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.

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.

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 hole is numerically simulated considering a very fine mesh in the order of 50 million cells distributed within a relatively small computational domain. Necklace vortices, including two horseshoe vortices (HVs) and a junction vortex (JV), are detected upstream from the cylinder. In many snapshots, the tails of the HVs stretch in the flow direction, while their size and length change considerably over time. Downstream of the cylinder, the influence of the trailing vortex from the cylinder roof is mainly limited to a zone near the cylinder top, whereas the effect of the separated shear layers (SSLs) from the cylinder sides is dominant within a larger region. The strength of vorticity associated with the trailing vortex is mainly notable within the “very near wake” area, where the strength of the upward velocity component of the wake vortices generated from the cylinder sides mitigates. This paper describes the distribution and origin of streaks and rollers on the scoured bed, i.e. the main cause of sediment transported downstream of the cylinder.