基于动理学理论的推移质输沙公式

根据Boltzmann方程得到了床面附近运动颗粒的速度分布函数,将其在速度空间上积分,同时考虑床面颗粒起动概率的影响得到了床面颗粒的冲刷率函数。在此基础上,将该函数代入Einstein提出的推移质输沙基本模式中得到了基于动理学理论的推移质输沙公式。研究结果表明:① 公式计算结果与实验数据吻合,相对误差为10%~50%,可用于高强度和低强度输沙,能够较好地反映出床面附近运动的推移质颗粒的统计属性;② 得到的推移质输沙率理论表达式与经典推移质输沙公式十分接近,同时大大改善了Einstein公式在高强度输沙情况下的计算结果,这也说明了本文理论推导的正确性。     

An empirical model of subcritical bedform migration

The ability to predict bedform migration in rivers is critical for estimating bed material load, yet there is no relation for predicting bedform migration (downstream translation) that covers the full range of conditions under which subcritical bedforms develop. Here, the relation between bedform migration rates and transport stage is explored using a field and several flume data sets. Transport stage is defined as the non‐dimensional Shields stress divided by its value at the threshold for sediment entrainment. Statistically significant positive correlations between both ripple and dune migration rates and transport stage are found. Stratification of the data by the flow depth to grain‐size ratio improved the amount of variability in migration rates that was explained by transport stage to ca 70%. As transport stage increases for a given depth to grain‐size ratio, migration rates increase. For a given transport stage, the migration rate increases as the flow depth to grain‐size ratio gets smaller. In coarser sediment, bedforms move faster than in finer sediment at the same transport stage. Normalization of dune migration rates by the settling velocity of bed sediment partially collapses the data. Given the large amount of variability that arises from combining data sets from different sources, using different equipment, the partial collapse is remarkable and warrants further testing in the laboratory and field.     

Hydraulic control of grain-size distributions in a macrotidal estuary

The Avon River estuary of Nova Scotia was studied with the intention of analysing the relations between grain-size distributions and hydraulics. The Avon is macrotidal; tidal ranges up to 15·6 m generate tidal currents up to 1·7 m s^?1. Maximum current speed increases from the mouth (seaward end) to the head (shoreward end) of the estuary. Mean grain size decreases from the estuary mouth to the head. Thus, there is an inverse relationship between mean grain size and current speed. Consequently, textural parameters do not directly reflect hydraulic conditions. Graphical dissection of cumulative frequency curves into their component grain populations reveals a large coarse population at the estuary mouth that is absent at the head. There are several relationships between hydraulics and cumulative curves. Shields’ criterion predicts that all sediment in the system can be transported so that the large coarse population at the estuary mouth is not a lag. Local maximum shear velocity nearly equals the settling velocity of the grain size at the boundary of the coarse (C) and intermediate (A) grain populations. This has been previously interpreted to signifiy a transition from traction to intermittent suspension transport, and implies that the C population is a function of traction and that the A population is related to intermittent suspension (Middleton, 1976). Each grain population is transported at a different rate; suspended grains travel almost an order of magnitude faster than grains moved by traction according to Einstein's transport formula. Sediment transport paths in the estuary were determined from bedform migration directions and the computed net sediment transport per tidal cycle using Engelund and Hansen's formula. The areal distribution of the transport paths, combined with the differential transport rates of each grain population, produces hydraulic sorting. Hydraulic sorting causes coarse sediment to be excluded from the estuary head and creates the inverse relationship between current speed and mean grain size.     

河床粗化过程中推移质输移特征试验研究

为了研究河床粗化破坏与形成过程中推移质的输移特征,基于一套新型的接沙系统,在上游无来沙条件下,进行了3组不同床沙级配的水槽试验,研究了递增梯级流量作用下河床粗化破坏与形成的过程,采集到一套高精度（0.1 g）、高频率（1 Hz）的实时推移质输沙率及分时段输沙级配数据,分析了累积输沙量、输沙率及输沙级配的变化特征。结果表明,粗化过程中累积输沙量随时间基本呈幂函数规律增长,且"粗化破坏再形成"的累积输沙量曲线出现明显转折点;推移质输沙率表现出明显的非恒定性,其粗化形成阶段的耗时要远大于粗化破坏阶段的时间,两者之比范围为3.5~20.5;推移质输沙级配中粗颗粒比例随时间变化趋势与输沙率相似,在输沙率达到峰值附近时,输沙级配与原始床沙级配相同。     

