Predictive equation for longitudinal dispersion coefficient

Dye tracing field data were collected in small, steep streams in Ontario and used to calculate longitudinal dispersion coefficients for these headwater streams. A predictive equation for longitudinal dispersion coefficient is developed using combined data sets from five steeper head – water streams and 24 milder and larger rivers. The predictive equation relates the longitudinal dispersion coefficient to hydraulic and geometric parameters of the stream and has been developed using multiple regression analysis. The newly developed equation shows impressive accuracy of predictions for longitudinal dispersion coefficient (R² = 0.86, RMSE = 25, Nash–Sutcliffe coefficient E_ns = 0.86 and Index of Agreement D = 0.96) for both small, steep headwater streams as well as large, mild rivers. The Froude number has been introduced as a third key parameter to capture the effect of slope of the reach – in addition to the aspect ratio and bed material surface roughness – on the longitudinal dispersion coefficient. The pronounced improvement in the accuracy of the prediction is due to the addition of the Froude number to capture the effect of the slope of the reach on longitudinal dispersion coefficient. Copyright © 2014 John Wiley & Sons, Ltd.     

Hydrological characteristics of vegetated river flows: a laboratory flume study

Abstract

Laboratory flume experiments were undertaken to measure the vertical profiles of mean flow velocity for three different flow discharges and four different stem densities of Hydrilla verticillata. The data were used to calculate three parameters, namely Manning's roughness coefficient, the Reynolds number and the Froude number. In addition, empirical equations were obtained for the vertical distribution of measured flow velocity within the transitional zone and above the plant canopy. The results show that: (a) the vertical distribution of measured flow velocity exhibits three zone profiles; (b) Manning's roughness coefficient decreases with increasing depth-averaged flow velocity; (c) the relationship between Manning's roughness coefficient and the depth-averaged flow velocity is within the smooth left inverse curve; (d) Manning's roughness coefficient significantly changes with increasing density of Hydrilla; (e) the Froude number is independent of the density of Hydrilla; and (f) both the Reynolds number and the Froude number increase with increasing depth-averaged flow velocity.

Citation Shi, J.Z., Li, Y.-H., Hughes, J.M.R., and Zhao, M., 2013. Hydrological characteristics of vegetated river flows: a laboratory flume study. Hydrological Sciences Journal, 58 (5), 1047–1058.

Editor Z.W. Kundzewicz     

Periodicity of Water-borne Hyphomycetes in Two Streams of Western Ghat Forests (India)

The seasonal variation in the occurrence of water-borne hyphomycetes in the two streams, viz. Kempu Hole and Kumaradhara, was investigated during 1983 and 1984. The fungi were isolated by using the four methods, viz. leaf litter analysis, water filtration and analysis of natural and induced foam. Thirty-six species of hyphomycetes in Kempu Hole and twenty species in Kumaradhara were recorded. Lunulospora curvula and Triscelophorus monosporus were observed in high frequency in all seasons in both the streams. The organisms like Dactylella aquatica, Camposporium pellucidum, Clavatospora filiformis, Dactylella oviparasitica, Flabellospora crassa, Tetracladium marchalianum, Tetraploa sp., Tetraploa aristata, Alatospora acuminata, Condylospora spumigena, Helicosporium sp. 1, Helicosporium sp. 2, Diplocladiella scalaroides, Phalangispora constricta and Isthmotricladia laeensis were found to occur with a very low frequency. In both the streams a maximum number of organisms were collected following the periods of heavy rains. The temperature and pH of stream water do not seem to affect the occurrence of hyphomycetes in streams of this region. On the other hand, the availability of substrates and the oxygen concentration of stream water seem to influence the occurrence of these fungi.     

