Free Surface Flows and Transport Processes

As is well known, the origin of alternate bars and meandering remains a matter of debate in the literature. This chapter concerns the hypothesis previously raised by a number of authors that large-scale turbulence, and more specifically large-scale horizontal coherent structures (LSHCS’s), are the reason for their occurrence, or at least a contributing factor. In order to properly assess the validity of such hypothesis, it is necessary to first develop an understanding of the dynamics of LSHCS’s occurring in open-channel and river flows, and establish their characteristic scales. This work is motivated by this need. The work is to be viewed as an extension of recent experimental studies on LSHCS’s in shallow flows to the case of deep flows. Accordingly, a laboratory flow having width-to-depth ratio of 7.1, and conveyed in a 1 m wide and 21 m long straight channel, is investigated. The flat channel bed was formed by a coarse silica sand. Flow velocity measurements were carried out with a 2D SonTekTM Micro ADV. Several techniques are used to treat the velocity signals, including continuous wavelet transform and quadrant and spectral density analyses. Special attention is paid to the time and length scales of the LSHCS’s, the effect of superimposition of the LSHCS’s on the mean flow, and the variation of turbulence structure over the flow depth. To the best knowledge of the writers, this is the first work where LSHCS’s have been detected in a deep open-channel flow. The work is used also to shed light on why the initiation of meandering in alluvial streams is not always preceded by the occurrence of alternate bars.

This chapter discusses and illustrates ice concerns associated with hydraulic engineering for water conveyance systems in cold, mountainous terrain, and aims to draw attention to the potential problems that may occur when water changes from liquid to solid. Hydraulic engineering involves liquid water, and commonly comprises the design of open-water channels (or reservoirs) linked to pressurized conduits (pump-lines, penstocks, siphons, and tunnels) that pass water down, up, over, or through mountainous terrain. The topics covered herein address fundamental aspects of ice formation and behavior. An important consideration is the relationship between the freezing temperature of water and flow pressure. Flow pressure can vary substantially in closed-conduit portions of hydraulic systems. The primary engineering concern is that ice formation should not hamper the operation of the system or its component parts. Should a concern arise about the operation of the system, the concern should be mitigated by re-designing the system or its parts, and managing the system by adjusting flow rates, and by monitoring water temperature at key locations.

Mathematical and computational models in river and canal hydraulics often require data that may not be available, or it might be available and accurate while other information is only roughly known. There is considerable room for the development of approximate models requiring fewer details but giving more insight. Techniques are presented, especially linearisation, which is used in several places. A selection of helpful mathematical methods is presented. The approximation of data is discussed and methods presented, showing that a slightly more sophisticated approach is necessary. Several problems in waves and flows in open channels are then examined. Complicated methods have often been used instead of standard simple numerical ones. The one-dimensional long wave equations are discussed and presented. A formulation in terms of cross-sectional area is shown to have a surprising property, that the equations can be solved with little knowledge of the stream bathymetry. Generalised finite difference methods for long wave equations are presented and used. They have long been incorrectly believed to be unstable, which has stunted development in the field. Past presentations of boundary conditions have been unsatisfactory, and a systematic exposition is given using finite differences. The nature of the long wave equations and their solutions is examined. A simplified but accurate equation for flood routing is presented. However, numerical solution of the long wave equations by explicit finite differences is also simple, and more general. A common problem, the numerical solution of steady flows is then discussed. Traditional methods are criticised and simple standard numerical ones are proposed and demonstrated. A linearised model for the surface profile of a stream is obtained, also to give solutions without requiring detailed bathymetric knowledge.

Zegrze Reservoir was built on the Narew River and its tributary Bug River in the period 1957–1963. The hydraulic conditions at the Bug River mouth had been studied with the use of hydrodynamic two dimensional model CCHE2D. Distribution of the sediment transport was recorded by the AISA hyperspectral scanner and shown as a remote sensing index of Red Edge Normalized Difference Vegetation Index—NDVI₇₀₅ and Total Suspended Solids—TSS. Results of suspended sediments concentration from the CCHE2D model had been converted to a graphical (vector) form and compared with remote sensing indexes. Relationship between remote sensing indexes and CCHE2D model simulation results had been evaluated using statistical method of Spearman correlation.