On the transition between 2D and 3D dunes

Sediment transport in sand-bedded alluvial channels is strongly conditioned by bedforms, the planimetric morphology of which can be either two- or three-dimensional. Experiments were undertaken to examine the processes that transform the bed configuration from two-dimensional (2D) dunes to three-dimensional (3D) dunes. A narrowly graded, 500 μm size sand was subjected to a 0·15 m deep, non-varying mean flow ranging from 0·30 to 0·55 m sec⁻¹ in a 1 m wide flume. Changes in the planimetric configuration of the bed were monitored using a high-resolution video camera that produced a series of 10 sec time-lapsed digital images. Image analysis was used to define a critical value of the non-dimensional span (sinuosity) of the bedform crestlines that divides 2D forms from 3D forms. Significant variation in the non-dimensional span is observed that cannot be linked to properties of the flow or bedforms and thus appears random. Images also reveal that, once 2D bedforms are established, minor, transient excesses or deficiencies of sand are passed from one bedform to another. The bedform field appears capable of absorbing a small number of such defects but, as the number grows with time, the resulting morphological perturbations produce a transition in bed state to 3D forms that continue to evolve, but are pattern-stable. The 3D pattern is maintained by the constant rearrangement of crestlines through lobe extension and starving downstream bedforms of sediment, which leads to bifurcation. The experiments demonstrate that 2D bedforms are not stable in this calibre sand and call into question the reliability of bedform phase diagrams that use crestline shape as a discriminator.     

Bedform spurs: a result of a trailing helical vortex wake

The formative conditions for bedform spurs and their roles in bedform dynamics and associated sediment transport are described herein. Bedform spurs are formed by helical vortices that trail from the lee surface of oblique segments of bedform crest lines. Trailing helical vortices quickly route sediment away from the lee surface of their parent bedform, scouring troughs and placing this bed material into the body of the spur. The geometric configuration of bedform spurs to their parent bedform crests is predicted by a cross‐stream Strouhal number. When present, spur‐bearing bedforms and their associated trailing helical wakes exert tremendous control on bedform morphology by routing enhanced sediment transport between adjacent bedforms. Field measurements collected at the North Loup River, Nebraska, and flume experiments described in previous studies demonstrate that this trailing helical vortex‐mediated sediment transport is a mechanism for bedform deformation, interactions and transitions between two‐dimensional and three‐dimensional bedforms.     

Variability in bedform morphology and kinematics with transport stage

Bedform geometry is widely recognized to be a function of transport stage. Bedform aspect ratio (height/length) increases with transport stage, reaches a maximum, then decreases as bedforms washout to a plane bed. Bedform migration rates are also linked to bedform geometry, in so far as smaller bedforms in coarser sediment tend to migrate faster than larger bedforms in finer sediment. However, how bedform morphology (height, length and shape) and kinematics (translation and deformation) change with transport stage and suspension have not been examined. A series of experiments is presented where initial flow depth and grain size were held constant and the transport stage was varied to produce bedload dominated, mixed‐load dominated and suspended‐load dominated conditions. The results show that the commonly observed pattern in bedform aspect ratio occurs because bedform height increases then decreases with transport stage, against a continuously increasing bedform length. Bedform size variability increased with transport stage, leading to less uniform bedform fields at higher transport stage. Total translation‐related and deformation‐related sediment fluxes all increased with transport stage. However, the relative contribution to the total flux changed. At the bedload dominated stage, translation‐related and deformation‐related flux contributed equally to the total flux. As the transport stage increased, the fraction of the total load contributed by translation increased and the fraction contributed by deformation declined because the bedforms got bigger and moved faster. At the suspended‐load dominated transport stage, the deformation flux increased and the translation flux decreased as a fraction of the total load, approaching one and zero, respectively, as bedforms washed out to a plane bed.     