Effects of sediment load on hydraulics of overland flow on steep slopes

Eroded sediment may have significant effects on the hydraulics of overland flow, but few studies have been performed to quantify these effects on steep slopes. This study investigated the potential effects of sediment load on Reynolds number, Froude number, flow depth, mean velocity, Darcy–Weisbach friction coefficient, shear stress, stream power, and unit stream power of overland flow in a sand‐glued hydraulic flume under a wide range of hydraulic conditions and sediment loads. Slope gradients were varied from 8·7 to 34·2%, unit flow rates from 0·66 to 5·26×10^?3 m² s^?1, and sediment loads from 0 to 6·95 kg m^?1 s^?1. Both Reynolds number (Re) and Froude number (Fr) decreased as sediment load increased, implying a decrease in flow turbulence. This inverse relationship should be considered in modeling soil erosion processes. Flow depth increased as sediment load increased with a mean value of 1·227 mm, caused by an increase in volume of sediment‐laden flow (contribution 62·4%) and a decrease in mean flow velocity (contribution 37·6%). The mean flow velocity decreased by up to 0·071 m s^?1 as sediment load increased. The Darcy–Weisbach friction coefficient (f) increased with sediment load, showing that the total energy consumption increased with sediment load. The effects of sediment load on f depended on flow discharge: as flow discharge increased, the influence of sediment load on f decreased due to increased flow depth and reduced relative roughness. Flow shear stress and stream power increased with sediment load, on average, by 80·5% and 60·2%, respectively; however, unit stream power decreased by an average of 11·1% as sediment load increased. Further studies are needed to extend and apply the insights obtained under these controlled conditions to real‐world overland flow conditions. Copyright © 2010 John Wiley & Sons, Ltd.     

Analysis of rill step–pool morphology and its comparison with stream case

In this paper, the morphology of step–pool features is analysed using rill measurements and literature data for streams. Close-range photogrammetry was used to carry out ground measurements on rills with step–pool units, shaped on a plot having slope equal to 14, 15, 22, 24 and 26%. Data were used to compare the relationships between H/L, in which H is the step height and L is the step length, and the mean gradient of the step–pool sequence, S_m, for streams or the slope of the step–pool unit, S, for rills. The relationship of H/L against S_m is widely used to test the occurrence of the maximum flow resistance condition in streams, which is associated with the range 1 ≤ (H/L)/S_m ≤ 2. Further analyses were carried out to compare both the formation process and the profile of the pool in rills with those related to streams. Moreover, for a single rill channel, an analysis of flow characteristics expressed in terms of Darcy–Weisbach friction factor and Froude number was developed. The results allowed us to state: (i) the relationships of H/L versus S_m and S are quite similar and the steepness ratio for streams, (H/L)/S_m, and for rills, (H/L)/S, generally ranges from 1 to 2; (ii) the formation process and the profile of the pool in rills are not consistent with those occurring in streams; (iii) in the rills, the longitudinal size of the pool is dominant with respect to the maximum scour depth; (iv) the presence of a sequence of step–pool units within a rill segment noticeably increases flow resistance compared to segments with a flat bed; (v) the Froude number of the flow over the sequence of step–pool units in rills is slightly below the range of 0.8–1 corresponding to the maximum flow resistance in step–pool units.     

An experimental study on the evolution law of roll wave parameters in overland flow

Roll waves commonly occur in overland flow and have an important influence on the progress of soil erosion on slopes. This study aimed to explore the evolution and mechanism of roll waves on steep slopes. The potential effects of flow rate, rainfall intensity and bed roughness on the laws controlling roll wave parameters were investigated. The flow rates, rainfall intensities and bed roughness varied from 5 to 30 L/min, 0 to 150 mm/h, and 0.061 to 1.700 mm, respectively. The results indicate that roll waves polymerize significantly along the propagation path, and bed roughness and rainfall affect the generation and evolution of roll waves. The wave velocity, length and height decreased with bed roughness, whereas the wave frequency increased with increasing bed roughness under fixed flow rate and rainfall intensity conditions. Rainfall increased the wave velocity and wavelength and decreased the wave frequency. The wave velocity, height and wavelength tended to increase with an increasing flow rate. Rainfall promoted the generation of roll waves, whereas bed roughness had the opposite effect. The generation of roll waves is closely related to the Froude number (Fr) and flow resistance. In this experiment, the range of the Reynolds number for the roll waves generated in the laminar region was 142–416, and the range of the flow resistance coefficient was 0.64–4.85. The critical value of the Fr for flow instability in the laminar region was approximately 0.57. Exploring the generation and evolution law of roll waves is necessary for understanding the processes and dynamic mechanisms of slope soil erosion.     

