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.

The soil particle movement under seepage flow is one of the predominant mechanisms responsible for incidents and failures of dams and streambanks. However, little attention has been paid to the critical hydraulic gradient under two-dimensional (2-D) seepage flow. In this study, a theoretical model was established under 2-D seepage flow to predict the critical hydraulic gradients for soil particle movement. In this model, the sediment particle rolling theory was used, while taking into account the relative exposure degree of the soil grains and the seepage direction. The model was validated through qualitative analysis and comparison with previous data, and showed considerable superiority over Terzaghi's model. In addition, the effect of the soil internal instability, implying that the critical hydraulic gradient of unstable soil is lower than that of stable soil, was discussed. Various parameters of the model were also analyzed. The results showed that the seepage direction angle was positively related to the critical gradient, whereas the void and the mean diameter of the soil were negatively related to it. Finally, the model proposes a calculation method for the particle movement initiation probability, which is regarded as a key parameter in the sediment transport model.

Studying the effects of different riparian vegetation densities on river channel evolution has practical significance for predicting the river channel evolution process during flood periods and ecological river engineering via the artificial planting of vegetation. In this study, we simulated the formation and evolution processes of river channels under different riparian vegetation coverage rates in laboratory conditions. The riparian vegetation coverage rates were set as 0, 20, 40 and 80%, on unilateral and bilateral sides of a river channel bank. Given the same flow and sediment boundary conditions, experiments were carried out in a 4 × 1.5 m tank. This paper focuses on the comparative analysis of main stream stability characteristics, bend migration characteristics, river bank erosion characteristics and sediment transport intensity. The results showed that different amounts of riparian vegetation cover created different characteristics of river channel evolution and strongly impacted the stability of the banks and bed. River channel evolution under unilateral vegetation cover is often accompanied by alternate development of the main stream and branch, and the bend stability under unilateral riverbank vegetation cover is worse than under bilateral cover. For a bilateral vegetation-covered river channel, a narrow and deep regime channel more easily forms with a higher vegetation coverage rate; the curvature of the stable river bend is smaller, but the adaptation period of the flow to the river channel bed increases. Planting of riparian vegetation played a positive role in the erosion resistibility, which effectively reduced the lateral migration rate of the riverbank. The higher the vegetation coverage rate, the greater the flow shear stress needed for the same river channel migration rate. While effectively reducing lateral migration, riparian vegetation coverage increased the vertical migration and led to a trend in overall scour depth along the riverbank.