Evolution and mechanics of a Miocene tidal sandwave

A remarkable exposure of Miocene marine molasse in western Switzerland records the evolution of a tidal sandwave over a period of approximately 2 1/2 months. The sandwave is composed of tidal ‘bundles’ in which a sandwave reactivation stage and full vortex stage can be recognized for the dominant flow (ebb tide) and a rippled flood apron overlain by high water drape for the reversed flow. Bundle thicknesses vary systematically through neap–spring cycles, with a periodicity of 27 demonstrating the semi-diurnal lunar control of sedimentation. Waves were an additional component, especially when superimposed on flood tides, producing near-symmetrical combined-flow ripple marks in the flood apron. Tidal current velocities are estimated using critical shear velocities for entrainment, the ripple-dune transition and the dune-plane bed transition. Using appropriate estimates of roughness lengths and a logarithmic velocity law, maximum tidal speeds at 1 m above the bed were approximately 0·6 m sec^?1 for ebbs and up to 0·5 m sec^?1 for floods. The enhancement by waves of bed shear stress (τ_wc/τ of approximately 2 for 1 m high waves) under flood currents implies flood tidal velocities closer to 0·2–0·3 m sec^?1. Peak instantaneous bedload sediment transport rates using a modified Bagnold equation are nearly 5 times greater under ebb tides than floods. The average net sediment transport rate at springs (0·04 kg m^?1 sec^?1) is over 10 times greater than at neaps (0·002 kg m^?1 sec^?1). Comparison with transport rates in modern tidal environments suggests that the marine molasse of Switzerland was deposited under spatially confined and relatively swift tidal flows not dissimilar to those of the present Dutch tidal estuaries.     

On Bagnold's sediment transport equation in tidal marine environments and the practical definition of bedload

Bagnold's sediment transport equation has proved to be important in studying tidal marine environments. This paper discusses three problems concerning Bagnold's transport equation and its practical application:

• 1 Bagnold's suspended-load transport equation and the total-load transport equation with are incorrect from the viewpoint of energy conservation. In these equations the energy loss due to bedload transport has been counted twice. The correct form should be for suspended-load transport and for total-load transport with
• 2 The commonly used Bagnold's transport coefficient K varies as a non-linear function of the dimensionless excess shear stress, which can be represented best by the power law , where the coefficient A and exponent B depend on sediment grain size D. The empirical values of A and B for fine to medium grained sands are determined using Guy et al.'s (1966) flume-experiment data.
• 3 The sediment transport rates predicted from this equation are compared with bedform migration measurements in the flume and the field. This comparison shows that the sediment transport rates measured from bedform migrations are higher than the predicted bedload transport rates, but comparable to the calculated total-load (bedload plus intermittent suspended-load) transport rates. This indicates that bedform migration involves both bedload and intermittent suspended-load transport. As a logical conclusion, bedform migration data should be compared with Bagnold's total-load transport equation rather than with his bedload transport equation. In this respect the term ‘bed material’ might be more appropriate than the term ‘bedload’ for estimating sediment transport rate from bedform migration data.

The sediment transport rates predicted from this modified Bagnold transport equation are in good agreement with field measurements of bedform migration rates in four individual tidal marine environments, which cover a wide range of sediment grain size, flow velocity and bedform conditions (ranging from small ripples, megaripples to sandwaves).     

明渠非恒定流流速分布及推移质运动研究进展

明渠非恒定流流速分布及非恒定流作用下推移质运动分别是水力学和泥沙运动力学研究中的重要问题之一。近几十年来,国内外许多学者在这些领域做过很多探索,取得了一定进展,也存在较多问题。在总结相关研究成果的基础上,简述了明渠非恒定流试验方法、流速分布、床面切应力、非恒定流输沙与水流运动不同步现象、产生原因、以及非恒定流推移质输沙公式等方面的成果,指出了现有研究中存在的不足,提出了需要进一步研究的关键问题:应用先进的量测仪器,研究非恒定流作用下非均匀沙运动输移规律。     

Large transverse bedforms and the character of boundary-layers in shallow-water environments

Theoretical work, laboratory studies, and field observations indicate that the oscillatory boundary layers generated by the tidal wave differ fundamentally in dynamics and kinematic structure from the unidirectional boundary layers of rivers. Unique to the former are mass-transport currents attributable to: (1) the wave motion itself, and (2) bed curvature in the presence of the oscillatory flow. The implication of this difference for bed-material transport is that the larger flow-transverse bedforms of shallow-water environments are divisible hydraulically between two major classes: (A) those related to tidal conditions, under which the fluid reverses in direction of flow with each reversal of the tide, permitting the initiation and maintenance of bed features by the spatially reversing, curvature-related mass transport, and (B) those related strictly to rivers and river-like flows, in which the fluid motion is unidirectional, and therefore the only mechanisms available for bedform initiation and maintenance are those creating a finite spatial lag between the transport rate and the bed waviness. Forms of Class B are best called dunes and bars, and only those attributable to Class A should be termed sand waves. The latter, restricted to oscillatory boundary layers of tidal origin, apparently correspond to the very much smaller; but also commonly symmetrical, ripple marks produced in wind-wave oscillatory boundary layers.     

