The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

A solution is presented for the change in water level in a well of finite diameter after a known volume of water is suddenly injected or withdrawn. A set of type curves computed from this solution permits a determination of the transmissibility of the aquifer.

Response of a finite-diameter well to an instantaneous charge of water. Paper No. H-21

Super-resolution reconstruction of turbulent velocity fields using a generative adversarial network-based artificial intelligence framework

The significance of riparian vegetation on river flow and material transport is not in dispute. Conveyance laws, sediment erosion and deposition, and element cycling must all be adjusted from their canonical rough-wall boundary layer to accommodate the presence of aquatic plants. In turn, the growth and colonization of riparian vegetation are affected by fluvial processes and river morphology on longer time scales. These interactions and feedbacks at multiple time scales are now drawing significant attention within the research community given their relevance to river restoration. For this reason, a review summarizing methods, general laws, qualitative cognition, and quantitative models regarding the interplay between aquatic plants, flow dynamics, and sediment transport in vegetated rivers is in order. Shortcomings, pitfalls, knowledge gaps, and daunting challenges to the current state of knowledge are also covered. As a multidisciplinary research topic, a future research agenda and opportunities pertinent to river management and enhancement of ecosystem services are also highlighted.

Flow dynamics and sediment transport in vegetated rivers: A review

Estimating the main hydrodynamic features of real vegetated water bodies is crucial to assure a balance between their hydraulic conveyance and environmental quality. Riparian vegetation stands have a high impact on vegetated channels. The present work has the aim to integrate riparian vegetation’s reflectance indices and hydrodynamics of real vegetated water flows to assess the impact of riparian vegetation morphometry on bulk drag coefficients distribution along an abandoned vegetated drainage channel fully covered by 9–10 m high Arundo donax (commonly known as giant reed) stands, starting from flow average velocities measurements at 30 cross-sections identified along the channel. A map of riparian vegetation cover was obtained through digital processing of Unnamed Aerial Vehicle (UAV)-acquired multispectral images, which represent a fast way to observe riparian plants’ traits in hardly accessible areas such as vegetated water bodies in natural conditions. In this study, the portion of riparian plants effectively interacting with flow was expressed in terms of ground-based Leaf Area Index measurements (LAI), which easily related to UAV-based Normalized Difference Vegetation Index (NDVI). The comparative analysis between Arundo donax stands NDVI and LAI map enabled the analysis of the impact of UAV-acquired multispectral imagery on bulk drag predictions along the vegetated drainage channel.

Bulk Drag Predictions of Riparian Arundo donax Stands through UAV-Acquired Multispectral Images

Vegetation on the banks and flooding areas of watercourses significantly affects energy losses. To take the latter into account, computational models make use of resistance coefficients based on the evaluation of bed and walls roughness besides the resistance to flow offered by vegetation. This paper, after summarizing the classical approaches based on descriptions and pictures, considers the recent advancements related to the analytical methods relative both to rigid and flexible vegetation. In particular, emergent rigid vegetation is first analyzed by focusing on the methods for determining the drag coefficient, then submerged rigid vegetation is analyzed, highlighting briefly the principles on which the different models are based and recalling the comparisons made in the literature. Then, the models used in the case of both emergent and submerged rigid vegetation are highlighted. As to flexible vegetation, the paper reminds first the flow conditions that cause the vegetation to lay on the channel bed, and then the classical resistance laws that were developed for the design of irrigation canals. The most recent developments in the case of submerged and emergent flexible vegetation are then presented. Since turbulence studies should be considered as the basis of flow resistance, even though the path toward practical use is still long, the new developments in the field of 3D numerical methods are briefly reviewed, presently used to assess the characteristics of turbulence and the transport of sediments and pollutants. The use of remote sensing to map riparian vegetation and estimating biomechanical parameters is briefly analyzed. Finally, some applications are presented, aimed at highlighting, in real cases, the influence exerted by vegetation on water depth and maintenance interventions.

