Previous studies on longitudinal solute transport in a pipe during acceleration from laminar to turbulent flow highlighted a disaggregation of the tracer cloud resulting in two peaks occurring downstream from a single pulse injection. It was hypothesized that the disaggregation was caused by the spatially nonuniform acceleration of flow at different radial locations. This study improves the previous understanding of solute transport during accelerating flow using novel laboratory measurements of pipe cross-sectional tracer distribution from planar laser-induced fluorescence and radial velocity profiles from an ultrasonic velocity profiler. Disaggregation of the tracer cloud was observed, with the tracer not being uniformly distributed within the cross-section at the first peak but cross-sectionally well-mixed at the second peak. The relative magnitude of the first peak, compared with the second peak, decreased with the time of injection (and therefore with increased Reynolds number) after the start of the acceleration. Radial velocity profiles showed that the central core of the flow exhibited a smooth, linear increase in velocity compared with the flow closer to the pipe boundary. The data also revealed, for the first time to our knowledge, that the transition time to different flow regimes increased with distance downstream. A model based on the 2D advection-dispersion equation, parameterized using experimental data, was employed to describe the flow and mixing processes during the acceleration. In addition to the combined effects of the radial velocity profile and radial diffusion coefficient, this study confirms that it is essential to also include the delay in the transition time at downstream locations to create the observed disaggregation.

In vegetated flows a reliable estimation of flow scales is crucial to understand and model mixing processes. This study presents velocity maps obtained using particle image velocimetry (PIV) within a cylinder array (diameters 4 <= d <= 20 mm) designed to mimic real emergent vegetation. Tests were undertaken over a comprehensive range of stem Reynolds numbers (100 <= Red <= 900), intended to characterize time-dependent hydrodynamic features, including their interactions. Time-averaged flow heterogeneities are found to be independent of Red. Vortex dynamics are seen to dominate turbulent fluxes of momentum, and are the relevant coherent structures driving mass transport. The range of characteristic time- and length-scales from these coherent structures was quantified and shown to be determined by the distribution of spaces between cylinders. This is due to: (1) neighboring cylinders forming clusters, leading to larger flow structures, and (2) the maximum size of the flow structures being constrained by the inter-stem space. It is concluded that the Delaunay criterion provides practitioners with a good approximation to the distribution of flow scales in vegetated flows.

Microbially mediated transformations, such as nitrification and biodegradation, play a crucial role in removing pollutants from rivers. Although in-stream removal rate coefficients are often assumed to be spatially and temporally constant, they are likely affected by the channel shape and size because these factors control contact between the water column and fixed biofilms. Here, we test the hypothesis that transformation rate constants are inversely proportional to the hydraulic radius (R: ratio of the channel cross-sectional area to wetted perimeter) in dye tracing experiments conducted in two U.K. rivers with contrasting morphologies: (1) the River Maun (shallow: mean bankfull R = 1.25 m) and (2) the River Calder (deep: mean bankfull R = 3 m). In each case, a slug of rhodamine WT was injected upstream of a wastewater outfall, and samples were collected downstream, staggered by the rhodamine travel time. Rate constants were derived for sucralose, ammonium, caffeine, and linear alkylbenzenesulfonate. Sucralose (persistent, hydrophilic, and exclusively of wastewater origin) was used as a conservative tracer to adjust model fits for dilution. Higher rate coefficients were observed for all biotransformed pollutants in the Maun compared to the Calder, supporting the hypothesis and highlighting the need to consider geomorphology in models of chemical behavior.

Understanding solute transport in pipe flows is essential for ensuring consistent water quality throughout the entire drinking water supply network. This study used four planar laser-induced fluorescence (PLIF) units for the first time to quantify the cross-sectional concentration distribution resulting from a single pulse of tracer injected at an upstream location under both steady and accelerating flow conditions. Compared with conventional fluorometers, PLIF provides a better measure of the cross-sectional mean concentrations because it allows the cross-sectional distribution of the tracer to be quantified. Under steady turbulent flow conditions, the tracer was cross-sectionally well-mixed, and the concentration uniformity increased with increasing Reynolds number. In laminar flows, as a result of minimal radial mixing, the tracer exhibited a spatial distribution created by the longitudinal differential advection, transforming from a central core to an annulus, which expanded toward the pipe boundary. Under accelerating flows, the temporal concentration profiles displayed two peaks and the tracer close to the source was not cross-sectionally well-mixed. With increasing discharge, the tracer became cross-sectionally well-mixed while retaining the two peak profiles. These results have implications for water quality modeling in unsteady conditions, especially in domestic plumbing, when boundary and biofilm interactions control important processes.

