Study on the vertical velocity distribution of flow under ice based on the fractal theory

The distribution of flow velocity under ice is an important reference for ice growth and ablation, sediment transport, bed evolution and water transport. Based on fractal theory and previous studies, the vertical distribution law of flow velocity under ice is studied. The results show that, based on the fractal theory and Einstein hypothesis, different existing vertical distribution formulas of velocity under ice can be derived based on the results of open channel flow. According to theoretical analysis, the distribution of flow velocity in ice sheet zone and bed zone is approximately mirror images, which both have fractal characteristics, and can be expressed by the double-logarithmic formula. The measured results prove that for curved channels, the distribution of flow velocity in the flow core area is uniform and does not follow the logarithmic distribution. The applicability or factor term should be considered in the application of the formula. In the stable freezing period, the fractal value of flow velocity distribution in the ice sheet zone is larger than that in the bed zone, and the flow velocity distribution is more uniform. However, at the ice stuck in the curve, the fractal value of flow velocity distribution in the bed zone is irregular due to the complexity of flow structure under ice. The research on the flow velocity under ice expands the application results of fractal theory in the research on the vertical distribution of flow velocity, the generalized structure of subglacial flow has certain reference significance for engineering application. © 2020, China Water Power Press. All right reserved.