The Vistula (Wisła) is the largest Polish river, which flows from the south to north through the whole Poland. Its source is in the south in the mountains and the mouth in the north at the Baltic Sea. The Vistula catchment includes 54% of Polish territory. The river was always a very important economic, cultural and even defensive axis of the country. The whole course of the river was changing through the time, but most important changes appeared within its estuary area in the XIX century. These were natural and anthropogenic changes, which resulted mainly from severe ice jam floods, very complicated hydraulic course of the Vistula over its estuary area and severe hydro-meteorological conditions. They caused high social and economic losses. The engineering solution to solve this problem was in the form of an artificial Direct Channel (Przekop) to the sea. This well designed and realized engineering solution serves well till the present time. Development of Direct Channel had to be accompanied by efficient ice-breaking and additional hydraulic structures. The paper presents the description of the Vistula River and its catchment, its estuary area called Żuławy, floods in the XIX century in this area, and finally the design and execution of Direct Channel together with other engineering structures. The paper ends with conclusions concerning the past, present and future.

In this paper, a method for numerical analysis of steady gradually varied flow in channel networks with hydraulic structures is considered. For this purpose, a boundary problem for the system of ordinary differential equations consisting of energy equation and mass conservation equations is formulated. The boundary problem is solved using finite difference technique which leads to the system of non-linear algebraic equations. The arising system is solved with modified Picard method. The presented methodology is applicable to any channel network type and any type of hydraulic structure.

In this paper, an extension to a recently introduced model for liquid-solid phase changes in free surface flow is explored by adding a new floating body simulation algorithm. The algorithm, based on the immersed boundary formulation of the Lattice Boltzmann method, is applied over a time dependent, arbitrary shaped, floating or immersed body in a free surface flow. Here, simulation and laboratory experiment of a floating ice cylinder was carried out to examine the accuracy of the proposed model. Numerical results confirm that the proposed algorithm satisfies the mass conservation, which has been difficult to be handled, and computes the involved free surface and heat transfer with reasonable accuracy.

Flow through submerged vegetation has been an active area of research due to its immense importance in the field of flood control, storm water management, soil erosion control, natural and manmade wetlands. But in situations of lower flow rate, the vegetation emerges out of the flow, rendering it the case of flow through emerged vegetation which also plays a significant role in the above-mentioned cases of practical applications. In the present study, the flow through rigid, emerged vegetation over a sinusoidal bed with small amplitude has been investigated. Biot’s equation of poro-elasticity has been applied to get the governing equations of the 2-D flow which have been solved analytically by the perturbation method to get the velocity field. Further, the solutions for the vertical shear stress distribution and the bed shear stress are obtained and the effects of the vegetation density on the velocity and shear stress are analyzed. The results indicate that the bed form also affects the longitudinal component of velocity significantly when the vegetation is less dense. The difference between the maximum and minimum velocity of flow near the trough and crest is almost 30%.

Constructed wetlands for wastewater treatment are increasingly recognized as a valid alternative to conventional water treatment methods with a high ecological value. Sediment transport and deposition processes play a key role in determining the treatment performance and the morphological evolution of a wetland, and must be carefully considered both in the design and the maintenance phase. This work presents a 2-D numerical study of the effect of vegetation density on sedimentation in wetlands. A depth-averaged hydrodynamic and mass transport model was applied to a rectangular wetland with uniform vegetation density and flat topography. Sediment settling and resuspension are represented in the model by a first-order source/sink term that depends on grain size and shear velocity. Results show that, for the same inflow discharge, the removal efficiency for relatively small grain sizes is lower in wetlands with higher vegetation density. This is a consequence of the more uniform flow distribution found in more densely vegetated wetlands. However, the condition of total removal of suspended sediment is achieved for higher grain sizes in more sparsely vegetated wetlands, meaning there is a range of relatively large grain sizes for which the removal efficiency is higher for higher vegetation densities.

