The approach of Reynolds-averaged Navier–Stokes equations (RANS) for the modeling of turbulent flows is reviewed. The subject is mainly considered in the limit of incompressible flows with constant properties. After the introduction of the concept of Reynolds decomposition and averaging, different classes of RANS turbulence models are presented, and, in particular, zero-equation models, one-equation models (besides a half-equation model), two-equation models (with reference to the tensor representation used for a model, both linear and nonlinear models are considered), stress-equation models (with reference to the pressure-strain correlation, both linear and nonlinear models are considered) and algebraic-stress models. For each of the abovementioned class of models, the most widely-used modeling techniques and closures are reported. The unsteady RANS approach is also discussed and a section is devoted to hybrid RANS/large methods.

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.

The direct numerical simulation of turbulence (DNS) has become a method of outmost importance for the investigation of turbulence physics, and its relevance is constantly growing due to the increasing popularity of high-performance-computing techniques. In the present work, the DNS approach is discussed mainly with regard to turbulent shear flows of incompressible fluids with constant properties. A body of literature is reviewed, dealing with the numerical integration of the Navier-Stokes equations, results obtained from the simulations, and appropriate use of the numerical databases for a better understanding of turbulence physics. Overall, it appears that high-performance computing is the only way to advance in turbulence research through the front of the direct numerical simulation.

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.

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.

Laboratory experiments and numerical simulations are performed to measure discharge coefficients in the case of a gate located on the upstream wall of a weir for flood storage. The effect of the gate slope and the side contraction have been taken into account. The study was first performed experimentally, when three series of tests were carried out with (and without) a broad crested weir located under the gate, at different values of the inclination angle of the weir upstream wall, and at different values of the shape ratio and the relative opening. In order to provide useful suggestions for those involved in sluice gate construction and management, three equations were obtained based on multiple regression, relating the discharge coefficient to different parameters that characterize the phenomenon at hand, separating the case when the broad-crested weir was present. Then numerical simulations were executed by means of the Reynolds-averaged Navier–Stokes (RANS) equations with the k-ε turbulence closure model and in conjunction with the volume of fluid (VOF) method, to validate the numerical results against the experimental and to possibly investigate phenomena not caught by the experimental measurements. Simulated discharges were very close to the observed ones showing that the proposed three-dimensional numerical procedure is a favorable option to correctly reproduce the phenomenon.