Transverse dispersion is of interest in natural watercourses, especially near outfalls. The application of simple analytical solutions to the transverse advection-dispersion equation in these scenarios, however, is challenging due to variations in channel characteristics. Thus, a new method has been developed for averaging reach characteristics to account for longitudinal variability when using analytical solutions to the advection-dispersion equation by combining travel time and length weighting. The new 'reach unification' approach incorporates the characteristics (such as velocity, width, or dispersion coefficient) of each different sub-reach to the equivalent single reach values needed to make a direct downstream prediction. To demonstrate reach unification, synthetic concentration profiles from a continuous injection into a simplified rectangular channel with three sub-reaches of varying velocity, depth, and friction, have been generated using finite difference modelling. The characteristics of these sub-reaches when combined with reach unification made perfect downstream analytical predictions, confirming the approach. The use of the streamtube model to represent changes in channel width is investigated. It is also shown that reach unification is of significant benefit to the inverse problem, analysing recorded concentration profiles to estimate the dispersion coefficient and relating it to reach characteristics.

There has been a recent increase of interest in sewer network water quality, both for pollutants and wastewater epidemiology. Of particular interest is the ability to perform cost-effective small-scale monitoring to understand the sewer network and perform source localization (the process of identifying the sources of materials of interest within the network), enabling prioritization of combined sewer overflow (CSO) interventions and targeted response to the detection of infectious diseases. Rhodamine WT fluorescent dye tracing was carried out in the combined sewer networks of four UK cities, for which network geometries were available. Over 100 dye concentration profiles were recorded, from which discharge, travel time (velocity), and dispersion were quantified. A simplified hydraulic and water quality (conservative solute transport) modeling approach was used to investigate dispersion further. A theoretical method for calculating dispersion over a reach with nonuniform properties was derived and used with the models and recorded data to develop a method for estimating the dispersion coefficient in sewers. Novel simultaneous injections into multiple manholes within one sewer network were conducted. Modeling of these injections validated the modeling approach and explained the measured concentration profiles, demonstrating both the potential of hydraulic and solute transport modeling and the new dispersion coefficient predictor for source localization. Such modeling can be used to develop sewer network "fingerprints" and source location probability plots based on residence time distribution (RTD) theory to maximize information from limited water quality monitoring. This will aid managers and operators in identifying potential intermittent sources of material within the network.

Vegetation notably influences transport and mixing processes and can thus be used for controlling the fate of substances in the hydro‐environment. Whilst most work covers fully vegetated conditions, the novelty of this paper is to focus on flows with real‐scale flexible willow patches. We aimed to investigate how longitudinal dispersion varies according to the spatial distribution, density and coverage of the patches and to evaluate the explanatory power of predictors that consider the hydraulics, vegetation and channel geometry. Salt tracer experiments were performed in a trapezoidal channel where we established 3–4 m long and 1–1.6 m wide patches of artificial foliated willows that reproduced the shapes and plant densities observed on woody‐vegetated floodplains. We examined sparsely distributed patches with low areal/volumetric coverage of 6–11%, and non‐vegetated conditions for reference. Flow depths and surface widths were 0.7–0.9 and 6–7 m, respectively, and the mean flow velocities ranged at 0.3–0.6 m/s. The emergent patches generated from a negligible to over a four‐fold increase in the longitudinal dispersion when compared with non‐vegetated conditions. The patches with a preferential location in low‐velocity areas, such as near banks, or with a high plant density and a blockage of the cross‐sectional flow area ⪆0.4, led to the largest dispersion and residence times. Patches under such configurations enhanced the normalized differential velocity defined as the difference between the highest (90th percentile) and lowest (10th percentile) cross‐sectional flow velocities divided by the mean velocity, thus increasing shear dispersion. As existing analytical predictors failed to estimate the effect of different patch configurations, we proposed the change in the normalized differential velocity between vegetated and corresponding non‐vegetated conditions as a basic predictor of the reach‐scale longitudinal dispersion coefficient under patchy vegetation. In contrast, we observed no clear relationship between flow resistance and dispersion. Thus, our findings indicated that bankside vegetation may allow for reduced peak concentrations and lengthened residence times, supporting pollutant management, while ensuring good flow conveyance. Such rare field‐scale analyses improve the estimation of solute transport in real vegetated flows.