Methods to estimate the mean surface velocity of shallow turbulent flows remotely are advantageous with respect to traditional measurement techniques because of their low cost, and little maintenance requirements. The measurement of the airborne acoustic field scattered by the water surface in time allows the reconstruction of the surface elevation at one location, based on the stationary phase method. Experimental data presented in this paper shows that when the mean surface velocity is larger than the minimum phase velocity of gravity capillary waves, the frequency power spectra of the free surface elevation in these flows scale almost linearly with the product of the wavenumber of the stationary waves and of the mean surface velocity. This scaling is exploited in order to estimate the mean surface velocity remotely, based on the remote acoustic measurement of the elevation with two ultrasonic transducers. This observation paves the way for the development of a new range of acoustic sensors that can measure the mean surface velocity of shallow turbulent flows remotely for a range of sub critical flow conditions.

Numerous studies have focused on flow and mixing within cylinder arrays because of their similarity to vegetated flows. Randomly distributed cylinders are considered to be a closer representation of the natural distribution of vegetation stems compared with regularly distributed arrays. In this study the flow fields associated with two arrays of regularly and randomly distributed cylinders are modelled in two dimensions, using ANSYS Fluent 16.1. The RSM turbulence model is used to model the turbulence closure, and all the variables are discretized using the second order upwind method. The resulting flow fields are used to run the solute transport model to characterize mixing within each geometry. For the same stem diameter and solid volume fraction, greater dispersion is evident in the random cylinder array compared with the regular array. Dispersion coefficient values are compared with those reported in the literature and a good agreement is shown. Turbulence length scales estimated from the velocity profiles and optimized dispersion coefficients are close to the cylinder diameter, which is in agreement with theories in the literature.

Groyne arrangements had been subject of numerous studies, which demonstrate that the first groyne plays a crucial role on the hydraulic behavior of the whole arrangement. This contribution presents the application of two 3D numerical techniques (RNG and LES) to compute one single sharp-groyne field in a rectangular channel. In the laboratory, flow velocities and water levels were measured in order to calibrate and verify the accuracy of the numerical models. Two turbulence parameters, namely the Reynolds Shear Stresses in the XY-plane and the Turbulent Kinetic Energy, were estimated and compared. Both numerical techniques present good agreement with the time average velocity components recorded in the laboratory. Nonetheless, as expected, the Large Eddy Simulation (LES) is more appropriate for the computation of turbulence characteristics, but more expensive in terms of computational costs.

A term expressing heat exchange between water and air is often present in models of thermal pollution spreading in rivers. The importance of this term depends strongly on temporal and spatial scale of the process as well on meteorological and hydrological conditions. Although heat exchange between the water and atmosphere has been studied for many years, its determination is still difficult in practical cases, and different simplifications are considered in practice. The objective of this study was to verify which of the input data needed for the net heat flux calculations are of utmost importance and which of them influences its final value most significantly. The analyses have been performed for several data sets collected in natural conditions.

A semi-empirical model is presented to estimate the time variation of scour depth at downstream of pier when two piers are arranged in tandem arrangement under clear water scour condition with uniform sediments. The methodology developed for computing the time variation of scour depth is based on the concept of the conservation of mass of sediment, considering the primary horseshoe vortex system to be the main agent of scouring and assuming a layer-by-layer scouring process. The proposed model agrees closely with the reported experimental data of time variation of scour depth at downstream piers in tandem pier arrangements under clear water condition with uniform sediments.