Evaluating the effectiveness of road‐crossing drainage culverts in ephemeral streams

The present study proposes a method for evaluating the effectiveness of road‐crossing drainage culverts in ephemeral streams. This approach is focused on estimating the culvert capacity in road–stream crossings and the probable runoff generated on the road from hydrological thresholds associated with hydromorphological criteria. In particular, discharges at bankfull and flood‐prone stages have been used in combination with 2.5 and 100‐year peak discharges. Different hydraulic variables have been considered for calculating the discharge through culverts under these conditions (e.g. tailwater and headwater depth, inlet control, pipe roughness, pipe cross‐area and slope, pipe outlet velocity, critical water depth, and flow rate over the road). Geomorphological factors such as bed stability, bed load transport, and channel roughness have also been considered because of their potential for obstructing the drains in this type of channel. In addition, a potential obstruction index (PI_OBSTR) has been calculated, as a dependent parameter of the obstacle index (I_OBST) and the potential build‐up of coarse sediments (PB_CS). The study has been carried out on the Mediterranean coast in the region of Murcia (Spain), where there are numerous examples of road–stream crossings equipped with culverts in ephemeral channels that could cause highly dangerous situations for road traffic. Copyright © 2012 John Wiley & Sons, Ltd.     

The impact of flow discharge on the hydraulic characteristics of headcut erosion processes in the gully region of the Loess Plateau

Headcut erosion is associated with major hydraulic changes induced by the gully head of concentrated flow. However, the variation in the hydraulic characteristics of the headcut erosion process is still not clear in the gully region of the Loess Plateau. A series of rainfall combined scouring experiments (flow discharges ranging from 3.6 to 7.2 m³ hr⁻¹, with 0.8 mm min⁻¹ rainfall intensity) were conducted on experimental plots to clarify the variation in the hydraulic parameters induced by gully head and erosion processes under different flow discharges. The results showed that concentrated flows in the catchment area and gully bed were turbulent (Reynolds number ranging from 1,876 to 6,693) and transformed between supercritical and subcritical (Froude number ranging from 0.96 to 3.73). The hydraulic parameters, such as the flow velocity, Reynolds number, shear stress, stream power, Darcy–Weisbach friction factor, and unit stream power in the catchment area were 0.45–0.59 m s⁻¹, 2086–6693, 1.96–5.33 Pa, 0.89–2.86 W m⁻², 0.08–0.16, and 0.023–0.031 m s⁻¹, respectively. When the concentrated flows dropped from the gully head, the hydraulic parameters in the gully bed decreased by 3.39–26.07%, 1.49–29.99%, 65.19–67.14%, 67.25–74.96%, 28.53–61.31%, and 67.82–77.14%, respectively, which contributed to the flow energy consumption at the gully head. As flow discharge increased, Reynolds number, shear stress, and stream power increased, while flow velocity, Froude number, unit stream power, and Darcy–Weisbach friction factor did not. The flow energy consumption at the gully head was 9.66–10.13, 13.25–13.74, 15.68–16.41, and 19.28–20.25 J s⁻¹, respectively, under different flow discharges and accounted for 60.58–68.50% of the flow energy consumption of the experimental plots. Generally, the sediment discharges increased rapidly at the initial stage, then increased slowly, and finally reached a steady state condition, which showed a significant declining logarithmic trend with experimental duration (P<.01) and increased with increasing flow discharge. Accordingly, the flow energy consumption was significantly correlated with the sediment yield. These findings could improve our understanding of the hydraulic properties and flow energy characteristics of headcut erosion.     

Roughness effect on the correction factor of surface velocity for rill flows

Flow velocity is one of the most important hydrodynamic variables for both channelized (rill and gullies) and interrill erosive phenomena. The dye tracer technique to measure surface flow velocity V_s is based on the measurement of the travel time of a tracer needed to cover a known distance. The measured V_s must be corrected to obtain the mean flow velocity V using a factor α_v = V/V_s which is generally empirically deduced. The V_s measurement can be influenced by the method applied to time the travel of the dye-tracer and α_v can vary in different flow conditions. Experiments were performed by a fixed bed small flume simulating a rill channel for two roughness conditions (sieved soil, gravel). The comparison between a chronometer-based (CB) and video-based (VB) technique to measure V_s was carried out. For each slope-discharge combination, 20 measurements of V_s, characterized by a sample mean V_m, were carried out. For both techniques, the frequency distributions of V_s/V_m resulted independent of slope and discharge. For a given technique, all measurements resulted normally distributed, with a mean equal to one, and featured by a low variability. Therefore, V_m was considered representative of surface flow velocity. Regardless of roughness, the V_m values obtained by the two techniques were very close and characterized by a good measurement precision. The developed analysis on α_v highlighted that it is not correlated with Reynolds number for turbulent flow regime. Moreover, α_v is correlated neither with the Froude number nor with channel slope. However, the analysis of the empirical frequency distributions of the correction factor demonstrated a slope effect. For each technique (CB, VB)-roughness (soil, gravel) combination, a constant correction factor was statistically representative even if resulted in less accurate V estimations compared to those yielded by the slope-specific correction factor.     

