Asymmetric turbulent channel flow, such as ice-covered river flow, is a century-old problem but still unsolved in hydraulics and fluid mechanics. This study finds exact solutions for its eddy (or turbulent) viscosity and mean velocity distributions, which are independent of any assumption without any fit parameter. Specifically, it first applies Guo’s quartic eddy viscosity and complete log-law from high-Reynolds-number pipe flow to symmetric turbulent channel flow. It then formulates a functional equation, involving both bottom and top plane shear velocities, to govern the eddy viscosity distribution in asymmetric channel flow. The analytic solution for the eddy viscosity then leads to a velocity distribution solution that includes four components: bottom shear velocity effect, top plane shear velocity effect, symmetric interaction between both about a critical point, and antisymmetric interaction between both. The velocity distribution solution agrees well with field data and so is applicable in ice-covered rivers. Laboratory data also confirm the velocity distribution structure, but a turbulent mixing intensity parameter depends on the Reynolds number. Therefore, future laboratory tests should focus on high-Reynolds-number flow.

Laminar radial flow between two parallel disks is a fundamental nonlinear fluid mechanics problem described by the Navier-Stokes (NS) equation, but is unsolved because (1) an exact solution is not found even with extensive references, and (2) it is unclear why radial flow remains laminar at high Reynolds numbers. This paper first presents exact velocity distribution solutions for developed radial inflows and outflows, proving that both flows are described by brief Jacobi elliptic sine-squared functions but with different characteristics. For inflow, a stable velocity distribution forms; for outflow, the velocity distribution may have an inflection point inducing flow instability or separation. Both velocity distributions become the classic parabolic law at low Reynolds numbers, but uniform (similar to turbulent velocity distributions) at high Reynolds numbers. Furthermore, both pressure and boundary shear stress follow an inverse-square law, but the friction factor is invariant. These results are instructive for studying nonuniform open-channel flow for which nonlinear inertia is of importance.

The second log-wake law is a small change of the first log-wake law (or Coles’ log-wake law) for turbulent pipe and symmetric channel flows but makes a big difference in modeling wall-bounded turbulent flows. It has been extended to antisymmetric Couette channel flows theoretically and open channel flows empirically. A recent study of natural river flows indicates that a river velocity distribution is a superposition of a complete antisymmetric channel flow solution due to water surface shear stress and a half symmetric channel flow solution due to gravity. The objective of this research then is to test this hypothesis under the effects of ice cover and wind-induced water surface shear stress with laboratory experiments. To this end, a special experimental device was designed to simulate the effects of gravity, ice cover, and wind-induced shear stress. With this device, 236 vertical distributions of streamwise velocity were measured with a particle image velocimetry (PIV) technique under various simulated conditions of ice cover and water surface shear stress, 75 of which are plotted in this paper. All measured velocity distributions are characterized by a bowl-shaped velocity distribution with a dip phenomenon, a typical boundary layer velocity distribution, or an S-shaped velocity distribution with an inflection. All of these three distribution patterns are well described by the second log-wake law, which also agrees with real-world river flow data. Based on the second log-wake law, an innovative three-point method is proposed for river discharge measurements.