Water structures are usually used to stabilise river bed, although they also are a cause of degradation processes like erosion and scouring. The aim of this study was to correlate scour geometry, characterized by the scour medium and maximal depth and its length with hydraulic and granulometric properties. The study presents results obtained for three laboratory models (with and without weir flow) with partially or totally erodible bed, with median grain size d₅₀ = 0.91 mm in clear-water and live-bed conditions. The experiment duration was sufficient to obtain equilibrium, stable scour shape. Analysed relationships were parameterized using linear and exponential functions. The intensity of the sediment transport was investigated using the modified principle of fluvial hydraulics—the Lane’s relation, originally derived from basic rules of the sediment transport as a qualitative expression.

Transportation of slurries in pressure pipelines is an example of a complex flow due to specific parameters of transported medium. For practitioners, the economy of designing and maintenance is usually the most important factor. For this reason, most of hydrotransport installations are fairly simple; however, they become more vulnerable to negative effects of the transient flow which can occur in pressure pipelines. As the consequence, the phenomenon may cause major damage, and thus, it should be precisely described. A deep analysis of transients in slurries is crucial, both from theoretical and practical points of view. In this paper, the experimental investigation of pressure wave celerity during the transient flow of slurries in the high density polyethylene pressure pipe was described. The value of this celerity has a significant influence on the pressure changes in the pipeline, and thus, its correct determination is crucial to calculate the actual maximal pressure increases or decreases. To achieve the aim, two sets of the physical tests were performed. The first series were carried out with use of a physical model, enabling the measurements of pressure characteristics caused by a rapid valve closure. The experiments were accomplished both for slurries of different densities and for water. The second series were carried out in a real hydrotransport installation. The analysis of the experimental data was compared with the theoretical equation for the wave celerity. Experimental data indicates a huge difference compared to the theoretical values of celerity. The results confirm the necessity for revision of the theoretical expression for the wave celerity.

The article presents a study on the influence of spatial distribution of boulders placed in the main channel on parameters of flow conditions. Restoration guidelines recommend boulders structures but engineering solutions must be individually adapted to local situation. The depth-averaged 2D numerical model of unsteady, free-surface flow in open channels was used to calculate spatial distribution of velocity magnitude, slope of water surface level and water depth. The impact of individual boulder on the flow conditions in river channels increases through the group arrangement. Model of the Wisłoka River section was changed by implementation of boulders in various configurations: a group of three or four placed in triangles or rhomboids, openwork deflectors, groups located by the banks, groups located alternately to form a curvilinear thalweg. The effect of boulders structure on velocity spatial distribution along the channel was calculated for discharge Q_10-day = 15 m3 s−1. Impact of single boulder structures on flow velocity is visible up to 20–30 m and increases for multiple single boulders structures up to 30–60 m. In addition, stability of individual boulder for discharge Q_1% and influence the flood hazard were tested.

The paper presents the analysis of the water hammer phenomenon in a steel pipeline with inserted fiber optic cable. Specifically, pressure wave velocity of the phenomenon is considered. The derivation of formula, which is presented, allows to calculate pressure wave velocity in the case where a cable with different Young’s modulus compared to the elasticity of the pipeline is inserted into it. The derivation was carried out using the mass balance. The results of experimental tests conducted using three different fiber optic cables are presented. Experimental studies show that inserting a cable into a pipeline has an attenuating effect on water hammer phenomenon.

The differential equation of the bed sediment movement in clear-water scour conditions was used and a new method for equilibrium time of scour calculation at water engineering structures with flow separation at the structure in clear-water scour conditions was elaborated. The proposed threshold criteria for equilibrium time of scour known from the literature are only depending on the size of the hydraulic structure, and not on hydraulic parameters of the flow. Ratio of the recalculated critical flow velocity to the local one at the head of the water engineering structure was proposed as the hydraulic threshold criterion in equilibrium time of scour calculation. Calculated test data revealed that with an increase in flow contraction rate and with an increase in approach flow Froude number, equilibrium time of scour increases as well. To verify the developed equilibrium time of scour evaluation method, calculated time of scour values were compared to computer modelled ones, and the results showed good agreement. This calculation method can be applied to water engineering structures with flow separation at the structure at steady-flow and clear-water conditions.