Dynamic simulation on hydraulic characteristic values of overland flow

The economic forest management is one of the main land use models on low hill gentle slope. In order to investigate the soil erosion properties of bare slope under economic forest, dynamic simulation on hydraulic characteristic values of overland flow was carried out under 0.5 mm min^?1, 1.2 mm min^?1 and 1.8 mm min^?1 rainfall intensities. Results indicated that runoff shear stress increased with increasing of slope length and their relationship can be described by quadratic equation. There were abnormal points at the length of 4 m and 5.5 m under rainfall intensity of 1.8 mm min^?1. The shallow flow was pseudo-laminar flow under 0.5 mm min^?1, 1.2 mm min^?1 and 1.8 mm min^?1 rainfall intensities, and the runoff at upslope was sluggish flow then changed to torrential flow at downslope with increasing of slope length. Critical Reynolds number varied from sluggish flow to torrential flow with 1.8 mm min^?1 rainfall intensity and was more than that under 0.5 mm min^?1. Reynolds number can be estimated by power function of slope length. And there was a positive correlation between runoff shear stress and both Froude number Fr and Reynolds number Re. We hope this study can provide scientific gist for soil erosion control under economic forest.     

淠河流域河源溪流鱼类空间分布格局及主要影响因素

淠河是安徽省内淮河右岸最大的支流,也是淮河中游重要的水源地.为了解淠河流域河源溪流鱼类的空间分布格局及其主要影响因素,本研究于2015年4—5月对6条河源溪流鱼类及其环境因子进行了调查.研究结果表明,6条溪流共采集鱼类19种,其中杂食性种类占57.9%,肉食性和植食性种类分别占26.3%和15.8%.所有种类中,宽鳍鱲(Zacco platypus)是主要优势种,绿太阳鱼(Lepomis cyanellus)为研究区域首次报道的外来入侵种.就6条溪流各样点的平均值而言,淠河西部3条溪流鱼类种类数及个体数均明显高于东部3条溪流,但重量却并没有类似趋势.Sorensen相似性分析表明,6条溪流鱼类组成具有较高相似性,且相对较小值主要位于高、低海拔溪流之间.除趋势对应分析二维空间排序与相似性分析结果一致.Pearson相关分析表明,影响鱼类种类数的主要是局域栖息地参数(包括海拔、流速、底质、水深、河宽和电导率)和溪流的空间位置参数(溪流级别、流量量级和下游量级);影响鱼类个体数和重量的均仅有局域栖息地参数中的底质因素.本研究结果可为淠河流域鱼类的保护和管理提供重要的基础资料.     

Sodicity effects on hydrological processes of sodic soil slopes under simulated rainfall

Soil salinization can occur in many regions of the world. Soil sodicity affects rainfall‐runoff relationships and related erosion processes considerably. We investigated sodicity effects on infiltration, runoff and erosion processes on sodic soil slopes for two soils from China under simulated rainfall. Five sodicity levels were established in a silt loam and a silty clay with clay contents of 8.5% and 46.0%, respectively. The soils, packed in 50 cm × 30 cm × 15 cm flumes at two slope gradients (22° and 35°), were exposed to 60 min of simulated rainfall (deionized water) at a constant intensity of 125 mm h^?1. Results showed that, for both soils, increasing soil sodicity had some significant effects on hydrological processes, reducing the infiltration coefficient (pr = ?0.69, P  < 0.01) and the quasi‐steady final infiltration rate (pr = ?0.80, P  < 0.01), and increasing the mean sediment loss (pr = 0.39, P  < 0.05); however, it did not significantly affect the cumulative rainfall to ponding (P  > 0.05). Moreover, increasing sodicity significantly increased the Reynolds number and the stream power (pr = 0.78 and 0.66, P  < 0.01, respectively) of the runoff, decreased Manning roughness and Darcy–Weisbach coefficient (pr = ?0.52 and ?0.52, P  < 0.05, respectively), but did not significantly affect the mean flow velocity, mean flow depth, Froude number and hydraulic shear stress. Stream power was shown to be the most sensitive hydraulic variable affecting sediment loss for both soils. Furthermore, as sodicity increased, the values of critical stream power decreased for both the silt loam (R ² = 0.29, P  < 0.05) and the silty clay (R ² = 0.49, P  < 0.05). The findings of this study were applied to a real situation and identified some negative effects that can occur with increasing sodicity levels. This emphasized the importance of addressing the influences of soil sodicity in particularly high risk situations and when predicting soil and water losses.     

