Computational Fluid Dynamics (CFD) has consolidated as a tool to provide understanding and quantitative information regarding many complex environmental flows. The accuracy and reliability of CFD modelling results oftentimes come under scrutiny because of issues in the implementation of and input data for those simulations. Regarding the input data, if an approach based on the Reynolds-Averaged Navier-Stokes (RANS) equations is applied, the turbulent scalar fluxes are generally estimated by assuming the standard gradient diffusion hypothesis (SGDH), which requires the definition of the turbulent Schmidt number, Sc_t (the ratio of momentum diffusivity to mass diffusivity in the turbulent flow). However, no universally-accepted values of this parameter have been established or, more importantly, methodologies for its computation have been provided. This paper firstly presents a review of previous studies about Sc_t in environmental flows, involving both water and air systems. Secondly, three case studies are presented where the key role of a correct parameterization of the turbulent Schmidt number is pointed out. These include: (1) transverse mixing in a shallow water flow; (2) tracer transport in a contact tank; and (3) sediment transport in suspension. An overall picture on the use of the Schmidt number in CFD emerges from the paper.

We present and discuss the results of a comprehensive study addressing the non-aerated region of the skimming flow in steep stepped spillways. Although flows in stepped spillways are usually characterized by high air concentrations concomitant with high rates of energy dissipation, the non-aerated region becomes important in small dams and/or spillways with high specific discharges. A relatively large physical model of such spillway was used to acquire data on flow velocities and water levels and, then, well-resolved numerical simulations were performed with a commercial code to reproduce those experimental conditions. The numerical runs benefited from the ability of using multi-block grids in a Cartesian coordinate system, from capturing the free surface with the TruVOF method embedded in the code, and from the use of two turbulence models: the ${k{-}\varepsilon}$ and the RNG ${k{-}\varepsilon}$ models. Numerical results are in good agreement with the experimental data corresponding to three volumetric flow rates in terms of the time-averaged velocities measured at diverse steps in the spillway, and they are in very satisfactory agreement for water levels along the spillway. In addition, the numerical results provide information on the turbulence statistics of the flow. This work also discusses important aspects of the flow, such as the values of the exponents of the power-law velocity profiles, and the characteristics of the development of the boundary layer in the spillway.

In this work, we investigate the temporal evolution of the jet-driven scour depth in a pothole lying on a cohesionless granular bed by using diverse approaches. First, we present new experiments which encompass cases with jet angles ranging from 45° to 90° from the horizontal, several initial water depths, and different particle sizes, supplementing experiments developed recently by the last two authors. In particular, we address relatively large angles, mostly absent in previous analyses. Our results initially confirm the existence of two very different stages in the scour process, essentially overlooked in datasets used to obtain the traditional formulas—developing and developed phases; they then provide unprecedented evidence of the very distinct behavior at 90°, characterized by a step-wise behavior. Second, after revisiting the rationale of a theory for the equilibrium condition developed elsewhere by the first author and a collaborator, we employ the existing and new datasets to determine the multiplicative constants embedded in the equilibrium scour formulas. Third, we present a novel theory for the temporal evolution of the scour depth during the developed phase (but with good prediction capabilities in the developing phase as well). By invoking the conservation of mass of sediment in the pothole, in addition to the energy conservation within the pothole and the phenomenological theory of turbulence, we obtain ordinary differential equations which we solve by numerical means. We validate the theory using our new and other datasets. Finally, we provide interesting interpretations of the scour process by using the results of the theory.

Recent empirical and numerical evidence shows that the Basset force plays an important role in the description of acceleration of relatively small sediment particles moving close to solid boundaries. This force can make the numerical solution of the equations of motion computationally time and memory consuming. This technical note presents a two-stage methodology to deal with the difficulties associated with computing the Basset force. The Basset term is first approximated based on a semiderivative (fractional mathematics), and then the integration time is redefined in terms of appropriate flow and particle time scales, thus, avoiding unnecessary computations. Important savings in computational time are reported.

In this paper, we focus on assessing the performance of diverse turbulence closures in the simulation of dilute sediment-laden, open-channel flows. To that end, we base our analysis on a framework developed in a companion paper of this special issue, which puts forward a standard sediment transport model (SSTM), a partial two-fluid model (PTFM) and a complete two-fluid model (CTFM), in three- and one-dimensional (3D and 1D) versions. First, we propose in this paper extensions of the transport equations for the Reynolds stresses, and of the equations of the K–ω model to two-phase flows, starting from the general two-fluid model. We consider the drag force to be the predominant force amongst all the interactions between the two phases (water and sediment). Second, under the framework of models formed by the SSTM, the PTFM and the CTFM, we discuss simulation results obtained by employing the Reynolds stress model (RSM), the algebraic stress model (ASM), and the K– \(\varepsilon\) and the K–ω models (in their standard and extended versions), paired with each member of the framework. To assess the accuracy of the models, we compare numerical results with the experimental datasets of Vanoni, Trans ASCE 111:67–133, 1946; Coleman, Water Resour Res 22(10):1377–1384, 1986; Muste and Patel, J Hydraul Eng 123(9):742–751, 1997; Nezu and Azuma, J Hydraul Eng 130:988–1001, 2004; Muste et al. Water Resour Res 41:W10402, 2005 . Third, we obtain from those comparisons the values of the Schmidt number that facilitate the agreement of model predictions with data. We conclude that the standard K– \(\varepsilon\) model, the ASM and the K–ω models all provide satisfactory descriptions of flow variables and sediment concentrations in open-channel flows; further, we show that the more complicated RSM does not provide much improvement in dilute sediment transport as compared to those previous models, even when it is paired with the CTFM. We also show that the inclusion of model extensions in the turbulence closures does not improve the predictions for dilute mixtures either. We find that our values for the Schmidt number agree well with available data, and we provide an explanation for the variation of the Schmidt number with the ratio of the fall velocity and the wall-friction (shear) velocity. Finally, we corroborate that the Schmidt number is the key parameter to obtain satisfactory predictions of sediment transport in suspension.

This article aims to provide a comprehensive appraisal on the current status of three-dimensional (3D) numerical modeling of local scour around instream hydraulic structures. Many computer models have been developed or are in development to simulate riverbed morphology. Local scour, however, is a special category that requires in general a 3D model based on some averaged/filtered form of the Navier-Stokes (NS) equations and a 3D sediment transport model. Only limited number of 3D scour codes are available for practical usage; there is also a lack of literature on the limitations of the models in capturing the scour-producing flow and the sediment transport solvers embedded within. For 3D local scour modeling, the main intrinsic uncertainty lies primarily in the sediment part. In this article, the basic theory and the state of the art of current 3D local scour models are reviewed, focusing primarily on the sediment solver, and future research needs are discussed.