Scour and Erosionincludes four keynote lectures from world leading researchers cutting across the themes of scour and erosion, together with 132 peer-reviewed papers from 34 countries, covering the principal themes of: - internal erosion - sediment transport - grain scale to continuum scale - advanced numerical modelling of scour and erosion - terrestrial scour and erosion- river and estuarine erosion including scour around structures, and - management of scour/erosion and sediment, including hazard management and sedimentation in dams and reservoirs. Scour and Erosionis ideal for researchers and industry working at the forefront of scour and erosion, and has applications in both the freshwater and marine environments. Scour and Erosionincludes four keynote lectures from world leading researchers cutting across the themes of scour and erosion, together with 132 peer-reviewed papers from 34 countries, covering the principal themes of: - internal erosion - sediment transport - grain scale to continuum scale - advanced numerical modelling of scour and erosion - terrestrial scour and erosion- river and estuarine erosion including scour around structures, and - management of scour/erosion and sediment, including hazard management and sedimentation in dams and reservoirs. Scour and Erosionis ideal for researchers and industry working at the forefront of scour and erosion, and has applications in both the freshwater and marine environments. Scour and Erosionincludes four keynote lectures from world leading researchers cutting across the themes of scour and erosion, together with 132 peer-reviewed papers from 34 countries, covering the principal themes of: - internal erosion - sediment transport - grain scale to continuum scale - advanced numerical modelling of scour and erosion - terrestrial scour and erosion- river and estuarine erosion including scour around structures, and - management of scour/erosion and sediment, including hazard management and sedimentation in dams and reservoirs. Scour and Erosionis ideal for researchers and industry working at the forefront of scour and erosion, and has applications in both the freshwater and marine environments. Scour and Erosionincludes four keynote lectures from world leading researchers cutting across the themes of scour and erosion, together with 132 peer-reviewed papers from 34 countries, covering the principal themes of: - internal erosion - sediment transport - grain scale to continuum scale - advanced numerical modelling of scour and erosion - terrestrial scour and erosion- river and estuarine erosion including scour around structures, and - management of scour/erosion and sediment, including hazard management and sedimentation in dams and reservoirs. Scour and Erosionis ideal for researchers and industry working at the forefront of scour and erosion, and has applications in both the freshwater and marine environments. Scour and Erosionincludes four keynote lectures from world leading researchers cutting across the themes of scour and erosion, together with 132 peer-reviewed papers from 34 countries, covering the principal themes of: - internal erosion - sediment transport - grain scale to continuum scale - advanced numerical modelling of scour and erosion - terrestrial scour and erosion- river and estuarine erosion including scour around structures, and - management of scour/erosion and sediment, including hazard management and sedimentation in dams and reservoirs. Scour and Erosionis ideal for researchers and industry working at the forefront of scour and erosion, and has applications in both the freshwater and marine environments. Scour and Erosionincludes four keynote lectures from world leading researchers cutting across the themes of scour and erosion, together with 132 peer-reviewed papers from 34 countries, covering the principal themes of: - internal erosion - sediment transport - grain scale to continuum scale - advanced numerical modelling of scour and erosion - terrestrial scour and erosion- river and estuarine erosion including scour around structures, and - management of scour/erosion and sediment, including hazard management and sedimentation in dams and reservoirs. Scour and Erosionis ideal for researchers and industry working at the forefront of scour and erosion, and has applications in both the freshwater and marine environments.

The US Federal Highway Administration (FHWA) is developing the next-generation scour programme – that is, NextScour – to improve scour analysis for safe and economical bridge foundation design. NextScour recognises that scour phenomena consist of two major components: (a) water and hydraulic forces and (b) erosion resistance of soils and their associated geotechnical effects. Consequently, the programme consists of two focus areas: NextScour-Hydraulic and NextScour-Geotechnical. NextScour seeks to research and develop a design tool that computes hydraulic loads across the bathymetric domain. When linked to geotechnically derived subsurface erosion maps/stratigraphy and information of NextScour, the design tool produces instantaneous three-dimensional scour bathymetries around all bridge foundation elements. A bridge replacement project from the Virginia Department of Transportation provided an excellent case study of the potential cost saving by considering NextScour proof-of-concept results in the design process. The J. Sterling Jones Hydraulics Research Laboratory erosion tests determined the erosion resistance of the clay layer at the bridge foundation, and a hydraulic force depth decay function was developed along with the soil depth. The proof-of-concept analysis showed a potential reduced pier scour estimate by 15.7 feet (ft) (4.8 m) and contraction scour estimate by 16.4 ft (5.0 m), 44 and 65% reductions from the original scour analysis, respectively. NextScour empowers FHWA’s future scour analysis with the goal to improve significantly the accuracy of bridge scour estimates.