Response of low‐angle dunes to variable flow

Current understanding of bedform dynamics is largely based on field and laboratory observations of bedforms in steady flow environments. There are relatively few investigations of bedforms in flows dominated by unsteadiness associated with rapidly changing flows or tides. As a consequence, the ability to predict bedform response to variable flow is rudimentary. Using high‐resolution multibeam bathymetric data, this study explores the dynamics of a dune field developed by tidally modulated, fluvially dominated flow in the Fraser River Estuary, British Columbia, Canada. The dunes were dominantly low lee angle features characteristic of large, deep river channels. Data were collected over a field ca 1·0 km long and 0·5 km wide through a complete diurnal tidal cycle during the rising limb of the hydrograph immediately prior to peak freshet, yielding the most comprehensive characterization of low‐angle dunes ever reported. The data show that bedform height and lee angle slope respond to variable flow by declining as the tide ebbs, then increasing as the tide rises and the flow velocities decrease. Bedform lengths do not appear to respond to the changes in velocity caused by the tides. Changes in the bedform height and lee angle have a counterclockwise hysteresis with mean flow velocity, indicating that changes in the bedform geometry lag changes in the flow. The data reveal that lee angle slope responds directly to suspended sediment concentration, supporting previous speculation that low‐angle dune morphology is maintained by erosion of the dune stoss and crest at high flow, and deposition of that material in the dune trough.     

A unified model for bedform development and equilibrium under unidirectional,oscillatory and combined‐flows

The development of bedforms under unidirectional, oscillatory and combined‐flows results from temporal changes in sediment transport, flow and morphological response. In such flows, the bedform characteristics (for example, height, wavelength and shape) change over time, from their initiation to equilibrium with the imposed conditions, even if the flow conditions remain unchanged. These variations in bedform morphology during development are reflected in the sedimentary structures preserved in the rock record. Hence, understanding the time and morphological development in which bedforms evolve to an equilibrium stage is critical for informed reconstruction of the ancient sedimentary record. This article presents results from a laboratory flume study on bedform development and equilibrium development time conducted under purely unidirectional, purely oscillatory and combined‐flow conditions, which aimed to test and extend an empirical model developed in past work solely for unidirectional ripples. The present results yield a unified model for bedform development and equilibrium under unidirectional, oscillatory and combined‐flows. The experimental results show that the processes of bedform genesis and growth are common to all types of flows, and can be characterized into four stages: (i) incipient bedforms; (ii) growing bedforms; (iii) stabilizing bedforms; and (iv) fully developed bedforms. Furthermore, the development path of bedform; growth exhibits the same general trend for different flow types (for example, unidirectional, oscillatory and combined‐flows), bedform size (for example, small versus large ripples), bedform shape (for example, symmetrical or rounded), bedform planform geometry (for example, two‐dimensional versus three‐dimensional), flow velocities and sediment grain sizes. The equilibrium time for a wide range of bed configurations was determined and found to be inversely proportional to the sediment transport flux occurring for that flow condition.     

感潮河网区水沙运动的数值模拟

根据感潮河网区水沙运动特征,建立了一维感潮河网区非恒定水沙数学模型,对河网区水沙运动和河床变形进行了数值模拟,并在水沙模拟的范围内着重对河网区内动边界的处理、挟沙力公式的选用、内边界含沙量的确定等问题进行了讨论,提出了解决问题的途径和技术处理方法。采用东江下游感潮河网区的水文和河道地形资料对所建模型进行了检验,模拟结果较好地反映了感潮河网区水沙运动的往复输运特征和河道冲淤的宏观效应。     

