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.

Many rivers in Taiwan have steep slopes, are subject to typhoon-induced flood flows, and contain soft bedrock that is exposed at many locations and easily erodible. The occurrence of extensive bedrock erosion has been a major threat to river infrastructure at many locations. Soft bedrock erosion, therefore, is an important process to consider for river projects in Taiwan. In this study, bedrock erosion models are reviewed. A specific model is proposed by combining two existing models incorporating both the hydraulic and abrasive scour mechanisms. The proposed bedrock erosion model is incorporated into a two-dimensional mobile-bed model, and the integrated model is tested by simulating bedrock erosion downstream of the Chi-Chi weir on the Choshui River in Taiwan. A calibration study is performed to determine appropriate values of the model parameters based on two and a half years of measured data. The model is then assessed based on a verification study that compares model predictions of bedrock erosion of...

Three-dimensional (3D) hydrostatic-pressure-assumption numerical models are widely used for environmental flows with free surfaces and phase interfaces. In this study, a new flow and sediment transport model is developed, aiming to be general and more flexible than existing models. A general set of governing equations are used for the flow and suspended sediment transport, an improved solution algorithm is proposed, and a new mesh type is developed based on the unstructured polygonal mesh in the horizontal plane and a terrain-following sigma mesh in the vertical direction. The new flow model is verified first with the experimental cases, to ensure the validity of flow and free surface predictions. The model is then validated with cases having the suspended sediment transport. In particular, turbidity current flows are simulated to examine how the model predicts the interface between the fluid and sediments. The predicted results agree well with the available experimental data for all test cases. The model is generally applicable to all open-channel flows, such as rivers and reservoirs, with both flow and suspended sediment transport issues.

A polygonal-mesh based numerical method is developed to simulate sediment transport in mobile-bed streams with free surfaces. The flow and sediment transport governing equations are depth-averaged and solved in the two-dimensional (2D) horizontal space. The flow and sediment transport are further coupled to the stream bed changes so that erosion and deposition processes are simulated together with the mobile bed changes. Multiple subsurface bed layers are allowed so that bed stratigraphy may be taken into consideration. The proposed numerical discretization is valid for the most flexible polygonal mesh type which includes all existing meshes in use such as the quadrilateral-triangle hybrid mesh. The finite-volume method is adopted such that the mass conservations of both water and sediment are satisfied locally and globally. The sediment transport and stream bed processes are formulated in a general way so that the proposed numerical method may be applied to a wide range of streams and suitable for practical stream applications. The technical details of the numerical method are presented; model verification and validation studies are reported using selected cases having physical model or field measured data. The developed model is intended for general-purpose use available to the public.

Contraction scour is often encountered in natural rivers due to natural geological controls, bridges, or river restoration structures. Such scour may be better predicted with multi-dimensional than one-dimensional models. The aim of this study is to investigate whether a two-dimensional depth-averaged model is adequate for modelling contraction scour. This study shows that improved predictions are obtained with the present model relative to previous model investigations. The study also shows that the current model is adequate for predicting contraction scour and model results are comparable with those of three-dimensional modelling except for the prediction of aggradation downstream of the contracted channel section.

Coupled two-dimensional (2D) morphodynamic and bank erosion models are gaining attentions in recent years. It has been shown that such models have advantages over the one-dimensional (1D) modeling approaches. In this paper, a previous 2D bank erosion model with the moving mesh method is extended to include the fixed mesh approach. Further, two practical streams with differing complexity are simulated to demonstrate the extended model. Both the moving mesh and fixed mesh methods are used in the modeling. The model consists of two components: a 2D flow and mobile-bed model for vertical bed changes and hydraulic forces acting on a bank and a lateral bank retreat model. The 2D vertical model and the lateral bank erosion model are coupled together spatially and temporally through a special procedure and a common mesh. With the experiences gained with practical stream modeling, the modeling procedure and key model input parameters are described. The study shows that the moving and fixed mesh methods together make the extended bank erosion model numerically robust and capable of predicting both the vertical bed changes and the lateral stream bank erosion for complex streams. Each individual method, however, has its own limitations in terms of model accuracy and efficiency. The moving mesh works well if bank retreat is relatively small, e.g., less than one channel width, and produces more accurate results than the fixed mesh method. The fixed mesh may be needed for ensuring numerical stability if a bank may be subject to significant retreat (e.g., more than one channel width). The fixed mesh method, however, is less accurate than the moving mesh method and a much refined mesh may be needed. Both methods need future research and improvements in terms of their model accuracy.