Elongated piers are a commonly found geometry in bridge pier design. This paper addresses the study of the flow around an elongated bridge pier, since not many studies exists concerning this geometry. To better understand the features of such pier geometry a set of measurements made upstream and downstream of an elongated bridge pier are presented. Mean and turbulent variables are presented and emphasis is given to the flow downstream of the elongated bridge pier. Results show a clockwise recirculation pattern downstream of the bridge pier and Strouhal numbers higher than those found for a circular cylinder. Along the flow axis, turbulent fluctuation clouds change in shape, when moving further downstream from the pier.

This paper presents results from a set of laboratory measurements of the roughness geometry function and subsurface porosity at different spatial scales and with different beds using the water displacement method. For water worked gravel beds, the roughness geometry function was determined in both the interfacial sublayer and subsurface layer while for non-water worked bed configurations the vertical variation of porosity was evaluated from the manually created bed surface to the bottom, i.e. solely within the subsurface layer. The results show that the capillary action in sediment beds can have a significant influence on the porosity-values at the bed surface and the transition to a flat subsurface bottom as it was found that the capillary action over-/underestimates the porosity close to the gravel bed bottom and surface, respectively. The results are subsequently used to discuss recent findings reported in the hydraulic engineering literature in regard to the vertical variation of porosity.

The paper presents the numerical modelling of the hydro-morphological evolution of a 10 km reach of the Po River in Italy. The simulation is performed with the freeware code iRIC, recently developed by an international community of scientists and practitioners. Starting from a non-detailed description of the studied area and using synthetic data, the reach has been modelled adopting a 2-D solver. Based on a Digital Elevation Model of the area, the domain is discretized by an unstructured grid with triangular meshes. First results show a promising capability of the model in reproducing the behaviour of the reach, both in terms of liquid flow and morphodynamics, if compared with historical data measured along the watercourse and reported in literature. In the future, additional simulations will be performed, enlarging the studied area and using detailed input data measured with traditional and innovative techniques.

Measurements of a 3D flow velocity field were conducted in lowland sandy bed river in Poland in two experiments during summer to check reliability of data gathered with the new model of Acoustic Doppler Velocimeter (Vectrino Profiler) in proximity of aquatic plants. For the purpose of this study a platform was built, on which two such velocimeters were mounted. This allowed for simultaneous measurements of flow velocity in front of and behind a single patch of submerged aquatic plants. Despite the promising readings from the first measurements, the results showed unexpected shapes in mean velocity profiles. The second experiment showed good agreement of signals from both devices, but it also revealed major differences in data quality compared with the first experiment. Further analysis showed that only few of all cells from each 35-cells section, which were simultaneously recorded by Vectrino, contained data with good characteristics of signal. The main results of this study showed that use of the Vectrino Profiler in natural conditions requires each time different setup, more densely stacked sections in each profile and constant changes of velocity range during the experiment to achieve best results.

The ‘-3’ scaling law of sand waves has often been verified in studies dealing with statistical properties of sand beds. Most of the data used for this verification were measured in laboratory studies in which it is possible to reach equilibrium conditions. Large scale rivers, on the other hand, are rarely characterized by steady flow conditions which means that true equilibrium conditions are special cases and a deviation from the ‘-3’ scaling law may therefore be expected. This issue is investigated in the present study by the analysis of the spectral behavior of river bed surfaces of the Elbe River in Germany. The emphasis of the study is placed on the spectral behavior at small wavelengths. The results show that the spectral behavior at small wavelengths deviates from the ‘-3’ scaling law and that this spectral region can be characterized by steeper slopes. The relationship between the spectral characteristics at small wavelengths and flow discharge is subsequently analyzed. The overall results support the hypothesis that the development of secondary dunes affects the spectral behavior at small wavelengths.