A full-scale study of Darcy-Weisbach friction factor for channels vegetated by riparian species

In this article, an open channel flow resistance equation, deduced applying dimensional analysis and incomplete self-similarity condition for the flow velocity distribution, was tested using measurements carried out in a full-scale channel equipped with three types of riparian plants (Salix alba L., Salix caprea L. and Alnus glutinosa L.). In the experimental channel, having banks lined with boulders, the vegetation branches were anchored in a concrete bottom. For each species, the measurements were carried out with plants having different amounts of leaves, different plant density and plant area index. The relationship between the scale factor Γ of the velocity profile and the Froude number was separately calibrated by measurements carried out without and with vegetation. The component of Darcy-Weisbach friction factor corresponding to the riparian vegetation f_v was calculated as the difference between the measured friction factor value (channel grain roughness + vegetation) and that calculated for the channel without vegetation in the same hydraulic conditions. Using these f_v values, the relationship between the scale factor Γ and the Froude number was calibrated. In this last relationship, a scaling coefficient a varying with the investigated vegetation type was introduced. This coefficient, as expected, gives the highest friction factor values for vegetation having branches with leaves. The theoretical flow resistance law, coupled with the relationship for estimating the Γ function having a scaling coefficient different for each investigated vegetation type, allowed an accurate estimate of the Darcy-Weisbach friction factor (errors less than or equal to 20% for 82.6% of the investigated cases). Finally, for the investigated vegetation species that are characterized by a condition with few leaves or leafless, the scaling coefficient a resulted strongly related to the bending stiffness. This analysis demonstrated that the highest Darcy-Weisbach friction factors correspond to vegetation species characterized by the highest values of bending stiffness. The friction factor values calculated for this last condition are characterized by errors that were less than or equal to ±20% for 90.6% of cases.     

Characterizing supraglacial meltwater channel hydraulics on the Greenland Ice Sheet from in situ observations

Supraglacial rivers on the Greenland Ice Sheet (GrIS) transport large volumes of surface meltwater toward the ocean, yet have received relatively little direct research. This study presents field observations of channel width, depth, velocity, and water surface slope for nine supraglacial channels on the south‐western GrIS collected between July 23 and August 20, 2012. Field sites are located up to 74 km inland and span 494–1485 m elevation, and contain measured discharges larger than any previous in situ study: from 0.006 to 23.12 m³/s in channels 0.20 to 20.62 m wide. All channels were deeply incised with near vertical banks, and hydraulic geometry results indicate that supraglacial channels primarily accommodate greater discharges by increasing velocity. Smaller streams had steeper water surface slopes (0.74–8.83%) than typical in terrestrial settings, yielding correspondingly high velocities (0.40–2.60 m/s) and Froude numbers (0.45–3.11) with supercritical flow observed in 54% of measurements. Derived Manning's n values were larger and more variable than anticipated from channels of uniform substrate, ranging from 0.009 to 0.154 with a mean value of 0.035 ± 0.027 despite the absence of sediment, debris, or other roughness elements. Ubiquitous micro‐depressions in shallow sections of the channel bed may explain some of these roughness values. However, we find that other, unobserved sources of flow resistance likely contributed to these elevated Manning's n values: future work should explicitly consider additional sources of flow resistance beyond bed roughness in supraglacial channels. We conclude that hydraulic modeling for these channels must allow for both subcritical and supercritical flow, and most importantly must refrain from assuming that all ice‐substrate channels exhibit similar hydraulic behavior, especially for Froude numbers and Manning's n. Finally, this study highlights that further theoretical and empirical work on supraglacial channel hydraulics is necessary before broad scale understanding of ice sheet hydrology can be achieved. Copyright © 2016 John Wiley & Sons, Ltd.     