长江中游城汉河段推移质输沙率计算公式

三峡水库蓄水运用后,城汉河段悬移质输沙量大幅度减少,推移质输沙量所占比重增加,造床作用日益凸显,故开展其推移质输沙率计算公式研究具有理论与实际意义。利用螺山和汉口水文站实测资料建立了推移质输沙率与流量之间的指数关系式,并据此推算了两站逐日推移质输沙率,结果表明:螺山站、汉口站输沙率均与流量的0.912 78次方成正比,多年（2009—2015年）平均推移质输沙量分别为137万t、152万t,主要集中在汛期。利用推移质实测资料对Engelund、Einstein、Yalin 3个公式进行了检验与修正,结果表明:修正前各公式计算结果比较分散,且与实测值偏差很大;修正后各公式计算精度显著提高,综合比较发现,修正后的Yalin公式精度最高,Engelund公式、指数关系式次之,Einstein公式精度相对较低。因此,修正后的Yalin公式更适合于城汉河段推移质输沙率计算,可用于该河段的演变分析与数学模型计算。     

Flow and sediment dynamics in a low sinuosity, braided river: Calamus River, Nebraska Sandhills

The interaction between channel geometry, flow, sediment transport and deposition associated with a midstream island was studied in a braided to meandering reach of the Calamus River, Nebraska Sandhills. Hydraulic and sediment transport measurements were made over a large discharge range using equipment operated from catwalk bridges. The relatively low sinuosity channel on the right-hand side of the island carries over 70% of the water discharge at high flow stages and 50–60% at low flow stages. As a result, mean velocity, depth, bed shear stress and sediment transport rate tend to be greater here than in the more strongly curved left-hand channel. The loci of maximum flow velocity, depth and bed shear stress are near the centre of the channel upstream of the island, but then split and move towards the outer banks of both channels downstream. Variations in these loci depend on the flow stage. Topographically induced across-stream flows are generally stronger than the weak, curvature-induced secondary circulations. Water surface topography is controlled mainly by centrifugal accelerations and local changes in downstream flow velocity. The averaged water surface slope of the study reach varies very little with discharge, having values between 0·00075 and 0·00090. As bed shear stress generally varies in a similar way to mean velocity, friction coefficients vary little, normally being in the range 0·07–0·13. These values are similar to those in straight channels with sandy dune-covered beds. Bedload is moved mainly as dunes at all flow stages. Grain size is mainly medium sand with coarse sand moved in thalwegs adjacent to the cut banks, and with fine sand at the downstream end of the island. These patterns of flow velocity, depth, water surface topography, bed shear stress, bedload transport rate and mean grain size can be accurately predicted using theoretical models of flow, bed topography and sediment transport rate in single river bends, applied separately to the left and right channels. During high flow stages deposition occurs persistently near the downstream end of the island, and cut banks are eroded. Otherwise, erosion and deposition occurs only locally within the channel as discharge varies. Abandonment and filling of a strongly curved channel segment may occur by migration of an upstream bar into the channel entrance at a high flow stage.     

The morphological dynamics of intertidal megaripples in the Mawddach Estuary, North Wales, and the implications for palaeoflow reconstructions

The morphology and migration rate of tidal bedforms are important because of their use in interpretation of modern and ancient sediment transport regimes. Tidal flow, megaripple morphology and migration were studied in the mesotidal Mawddach Estuary, North Wales, to examine the veracity of published flow-bedform relationships, quantify spatial variations in migration and assess consequences for palaeoflow reconstruction. Two transects were surveyed along a megarippled intertidal shoal (mean grain size 280 μm) for a period of 22 semi-diurnal tidal cycles. A vertical array of current meters recorded tidal current profiles at the centre of one of the transects. Flood tidal currents dominate at Fegla Fach shoal, with peak velocities over 1 m s^?1 at spring tides, and 0.5 m s ^?1 at neaps, and bed sediment transport was also flood-dominated. Over the lunar cycle, the morphology of the megaripples on the survey lines was divisible into three phases: 1 the neap mode-consisting of near-moribund two-dimensional (2-D) flood-orientated megaripples of wavelength c. 6 m and height c. 0.2 m; 2 a transitional mode-where, on rising tidal ranges, scour pits formed and developed into 3-D megaripples which underwent net migration with the flood tide; 3 the spring mode-consisting of 3-D megaripples of wavelength c. 4 m and height c. 0.2 m. Despite complete re-orientation by the ebb tide, these were recognizable from one low water survey to the next, and net migration was c. 1 m per tide with the flood tide. We infer the presence of the equilibrium ‘spring tidal form’ occurring as flood-orientated megaripples during the flood tide. The data support previously reported separation of 2-D and 3-D megaripples at a depth to grain size ratio of 8000, and at a depth-mean velocity of the dominant tide (U_maxdom) of 0.75-0.8 m s^?1. A migration threshold exists at U_maxdom of c. 0.53-0.57 m s^?1. Measures of migration which might be used on preserved sections have been applied to the data. These measures systematically overestimated bedform migration at most stages of the lunar cycle (by <25% at spring tides and <140% in the post-spring transition period), but were accurate when the megaripples had developed into their 'spring tidal form’. There is significant variation of migration rates within the survey populations. We conclude that whilst the occurrence of megaripple cross-sets may be used as a palaeoflow indicator, and sedimentary structures associated with 2-D to 3-D transitions may also be indicative of palaeoflows, there are likely to be significant uncertainties involved in using tidal bundles as an indication of sediment transport rates.     