This work aimed to examine the impact of rapid hydraulic structures on water temperature and dissolved oxygen concentration in the Porębianka mountain stream. This has been achieved by measurements of hydraulic characteristics and physiochemical properties of water such as water temperature and dissolved oxygen concentration. It has been shown that rapid hydraulic structures exhibit a large spatial diversity in morphology and flow paths, that manifests in the spatial heterogeneity of thermal conditions and oxygen concentrations at a single structure scale. The results have demonstrated that pools between the rapid have higher oxygen concentrations when compared to the rapid region. The highest concentrations of oxygen occured in pools located close to the upstream edge of the rapid ramp where the flow undergoes gradual acceleration. Elevated concentrations of dissolved oxygen were also observed in the dissipation basin. The lowest concentrations were observed at stream banks. The results emphasise the relative importance of site-specific characteristics on physiochemical properties of flow, which might help to understand multi-scale processes across rivers and improve future plans of restoration practices in mountain streams.

The temporal retention in storage zones (SZs) has a strong influence on mass transport processes in natural streams. It has been shown that solute retention affects solute breakthrough curves (BTCs) by producing longer tails and thereby increasing their skewness. In terms of ecological effects, this retention increases the contact time of solute with aquatic interfaces and living species, which can lead to degradation of eco-systems when the transported substances are pollutants. An important question that arises is whether the currently available metrics can adequately represent complex retention processes. In this study, we examine the performance of two existing metrics: the hydrological retention factor (R _H ) and the fraction of median travel time due to transient storage (F _med ). The results presented are based on two conservative tracer tests. The tracer tests were performed in streams with distinct morphological, sediment composition, vegetation and hydraulic characteristics. The recorded concentration-time series were used to derive storage zone parameters such as storage zone area, exchange coefficient and mean residence time. The storage zone parameters were computed using a multiple storage zone model STIR with two separate exponential residence time models for transient storage, representing short timescale (STS) and long timescale storage (LTS) processes. The retention metrics were estimated separately for short and long timescale retention, and for the combined retention. The cross-correlation between the retention metrics and the storage parameters was analyzed using Pearson’s R- and significance p-values. In general, the results reveal a poor correlation between retention metrics and storage zone parameters, except for the exchange rate associated with long timescale storage, α₂. A strong cross-correlation is instead found between the retention metrics.

Experimental investigation was carried out to investigate the flow turbulent structure, including the Reynolds stresses distribution in non-uniform sand bed channels with and without seepage. Steady flows over non-uniform sand bed channel were simulated experimentally with downward seepage applied through the boundary. Measured time average velocity and Reynolds stresses increase with the presence of seepage. The quadrant analysis suggests that the relative contributions of bursting events increased throughout the flow layer and the thickness of the zone of dominance of sweep event increases with seepage which is responsible for increment in bed material transport. The mean time of occurrence of ejections and sweeps in downward seepage are more persistent than those in no seepage.

Due to the abundant runoff and sediment flux from the Yellow River, the Yellow River Delta (YRD) is one of the quickest continent-building areas worldwide. The YRD land area growth rate was controlled mainly by the amount of provided runoff and sediment. In this paper, the runoff and sediment load of Lijin hydro gauge station, located at the entrance of the YRD, are selected as the representatives, and the relationship between the supplements of the water/sediment and the land area is analyzed by correlation methods; besides, the variation trends of the incoming runoff and sediment load are illustrated based on the Mann–Kendal statistics test. The results indicate that, in the period of record, the annual land area is in perfect linear correlation with the accumulated annual runoff, as well with the accumulated annual sediment load; both the annual runoff and annual sediment load fluxes from Lijin station are in significantly decreasing trends. At last, considering the crisis the YRD faced, rational allocation of the water and sediment resources is put forward.

In the paper a one-dimensional riverbed model is proposed. In the model the bed load sediment transport is described by an analytical formula. This formula doesn’t contain phenomenological parameters and takes into account the influence of the bed shear stress, the local bed slope, granulometrical and physical-mechanical parameters of the bed material. Three types of riverbed problems are solved by using the proposed model: the problem of bed degradation under the influence of the purified water flow, the problem of bed aggregation and the problem of the trench evolution under the influence of the transit flow. The comparison analysis of the predicted data with the established experimental data and the data obtained by the other models was carried out. It was shown that the proposed model adequately describes the bed evolution; in all three problems, the accuracy of the predicted data is sufficient for practice.

