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Highlights: [•] Non-uniform flow and drag force through the grass were studied semi-analytically. [•] Max. shear stress exists either at the top of the grass layer or on the ground. [•] An inflection point appears near the interface for the submerged case as expected. [•] The flow profile of the mixed type grass is successfully and smoothly plotted. [•] A new approach to better understand the mechanism of vegetated flows was proposed. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates energy losses in compound channel under non-uniform flow conditions. Using the first law of thermodynamics, the concepts of energy loss and head loss are first distinguished. They are found to be different within one sub-section (main channel or floodplain). Experimental measurements of the head within the main channel and the floodplain are then analyzed for geometries with constant or variable channel width. Results show that head loss differs from one sub-section to another: the classical 1D hypothesis of unique head loss gradient appears to be erroneous. Using a model that couple 1D momentum equations, called “Independent Sub-sections Method (ISM)”, head losses are resolved. The relative weights of head losses related to bed friction, turbulent exchanges and mass transfers between sub-sections are estimated. It is shown that water level and the discharge distribution across the channel are influenced by turbulent exchanges for (a) developing flows in straight channels, but only when the flow tends to uniformity; (b) flows in skewed floodplains and symmetrical converging floodplains for small relative flow depth; (c) flows in symmetrical diverging floodplains for small and medium relative depth. Flow parameters are influenced by the momentum flux due to mass exchanges in all non-prismatic geometries for small and medium relative depth, while this flux is negligible for developing flows in straight geometry. The role of an explicit modeling of mass conservation between sub-sections is eventually investigated. [Copyright &y& Elsevier]

Abstract: Existing analytical solutions to 2D and 3D contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. An approximate method is developed herein for coordinate mapping of 2D (vertically-averaged) transport solutions to non-uniform steady-state irrotational and divergence-free flow fields in single-layer aquifers. The method enables existing analytical transport solutions to be applied to aquifer systems with wells, non-uniform saturated thickness, surface water features, and (to a limited degree) heterogeneous hydraulic conductivity and recharge. This mass-conservative coordinate mapping approach is inexact in its approximation of the dispersion process but is still sufficiently accurate for many simple flow systems. The degree of model error is directly proportional to the variation of velocity magnitude within the domain. These mapped analytical solutions are compared to numerical simulation results and the coordinate mapping errors are investigated. The methods described herein may be used in the traditional capacity of analytical transport models, i.e., screening and preliminary site assessment, without sacrificing accuracy by assuming locally uniform flow conditions or applying an ad-hoc coordinate transformation. The solutions benefit from the traditional advantages of analytical methods, particularly the removal of artifacts due to spatial and temporal discretization: no time-stepping or numerical discretization is required. [Copyright &y& Elsevier]

Abstract: This study investigates turbulence structures in steady and non-uniform flows. Equations of Reynolds shear stress and turbulent velocity fluctuations are derived and their physical interpretations are explained. The theoretical results show that, different from previous studies, the variation of water surface can generate the wall-normal velocity, resulting in deviations of Reynolds shear stress and turbulence intensities from those in uniform flows. A self-similarity relationship is found between the Reynolds shear stress and turbulence intensities in non-uniform flows. The existence of self-similarity indicates that the effect of non-uniformity does not influence the mixing length. An empirical equation has been proposed to express the relationship based on experimental data available in the literature. Good agreement is achieved between the measured and predicted turbulence intensities by applying the self-similarity relationship. [Copyright &y& Elsevier]

Abstract: Advective transport from a finite line contamination source to an extraction well with regional flow depends on interplay of radial and regional flows, a scheme commonly encountered in capture zone delineation. We have investigated travel-time distribution from a finite line contamination source and the associated breakthrough curves (BTCs) observed at an extraction well. The resulting travel-time distribution and BTCs depend on dimensionless source length, dimensionless pumping rate, and inclined angle of the source with respect to the regional flow, where the dimensionless terms are lumped parameters involving source length, pumping rate, distance between the source and the extraction well, aquifer thickness, and regional flow discharge. The observed concentration at the extraction well increases with time in a sub-linear manner. When the source orientation is perpendicular to the regional flow, the dimensionless first arrival time only depends on the dimensionless pumping rate whereas the dimensionless steady-state arrival time depends on both the dimensionless pumping rate and the dimensionless source length. The steady-state concentration at the extraction well is sensitive to the dimensionless source length and the inclined angle of the source with respect to the regional flow, but not sensitive to the dimensionless pumping rate. Two special cases where the extraction well is very close to the source and the regional flow can be negligible have also been discussed. [Copyright &y& Elsevier]

Abstract: A numerical experiment is carried out to investigate the suitability of a Boussinesq-type momentum model for simulating transcritical flows at short length transitions in open channel flow measuring structures. Two one-dimensional Boussinesq-type equation models, which incorporate different degrees of dynamic pressure corrections, are considered for this purpose. A finite difference method is employed to discretise and solve the equations. The models are then applied to simulate different test cases for flows in such channels with predominant non-hydrostatic pressure distribution effects. A comparison of the computed results with the corresponding experimental data is presented. Results of this study reveal that the proposed model, which includes a higher-order correction for the effect of the centrifugal pressure, describes well even relatively abrupt changes from sub- to super-critical flow state. [Copyright &y& Elsevier]

Backward location and travel time probabilities, which provide information about the former location of contamination in an aquifer, can be used to identify unknown contamination sources. Backward location probability describes the possible upgradient positions of contamination at a known time in the past, and backward travel time probability describes the time required for contamination to travel from a known upgradient location to an observation point. These probabilities are related to adjoint states of resident concentration, and their governing equation is the adjoint of a forward contaminant transport model. Using adjoint theory to obtain the appropriate governing equation, we extend the backward probability model for conservative solutes to more general non-uniform and transient flow fields. In particular, we address three important extensions, spatially-varying porosity, transient flow and temporally-varying porosity, and internal distributed sources and sinks of solute and water. For the first time we learn that forward and backward location and travel time probabilities are not necessarily equivalent to adjoint states, but are related to them. The extensions are illustrated using a vertically-integrated groundwater model, creating transient flow by a step change in pumping and using areal recharge as an internal distributed source. Both the movement and spread of probabilities are affected. With internal sources of water, there are two interpretations of backward probability, depending on whether or not the source of water is also a source of solute. The results demonstrate how the backward probability model can be applied to other, perhaps more important, non-uniform and transient flow conditions, with time- and space-varying water storage, such as time-varying pumping or unsaturated (or saturated–unsaturated) flow and transport with spatially- and temporally-varying moisture content. [Copyright &y& Elsevier]