Formation and preservation of open-framework gravel strata in unidirectional flows

Open‐framework gravel (OFG) in river deposits is important because of its exceptionally high permeability, resulting from the lack of sediment in the pore spaces between the gravel grains. Fluvial OFG occurs as planar strata and cross strata of varying scale, and is interbedded with sand and sandy gravel. The origin of OFG has been related to: (1) proportion of sand available relative to gravel; (2) separation of sand from gravel during a specific flow stage and sediment transport rate (either high, falling or low); (3) separation of sand from gravel in bedforms superimposed on the backs of larger bedforms; (4) flow separation in the lee of dunes or unit bars. Laboratory flume experiments were undertaken to test and develop these theories for the origin of OFG. Bed sediment size distribution (sandy gravel with a mean diameter of 1·5 mm) was kept constant, but flow depth, flow velocity and aggradation rate were varied. Bedforms produced under these flow conditions were bedload sheets, dunes and unit bars. The fundamental cause of OFG is the sorting of sand from gravel associated with flow separation at the crest of bedforms, and further segregation of grain sizes during avalanching on the steep lee side. Sand in transport near the bed is deposited in the trough of the bedform, whereas bed‐load gravel avalanches down the leeside and overruns the sand in the trough. The effectiveness of this sorting mechanism increases as the height of the bedform increases. Infiltration of sand into the gravel framework is of minor importance in these experiments, and occurs mainly in bedform troughs. The geometry and proportion of OFG in fluvial deposits are influenced by variation in height of bedforms as they migrate, superposition of small bedforms on the backs of larger bedforms, aggradation rate, and changes in sediment supply. If the height of a bedform increases as it migrates downstream, so does the amount of OFG. Changes in the character of OFG on the lee‐side of unit bars depend on grain‐size sorting in the superimposed bedforms (dunes and bedload sheets). Thick deposits of cross‐stratified OFG require high bedforms (dunes, unit bars) and large amounts of aggradation. These conditions might be expected to occur during high falling stages in the deeper parts of river channels adjacent to compound‐bar tails and downstream of confluence scours. Increase in the amount of sand supplied relative to gravel reduces the development of OFG. Such increases in sand supply may be related to falling flow stage and/or upstream erosion of sandy deposits.     

推移质输沙率的非线性研究

目的是从非线性科学角度探讨泥沙运动的规律。通过分析非均匀沙起动的影响因素得到了尖点突变模型的状态变量和控制变量,建立了能描述推移质运动的尖点突变模型。在尖点突变标准方程的基础上,应用尖点突变理论的坐标变换和拓扑变换,导出了输沙强度和水流参数的函数关系式。将输沙强度作为状态变量,水流参数和床沙密实系数作为控制变量。用水槽实验资料和其它推移质输沙率公式进行了对比验证。验证结果表明,计算值与其它推移质输沙率公式和水槽实验结果基本相符,误差一般在-90%～80%之间。说明建立的推移质输沙率公式是合理的,能够反映泥沙的起动和输移规律。     

床面附近泥沙交换率在悬移质输沙计算中的应用

总结并分析了关于悬移质运动方程的源/汇项或底部边界条件的已有的处理方法.认为在悬移质输沙计算中,这些方法因引入了平衡输沙概念、忽略了推移质颗粒对悬移质运动的影响或因缺乏床面附近泥沙质量交换率的理论表达式,均存在着某些不足.运用床面附近泥沙质量交换率理沦,对一般的悬移质输沙方程的底部边界条件进行了新的探讨,并提供了关于一维和垂向二维悬移质输沙的计算实例.