Anchor ice formation in streams: a field study

In northern steep streams anchor ice is commonly observed during winter, and plays a key role when considering in‐stream conditions. The understanding, however, of the nature of anchor ice formation is less understood, in particular, under natural conditions. In the following, observations of anchor ice formation in three stream environments with different physical characteristics are presented. Results demonstrate that anchor ice not only form in riffle areas, but also in shallow and slow running stream sections. No linkage between spatial distribution of anchor ice and calculated dimensionless numbers (Froude and Reynolds number) was found. Furthermore, analyses on growth and density showed that anchor ice may be distinguished by two main types. (1) Type I: Lower density forming on top of substrata. (2) Type II: Higher density forming between the substrata filling interstitial spaces. Distribution of anchor ice Types I and II suggests a relation between intensity of turbulence expressed by the Reynolds number, growth pattern and density. As anchor ice has both physical and biological implications on in‐stream environments, findings from the present study may be of particular interest to cold region freshwater stream management. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparing the stream re-aeration coefficient estimated from ANN and empirical models / Comparaison d'estimations par un RNA et par des modèles empiriques du coefficient de réaération en cours d'eau

Abstract

Dissolved oxygen (DO) is one of the most useful indices of river's health and the stream re-aeration coefficient is an important input to computations related to DO. Normally, this coefficient is expressed as a function of several variables, such as mean stream velocity, shear stress velocity, bed slope, flow depth, and Froude number. However, in free surface flows, some of these variables are interrelated, and it is possible to obtain simplified stream re-aeration equations. In recent years, different functional forms have been advanced to represent the re-aeration coefficient for different data sets. In the present study, the artificial neural network (ANN) technique has been applied to estimate the re-aeration coefficient (K ₂) using data sets measured at different reaches of the Kali River in India and values obtained from the literature. Observed stream/channel velocity, bed slope, flow depth, cross-sectional area and re-aeration coefficient data were used for the analysis. Different combinations of variables were tested to obtain the re-aeration coefficient using an ANN. The performance of the ANN was compared with other estimation methods. It was found that the re-aeration coefficient estimated by using an ANN was much closer to the observed values as compared with the other techniques.     

Contrasts among macrophyte riparian species in their use of stream water nitrate and ammonium: insights from 15N natural abundance

We examined the relevance of dissolved inorganic nitrogen (DIN) forms (nitrate and ammonium) in stream water as N sources for different macrophyte species. To do this, we investigated the variability and relationships between ¹⁵N natural abundance of DIN forms and of four different macrophyte species in five different streams influenced by inputs from wastewater treatment plants and over time within one of these streams. Results showed that ¹⁵N signatures were similar in species of submersed and amphibious macrophytes and in stream water DIN, whereas ¹⁵N signatures of the riparian species were not. ¹⁵N signatures of macrophytes were generally closer to ¹⁵N signatures of nitrate, regardless of the species considered. Our results showed significant relationships between ¹⁵N signatures of DIN and those of submersed Callitriche stagnalis and amphibious Veronica beccabunga and Apium nodiflorum, suggesting stream water DIN as a relevant N source for these two functional groups. Moreover, results from a mixing model suggested that stream water DIN taken up by the submersed and amphibious species was mostly in the form of nitrate. Together, these results suggest different contribution to in-stream N uptake among the spatially-segregated species of macrophytes. While submersed and amphibious species can contribute to in-stream N uptake by assimilation of DIN, macrophyte species located at stream channel edges do not seem to rely on stream water DIN as an N source. Ultimately, these results add a functional dimension to the current use of macrophytes for the restoration of stream channel morphology, indicating that they can also contribute to reduce excess DIN in streams.     

Wave hierarchies in alluvial river flows

Abstract

The long wave equations governing the flow in alluvial rivers and channels are considered. The linearized equations are re-cast in the form of a single equation of wave hierarchy type as discussed by Whitham (1974). The dynamic and kinematic waves are of third and second order respectively. Behaviour at the wave fronts is considered and a roll-wave type instability is revealed.

For stable flow, the theory is used to make both qualitative and quantitative predictions in the areas of short and long term floods, tidal waves and channel dredging.

The non-uniformity in the quasi-steady theory on bedform development [see, for example, Reynolds (1985)] as the Froude number, F, approaches unity is also discussed, and appropriate scalings are obtained to derive a theory which remains valid when F ～ 1.