https://www.mdpi.com/2073-4441/13/2/116/pdf

Flow Resistance in Open Channel Due to Vegetation at Reach Scale: A Review

A new discharge computational model is proposed on the basis of the integration of the velocity profile across the flow cross-section in an internally corrugated pipe flowing partially full. The model takes into account the velocity profiles in the pressurised pipe to predict the flow rate under free-surface flow conditions. The model was evaluated through new laboratory experiments as well as a literature datasets. The results show that flow depth and pipe slope may affect the model accuracy; nevertheless, a prediction error smaller than 20% is expected from the model. Experimental results reveal the influence of the pipe slope and flow depth on the friction factor and the stage-discharge curves: the friction factor may increase with pipe slope, while it reduces as flow depth increases. Hence, a notable change of pipe slope may lead to the variation of the stage-discharge curve. A part of this study deals with numerical simulation of the velocity profiles and the stage-discharge curves. Using the Reynolds-Averaged Navier-Stokes (RANS) equations, numerical solutions were obtained to simulate four experimental tests, obtaining enough accurate results as to velocity profiles and water depths. The results of the simulated flow velocity were used to estimate the flow discharge, confirming the potential of numerical techniques for the prediction of stage-discharge curves.

https://www.mdpi.com/2073-4441/10/5/638/pdf

Experimental and Numerical Study of Free-Surface Flows in a Corrugated Pipe

The turbulent flow in natural rough beds is a complex subject, still poorly understood despite the longstanding effort of several researchers. In the present work, a turbulent open-channel flow experiment, with a pebble bed at Reynolds and Froude numbers, respectively, Re = 4.65 × 104 and Fr = 0.186, has been simulated using the Large-Eddy Simulation (LES) technique, in which the wall-adapting local eddy viscosity subgrid scale closure model is used and in the presence of an air-water interface to take into account the effects of the interface deformation in the flow turbulence statistics under a low relative submergence condition. The simulations have been compared with a companion experiment, where the channel bottom is constituted by four pebble layers. For the simulations, the pebble-bed surface has been captured with a high-resolution three-dimensional laser scanner and used to morphologically characterize the numerical channel bottom. Results are presented in terms of turbulence statistics and turbulent laws, showing a good agreement with those obtained in the experiment. Since a good convergence between simulation and experimental results was obtained, the LES dataset was used to compute the Turbulent Kinetic Energy (TKE) dissipation rate across the water depth. The mesh resolution allows showing a detailed TKE dissipation rate distribution across the water depth. Moreover, the equilibrium between TKE production and dissipation was checked to verify the overlap layer existence under low relative submergence condition. Finally, a new procedure for vortex-visualization is implemented, based on the relationship between the vorticity and the TKE dissipation rate.

Large-eddy simulation of turbulent natural-bed flow

The issue of the resistance to flow in open channels with vegetation has been considered by several researchers mainly experimentally, but the case of rigid emergent vegetation with linear stem arrangement is scarcely investigated. In the present work, the results are presented of an experimental investigation related to the case of rigid emergent vegetation that has been modeled by placing small rods on the bottom of a laboratory flume in aligned configuration. Tests have been executed by varying the flow rate, the bottom slope and the number and the diameter of the rods, by directly measuring the drag force exerted by the flow on a given number of rods, and the water-level profiles. A new expression has been devised for the drag coefficient as a function of the vegetation density, weakly dependent on the stem Reynolds number that allows the use of the former also in large-scale cases. The experimentally measured forces exerted by the flow on the rods have been also compared with the results obtained by applying the momentum equation in integral form to given control volumes, exhibiting a general agreement, but also showing that the use of this technique for the evaluation of the drag coefficients can give rise to not negligible errors. One of the experimental tests has been numerically simulated with the RANS technique (Reynolds-Averaged Navier–Stokes equations), and it is found that the results, mainly in terms of water-level profiles, confirm the ability of such a numerical technique in investigating this complex category of flow cases.

Investigation of flow resistance exerted by rigid emergent vegetation in open channel

Coastal finite structures, bridge piers, and bank protection structures may become submerged during storm surges. In the present study, a turbulent flow field around a submerged pile within a scour...

Agostino Lauria

Papers

Flow Resistance in Open Channel Due to Vegetation at Reach Scale: A Review

Experimental and Numerical Study of Free-Surface Flows in a Corrugated Pipe

Large-eddy simulation of turbulent natural-bed flow

Investigation of flow resistance exerted by rigid emergent vegetation in open channel

Large eddy simulation of the turbulent flow field around a submerged pile within a scour hole under current condition