Flow resistance due to vegetation is of interest for a wide variety of hydraulic engineering applications. This note evaluates several practical engineering functions for estimating bulk drag coefficient ( $C_D$) for arrays of rigid cylinders, which are commonly used to represent emergent vegetation. Many of the evaluated functions are based on an Ergun-derived expression that relates $C_D$ to two coefficients, describing viscous and inertial effects. A re-parametrization of the Ergun coefficients based on cylinder diameter (d) and solid volume fraction (φ) is presented. Estimates of $C_D$ are compared to a range of experimental data from previous studies. All functions reasonably estimate $C_D$ at low φ and high cylinder Reynolds numbers ( ${\mathsf{R}}_{\mathsf{d}}$). At higher φ they typically underestimate $C_D$. Estimates of $C_D$ utilizing the re-parametrization presented here match the experimental data better than estimates of $C_D$ made using the other functions evaluated, particularly at low φ and low ${\mathsf{R}}_{\mathsf{d}}$.

Understanding solute mixing within real vegetation is critical to predicting and evaluating the performance of engineered natural systems such as storm water ponds. For the first time, mixing has been quantified through simultaneous laboratory measurements of transverse and longitudinal dispersion within artificial and real emergent vegetation. Dispersion coefficients derived from a routing solution to the 2‐D Advection Dispersion Equation (ADE) are presented that compare the effects of vegetation type (artificial,Typha latifoliaorCarex acutiformis) and growth season (winter or summer). The new experimental dispersion coefficients are plotted with the experimental values from other studies and used to review existing mixing models for emergent vegetation. The existing mixing models fail to predict the observed mixing within natural vegetation, particularly for transverse dispersion, reflecting the complexity of processes associated with the heterogeneous nature of real vegetation. Observed stem diameter distributions are utilized to highlight the sensitivity of existing models to this key length‐scale descriptor, leading to a recommendation that future models intended for application to real vegetation should be based on probabilistic descriptions of both stem diameters and stem spacings.

Green roofs have been adopted in urban drainage systems to control the total quantity and volumetric flow rate of runoff. Modern green roof designs are multi-layered, their main components being vegetation, substrate and, in almost all cases, a separate drainage layer. Most current hydrological models of green roofs combine the modelling of the separate layers into a single process; these models have limited predictive capability for roofs not sharing the same design. An adaptable, generic, two-stage model for a system consisting of a granular substrate over a hard plastic ‘egg box’-style drainage layer and fibrous protection mat is presented. The substrate and drainage layer/protection mat are modelled separately by previously verified sub-models. Controlled storm events are applied to a green roof system in a rainfall simulator. The time-series modelled runoff is compared to the monitored runoff for each storm event. The modelled runoff profiles are accurate (mean Rt2 = 0.971), but further characterization of the substrate component is required for the model to be generically applicable to other roof configurations with different substrate.

This paper provides a computational fluid dynamics (CFD)‐based modeling framework for predicting flow field, turbulence, and mixing characteristics within vegetated environments such as ponds and wetlands. The framework has been implemented within a commercial CFD code—ANSYS Fluent 19—via a set of user‐defined functions. Following the approach outlined by King et al. (2012, https://doi.org/10.1017/jfm.2012.113), the standard k‐ε turbulence closure model has been modified to capture the energy transfer at the vegetation/clear flow shear interface and within the vegetation. The implementation assumes that vegetation is vertical, but nonorthogonal flow in the horizontal plane is accounted for. Values for the drag coefficient and the mixing coefficients are estimated based on the vegetation stem diameter and density. Following Tanino and Nepf (2008, https://doi.org/10.1017/S0022112008000505), a switch has been incorporated to account for the fact that the relevant length scale changes from stem diameter to stem spacing as stem density increases. A set of model parameters is proposed, based on a reevaluation of previously published laboratory data and theoretical analysis. Five different experimental data sets are used to demonstrate that the model is able to predict mixing within fully vegetated systems and due to both vertical and horizontal shear layers. The framework was developed to provide a practical prediction tool for engineering purposes, in particular for the estimation of residence time distributions in real partially vegetated stormwater management ponds. Its implementation here within a commercial CFD package potentially facilitates application to complex pond geometries, including patches of different types of vegetation with different bulk stem diameter and density characteristics.

Longitudinal dispersion processes are often described by the advection dispersion equation (ADE), which is analogous to Fick’s law of diffusion, where the impulse response function of the spatial concentration distribution is assumed to be Gaussian. This paper assesses the validity of the assumption of a Gaussian impulse response function, using residence time distributions (RTDs) obtained from new laboratory data. Measured up- and downstream temporal concentration profiles have been deconvolved to numerically infer RTDs for a range of turbulent, critical, and laminar pipe flows. It is shown that the Gaussian impulse response function provides a good estimate of the system’s mixing characteristics for turbulent and critical flows, and an empirical equation to estimate the dispersion coefficient for the Reynolds number, R, between 3,000 and 20,000 is presented. For laminar flow, here identified as R<3,000, the RTDs do not conform to the Gaussian assumption because of insufficient available time for the...

Experimental data characterising dispersion within Typha latifolia were previously collected in a laboratory setting. This mixing characterisation was combined with previously proposed computational fluid dynamics modelling approaches to predict residence time distributions for vegetated stormwater treatment pond layouts (including a wetland) derived from Highways England design guidance. The results showed that the presence of vegetation resulted in residence times closer to plug flow, indicating significant improvements in stormwater treatment capability. The new modelling approach reflects changes in residence time due to mixing within the vegetation, but it also suggests that it is more important to include vegetation within the model in the correct location than it is to accurately characterise it. Estimates of hydraulic efficiency suggest that fully vegetated stormwater ponds such as wetlands should function well as a treatment device, but more typical ponds with clear water need to be designed to be between 50% and 100% larger than their nominal residence times would suggest when designed against treatment criteria.