Numerous studies focus 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. This study builds on previous work based on a single, fixed, cylinder diameter to consider non‐uniform cylinder diameter distributions. The flow fields associated with arrays of randomly distributed cylinders are modeled in two dimensions using the ANSYS Fluent Computational Fluid Dynamics software with Reynolds Stress Model turbulence closure. A transient scalar transport model is used to characterize longitudinal and transverse mixing ( D x and D y ) within each geometry. The modeling approach is validated against independent laboratory data, and the dispersion coefficients are shown to be comparable with previous experimental studies. Eight different cylinder diameter configurations (six uniform and two non‐uniform) are considered, each at 20 different solid volume fractions and with seven different transverse positions for the injection location. The new dispersion data cover a broad range of solid volume fractions, for which simultaneous estimates of D x and D y have not been available previously. There are no systematic differences in non‐dimensional D x and D y between uniform and non‐uniform cylinder diameter distributions. When non‐dimensionalized by cylinder diameter, both dispersion coefficients are independent of solid volume fraction. When non‐dimensionalized by cylinder spacing, both longitudinal and transverse dispersion can be described as linear functions of the ratio of cylinder diameter to cylinder spacing.

This study describes an artificial vegetation model, based on the morphological characteristics of real species, to study vegetated hydrodynamics and solute transport. A thorough description of the proposed morphology is given, alongside the system built to provide a full experimental characterization of velocity and solute transport. Although previous studies have focused on obtaining similar descriptions of the flow within artificial vegetated arrays, most are faced with the same physical constraints, namely, obstructions preventing uniform illumination around stems, so only velocity fields over small gaps are obtained. This limits the scope and level of detail of the obtained data. A custom-made LIF-PIV system is presented, with the potential to provide velocity and solute transport characterizations, that can help expand on the current understanding of mixing in emergent vegetation, over flow scales ranging from diameter to reach-scale variations in velocity and concentration. Data obtained confirms the capabilities of the system.

Temporal concentration profiles resulting from an injected pulse of fluorescent tracer were recorded at multiple locations along a pipe during controlled unsteady flow conditions. A linear temporal change in discharge over durations of 5, 10, or 60 s for both accelerating and decelerating flow conditions was studied. Tests were performed for flows that changed within the turbulent range, between Reynolds numbers of 6,500 and 47,000, and for laminar to turbulent flows, between Reynolds numbers of 2,700 and 47,000. Analysis of the data shows the limitations of employing steady-state routing of temporal concentration profiles in unsteady flow. Employing a flow weighted time routing approach, using tracer mean velocity and dispersion coefficients, provides accurate predictions of mixing in unsteady flow. For decelerating flows, longitudinal dispersion coefficients were lower than for the equivalent mean steady discharge. Previously unreported disaggregation of the tracer cloud was observed during all experiments accelerating from laminar to turbulent conditions.

Manholes in combined sewers may become surcharged during storm events, resulting in complex mixing conditions. Although manhole hydrodynamics are reasonably well understood, predicting mixing across a surcharged manhole remains a challenge. An analytical compartmental mixing model for manholes, based on jet theory, has been further developed and applied to generate cumulative residence time distributions (CRTDs), which describe mixing. The modeled CRTDs were compared with the experimentally derived CRTDs of over 850 manhole configurations to evaluate how well the new compartmental model represents physical processes. The model underpredicts short-circuiting in manholes with manhole diameter to pipe diameter ratios greater than 4.4 and consequently overestimates mixing. Otherwise, the modeled CRTDs show good agreement with the experimental CRTDs. The new compartmental model represents key manhole hydrodynamics that are not represented in current software modeling packages, which assume manholes are instantaneously well-mixed. The compartmental model provides good predictions of the experimental downstream concentration profiles, although with reduced peak concentrations in those manhole configurations where short-circuiting is not well-predicted. Despite this, the compartmental model still predicts concentrations downstream of a manhole in closer agreement with the recorded data than the complete instantaneously well-mixed assumption. As an analytical model requiring no inputs other than manhole geometry, the new compartmental model applies to a wide range of manhole configurations, is robust, and is useful for predicting manhole mixing in practical applications.

Transverse solute mixing across a vegetation generated horizontal shear layer was quantified using laser induced fluorometry techniques for artificial and real vegetation. A two-dimensional finite difference model (FDM) was developed to describe transverse concentration profiles for flows containing transverse variations in velocity and transverse dispersion, from a steady solute input. The FDM was employed inversely, to optimize the parameters describing the transverse distribution of the transverse dispersion coefficient for vegetation generated shear layers. When laboratory data are available, continuous function descriptions produce slightly improved FDM modelled solute concentration profiles compared with simplified step discontinuity velocity and dispersion inputs. When laboratory data are not available, estimates of step or continuous transverse distributions from other work enable concentration profiles to be predicted with a similar goodness of fit. This paper presents a validated, simple, robust finite difference model to describe the mixing of solutes in a channel containing marginal vegetation.

