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

応用水文 = Applied hydrology

Part I presents the statistical theory of turbulence, and Part 2 the coherent structures in open-channel flows and boundary layers. The book is intended for advanced students and researchers in hydraulic research, fluid mechanics, environmental sciences and related disciplines. References Index.

Turbulence in open-channel flows

The advent of airborne LIDAR sparked a renewed research drive in two-dimensional hydraulic modelling at the turn of the millennium due to its ability to rapidly generate accurate DEMs over wide areas. Terrestrial LIDAR applies the same principle but uses a mobile ground-based platform, allowing rapid collection of terrain data in urban areas at decimetric scale. Here we apply two computationally efficient hydraulic models to DEMs of a small urban test site in Alcester, UK, derived from terrestrial and airborne LIDAR data at 10 cm and 1 m scales. The first model, LISFLOOD-FP, is a 2D raster-based model employing a simplified formulation of the de St. Venant equations, whilst the second model, ISIS-FAST, employs a proprietary rapid flood spreading algorithm. The response of the models to changes in DEM resolution and data source are analysed and compared across two event scales. For the first time we show that a flood wave propagating across an urban domain responds to small scale topographic features, such as street kerbs and road surface camber, which are not represented in airborne data but which are resolved by the terrestrial laser scanner. Importantly these features are preserved even if the 10 cm terrestrial data are degraded to the 1 m scale of the airborne DEM. The results indicate that inclusion of these features improves the representation of hydraulic connectivity over the DEM, and hence flood risk estimation. LISFLOOD-FP is shown to be more robust to changes in DEM resolution than ISIS-FAST due to the momentum conservation inherent to the simplified shallow water formulation, but the reduced computational requirements of ISIS-FAST at 10 cm scale allow it to be used for ensemble simulations. The extra detail inherent in terrestrial laser scanning data is advantageous where accurate representation of surface features is required, with potential benefit to high asset-value flood risk analysis and future studies into coupled surface/sewer and pluvial urban inundation models. Language: en

Using terrestrial laser scanning data to drive decimetric resolution urban inundation models

A review of open channel turbulence, focusing especially on certain features stemming from the presence of the free surface and the bed of a river. Part one presents the statistical theory of turbulence; Part two addresses the coherent structures in open-channel flows and boundary layers.

Turbulence in Open-Channel Flows

Despite the existing knowledge concerning the hydrodynamic processes at river junctions, there is still a lack of information regarding the particular case of low width and discharge ratios, which are the typical conditions of mountain river confluences. Aiming at filling this gap, laboratory and numerical experiments were conducted, comparing the results with literature findings. Ten different confluences from 45 ∘ to 90 ∘ were simulated to study the effects of the junction angle on the flow structure, using a numerical code that solves the 3D Reynolds Averaged Navier-Stokes (RANS) equations with the k- ϵ turbulence closure model. The results showed that the higher the junction angle, the wider and longer the retardation zone at the upstream junction corner and the separation zone, and the greater the flow deflection at the entrance of the tributary into the post-confluence channel. Furthermore, it was shown that the maximum streamwise velocity does not necessarily increase with the junction angle and that it is not always located in the contraction section.

Effect of the Junction Angle on Turbulent Flow at a Hydraulic Confluence

The turbulence characteristics within flows over water-worked gravel beds (WGBs) and screeded gravel beds (SGBs) were examined by measuring the instantaneous flow velocity field using a two-dimensional particle image velocimetry system. To compare the responses of a WGB and an SGB to velocity and various turbulence characteristics, the flow Froude number was kept identical for both the beds that remained immobile. The roughness structures of both the beds were measured using a laser scanner. The results showed that the bed surface roughness was higher in the WGB than in the SGB. However, the longest axis of the gravels of WGBs was oriented streamwise owing to the action of water work, but the gravels of SGBs were randomly poised. The distribution of bed roughness fluctuations was negatively skewed in the WGB and positively skewed in the SGB. Double averaging methodology was applied to analyze the flow parameters. In this paper, the vertical profiles of the double-averaged streamwise velocity and the turbulence parameters, specifically the spatially averaged (SA) Reynolds shear and normal stresses, form-induced shear and normal stresses, turbulent kinetic energy (TKE) and form-induced TKE fluxes, quadrant analysis of SA Reynolds shear stress, etc., are presented and analyzed critically by focusing on comparisons between a WGB and an SGB. A comparative study reveals that in the near-bed flow zone, the SGB underestimates the turbulence parameters compared to the WGB. Therefore, in order to represent the prototypical flow in laboratory, the experiments should be performed in a WGB.

Hydrodynamics of water-worked and screeded gravel beds: A comparative study

The development of a shared understanding of current flood risk amongst stakeholders is one of the main goals of flood risk management. This priority suggests that stakeholders must understand the possible impacts on their property and assets, and measures they can take to mitigate the risk. Nowadays, flood maps are considered to be a potentially valuable tool for improving this understanding, but some drawbacks related to the use of flood maps for risk communication has been highlighted in the literature. An alternative and novel approach is provided by 3-D representations of flood inundation, so that supplementing flood maps with 3D visualization techniques is increasingly seen as a powerful tool with which to engage people with flood hazards. In this context, the detailed representation of the urban areas is important not only to set an accurate out-of-bank river model, essential for reliable simulations of flow dynamics inside the urban districts, but could be also a key element for the generation of realistic 3D views able to enhance risk perception and communication. In the framework described so far, 3D point cloud data provided by a terrestrial laser scanner could play an interesting role. Therefore, the main novelty introduced by this work is the combination of 2D flood simulations, 3D visual techniques and airborne/terrestrial laser scanning in order to develop new approaches for risk communication and perceptions. The potential of the methods developed here has been discussed in relation to a hypothetical flood event of the Crati river, flowing through the old city of Cosenza (South of Italy).

Nadia Penna

Papers

Effect of the Junction Angle on Turbulent Flow at a Hydraulic Confluence

Hydrodynamics of water-worked and screeded gravel beds: A comparative study

Terrestrial and airborne laser scanning and 2-D modelling for 3-D flood hazard maps in urban areas: new opportunities and perspectives

Characterization of the settling process for wastewater from a combined sewer system.

Three-dimensional analysis of local scouring induced by a rotating ship propeller