Numerical modeling of changing parameters on a gravel bar during different discharges in a small mountain river is presented here. The study bar is one of the best developed bars of the upper Wisłoka. Within its reach, the river may erode its banks and transport bed material. Flowing out from the Magurski National Park, the Wisłoka may be assumed as being close to a natural river. As fluvial processes are very dynamic there, the bar and channel transformations occur every year. Granulometry measurements demonstrated high variation of bed material composition in different parts of the bar and the channel. The bed material was classified as fine gravel, coarse gravel, cobbles, and coarse sand. This simulation was performed based on a 2015 measurement campaign; however, in situ measurements were started in 2008. From among a wide spectrum of parameters yielded by numerical simulations, the study focused on average vertical velocity and bed shear stresses. They were compared to critical parameters of the bed material movement. The simulations were performed for different flows, from low discharges to bankfull ones, and they indicated potential dynamic changes in the bed activity.

The presented research analyses the impact of deflectors on sediment transport processes. The basis for analysis is a hydrodynamic model of downstream part of the Flinta river. The geometry reproduction was performed using spatial data: digital elevation model (DEM) and cross-sections of considered reach. The computations were calculated in HEC-RAS 5.0.1, a common software used to calculate water surface profiles and sediment transport. In the research, two calculation variants were analysed: (1) with initial geometry of channel, and (2) with geometry after introducing deflectors. In order to take into account uncertainty, five scenarios of 10-year flow hydrographs were tested. To calculate the intensity of sediment transport, the Engelund-Hansen formula was used. The results suggest a possible initiation of local scours near the structures.

This paper presents the results of a numerical model study on the effect of ice on the proposed bridge piers in the Vistula River outlet and its effect on flow conditions in the river. The model DynaRICE is used in this study, which is a two-dimensional hydro-ice dynamic numerical model developed for dynamic ice transport and jamming in rivers. To simulate river hydrodynamics in the vicinity of the bridge piers, two-dimensional numerical model basing on finite volume technique was also used. Simulation results indicated notable effect of new structure on water and ice flow pattern. Ice forces on structures were also determined, but the load was not considerably high.

Using 25 tracer experiments, parameters of the transient storage model (TSM) were evaluated for a reach of the river Brock in north-west England with the primary aim of investigating their dependence on flow rate. Since only a very few previous studies have considered this issue, these new results aid our understanding on how the TSM could be applied to a reach at flow rates beyond the range of flow rates for which observations of solute transport exist. Velocity increased with increasing flow rate in a manner consistent with current knowledge. In contrast, and unexpectedly, the dispersion coefficient reduced (weakly) with increasing flow rate and the values were rather scattered. The transient storage exchange rate increased with increasing flow rate, which corroborates some of the sparse existing knowledge of this parameter’s behaviour. The ratio of transient storage area to main channel area was essentially constant over the range of flow rates examined, which is consistent with some studies on single reaches.

The paper presents results of analysis of the industrial sewage discharge influence at km 688 + 250 of the Vistula River on water quality. During the analysis, two-dimensional models of flow, impurities and temperature transport were used. Hydrological conditions of the analyzed section of the river, characteristic flows and bathymetry of the riverbed in the first instance were defined. Calculations of velocity distribution at steady flow conditions were carried out for the mean of the observed low discharges MLQ = 293 m3 s−1. For this purpose, a simplified two-dimensional kinematic model for variable depth of flow was used. The analysis of the impact of the discharge of impurities in steady flow conditions was performed by solving an equation of unsteady transport of pollution. Numerical simulations were carried out for pollution in the form of a non-degradable substance (tracer) and water temperature higher than measured in summer and winter conditions. The analysis included distribution of concentration of contaminants at the discharge site, as well as its range along the river bank.