Pesticide losses from agricultural land to water can result in the environmental deterioration of receiving systems. Mathematical models can make important contributions to risk assessments and catchment management. However, some mechanistic models have high parameter requirements which can make them difficult to apply in data poor areas. In addition, uncertainties in pesticide properties and applications are difficult to account for using models with long run-times. Alternative, simpler, conceptual models are easier to apply and can still be used as a framework for process interpretation. Here, we present a new conceptual model of pesticide behaviour in surface water catchments, based on continuous water balance calculations. Pesticide losses to surface waters are calculated based on the displacement of a limited fraction of the soil pore water during storm events occurring after application. The model was used to describe the behaviour of metaldehyde in a small (2.2 km2) under-drained catchment in Eastern England. Metaldehyde is a molluscicide which has been regularly detected at high concentrations in many drinking water supply catchments. Measured peak concentrations in stream water (to about 9 μg L-1) occurred in the first few storm events after application in mid-August. In each event, there was a quasi-exponential decrease in concentration during hydrograph recession. Peak concentrations decreased in successive events - responding to rainfall but reflecting an effective exhaustion in soil supply due to degradation and dissipation. Uncertain pesticide applications to the catchment were estimated using land cover analysis of satellite data, combined with a Poisson distribution to describe the timing of application. Model performance for both the hydrograph (after calibration of the water balance) and the chemograph was good and could be improved via some minor adjustments in assumptions which yield general insights into the drivers for pesticide transport. The use of remote sensing offers some promising opportunities for estimating catchment-scale pesticide applications and associated losses.

In this paper, we develop and validate a rigorous modeling framework, based on Duhamel's Theorem, for the unsteady one‐dimensional vertical transport of a solute across a flat sediment‐water interface (SWI) and through the benthic biolayer of a turbulent stream. The modeling framework is novel in capturing the two‐way coupling between evolving solute concentrations above and below the SWI and in allowing for a depth‐varying diffusivity. Three diffusivity profiles within the sediment (constant, exponentially decaying, and a hybrid model) are evaluated against an extensive set of previously published laboratory measurements of turbulent mass transfer across the SWI. The exponential diffusivity profile best represents experimental observations and its reference diffusivity scales with the permeability Reynolds number, a dimensionless measure of turbulence at the SWI. The depth over which turbulence‐enhanced diffusivity decays is of the order of centimeters and comparable to the thickness of the benthic biolayer. Thus, turbulent mixing across the SWI may serve as a universal transport mechanism, supplying the nutrient and energy fluxes needed to sustain microbial growth, and nutrient processing, in the benthic biolayer of stream and coastal sediments.

Many water quality and ecosystem functions performed by streams occur in the benthic biolayer, the biologically active upper (~5 cm) layer of the streambed. Solute transport through the benthic biolayer is facilitated by bedform pumping, a physical process in which dynamic and static pressure variations over the surface of stationary bedforms (e.g., ripples and dunes) drive flow across the sediment‐water interface. In this paper we derive two predictive modeling frameworks, one advective and the other diffusive, for solute transport through the benthic biolayer by bedform pumping. Both frameworks closely reproduce patterns and rates of bedform pumping previously measured in the laboratory, provided that the diffusion model's dispersion coefficient declines exponentially with depth. They are also functionally equivalent, such that parameter sets inferred from the 2D advective model can be applied to the 1D diffusive model, and vice versa. The functional equivalence and complementary strengths of these two models expand the range of questions that can be answered, for example, by adopting the 2D advective model to study the effects of geomorphic processes (such as bedform adjustments to land use change) on flow‐dependent processes and the 1D diffusive model to study problems where multiple transport mechanisms combine (such as bedform pumping and turbulent diffusion). By unifying 2D advective and 1D diffusive descriptions of bedform pumping, our analytical results provide a straightforward and computationally efficient approach for predicting, and better understanding, solute transport in the benthic biolayer of streams and coastal sediments.

New results from surface PIV (Particle Image Velocimetry) measurements are presented. Surface PIV can potentially provide researchers with a cheap and versatile method for mapping 2D flow fields. This technique was evaluated in a laboratory flume with a random distribution of rigid plastic straws, to simulate flows through emergent vegetation. Velocities were computed via an open-source tool for conventional PIV, and a sensitivity analysis conducted, in which the factors seeding particle size, particle image density, size of interrogation window, number of passes and contrast were evaluated. Results show that, with the appropriate settings, 98.7\(\%\) of data points were considered to be reliable. It was found that the best quality velocity maps were obtained with small seeding particles and intermediate window resolutions (16\(\,\times \,\)16 pixels). The practical use of this technique is illustrated by using the data to identify the portion of flow through vegetation occupied by wakes. For this, a straightforward criterion, related to the incident flow conditions and generated vorticity, is proposed. Further refinements of this research can lead to applications in several branches of fluid mechanics, such as in situ measurements of the flow field and analysis of scalar dispersion processes in ecohydraulics.