight sandstone gas reservoir. The reservoir has poor seepage capacity, strong heterogeneity, high mineralization of formation water and extremely scarce water resources on the site. These unfavorable factors have brought great difficulties to the on-site mining process. Now, a nano-composite green environmental protection slick water fracturing fluid system CQFR can be quickly dissolved because of the larger specific surface area, and the small molecular size makes the damage to the reservoir less than 5%, and the average drag reduction effect can reach more than 73%. It can quickly and well dissolve and maintain performance under high salinity conditions and fracturing flowback fluids. It responds well to the complex reservoir conditions on the construction site and makes the flowback fluid recyable, which greatly reduces the consumption of water resources on the construction site and effectively improves the construction efficiency and economic benefits.
文摘By introducing a water depth connecting formula, the hydraulic equations in the dividing channel system were coupled and the relation of discharge distribution between the branches of the dividing channels can be yielded. In this manner, a numerical model for the confluent channels was established to study the variation of backwater effects with the parameters in the channel junction. The meeting of flood peaks in the mainstream and tributary can be analyzed with this model.The flood peak meeting is found to be a major factor for the extremely high water level in the mainstream during the 1998 Yangtze River flood. Subsequently the variations of discharge distribution and water level with channel parameters between each branch in this system were studied as well. As a result, flood evolution caused by Jingjiang River shortcut and sediment deposition in the entrance of dividing channels of the Yangtze River may be qualitatively elucidated.It is suggested to be an effective measure for flood mitigation to enhance regulation capability of reservoirs available upstream of the tributaries and harness branch entrance channels.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.52020105006,12272281).
文摘The accumulation of aquatic vegetation in open channels,such as leaves,weeds,and large wood,poses a threat to the safety of hydraulic structures and disrupts the normal operation of hydropower stations,resulting in substantial economic losses.Studying the hydraulic characteristics with vegetation accumulation is a prerequisite for solving this engineering challenge.The effects of vegetation accumulation on the hydraulic characteristics with three types of vegetation were investigated using experimental and numerical simulation methods.The results indicate both backwater rise and head loss increase exponentially with blockage ratio.Furthermore,vegetation accumulation results in an uneven vertical distribution of streamwise velocity,leading to the formation of low-velocity regions and backflow vortexes in the upper water layer.For all cases,the bottom gap velocity increases markedly,forming a high-velocity jet region.The maximum jet velocity remains constant in the near wake region and the decay rate in the far wake region is positively correlated with the blockage ratio.Bed shear stresses in the corresponding region are 1-6 times higher than before vegetation accumulation,increasing the potential for riverbed erosion.This study extends the existing knowledge of vegetation accumulation hydrodynamics to provide a basis for the safe operation of hydraulic structures and river management.
基金supported by the National Natural Science Foundation of China(No.42202178)Science Foundation of China University of Petroleum(Beijing)(No.2462023YJRC034).
文摘River-dominated lacustrine deltas typically consist of multiple lobes due to autogenic lobe switching that occurs over short time scales.However,the switching patterns of multiple lobes in these deltas remain poorly understood,and the architectural features attributed to lobe switching are also lacking.By integrating Delft3D simulations,flume experiments,and modern deposit analysis,we proposed that autogenic lobe switching follows a cyclic pattern.Autocyclicity begins with the formation of an offshore lobe and concludes after a series of longshore lobe growth events,marked by longshore avulsions occurring along the sides of offshore distributary channels.Longshore avulsions follow a sequence that usually occurs earlier distally than proximally and subsequently occurs on one longshore side and then on the other side.Each lobe begins with rapid growth,which gradually slows and then stops once a channel avulsion is influenced by the backwater effect that triggers lobe switching.Three signals indicate lobe switching:a decrease in progradation rate,foreset slope steepening coupled with topset slope gentling,and the deposition of mud-dominated sediments.The number of autocyclic events never exceeds seven.The first two autocyclicities contribute to more than 55%of delta length and 70%of delta area.The lobes are separated by 1-6 stages of mud-dominated accretion beds that exhibit a downstream-inclined shape and convexup or lateral overlapping pattern.This study conducts a coupled growth-geometric assessment to establish an architectural pattern for river-dominated lacustrine deltas.This architectural pattern offers valuable insights into predicting sandy lobe distribution in river-dominated lacustrine delta reservoirs,and the architecture of muddy accretion beds aids in predicting the rule of oil-water movement and distribution of remaining oil.
基金supported by the National Natural Science Foundation of China(Grant Nos.52020105006,12272281,U2340216).
文摘A coastal forest combined with a backward-facing step is an efficient facility to reduce tsunami damage to residential areas behind sea embankments.This study establishes a generalized model,and experimentally explores the water level changes upstream of the vegetation-step mitigation model as well as its energy dissipation effect under different initial Froude numbers,step heights,and vegetation conditions.The results show that the relative backwater rise increases with the growth of vegetation density,patch length and initial Froude number,representing a slowing down of the tsunami inundation.As for energy dissipation,it is mainly caused by the additional resistance of the vegetation and the hydraulic jump.And the vegetation condition not only affects the energy dissipation due to stem-scale turbulence within the patch,but also changes the hydraulic jump process of water falling from the step in cooperation with the step height.As a result,the energy dissipation efficiency always increases with the growth of vegetation density,vegetation patch length and step height.With the criterion that the energy dissipation efficiency and its growth rate can hardly change with vegetation parameters,this study innovatively defines the threshold slope and gives the principle of judging the most cost-effective vegetation conditions at different step heights.These results are expected to provide an important reference for the design of composite tsunami mitigation facilities.
