Analytical Models of Velocity, Reynolds Stress and Turbulence Intensity in Ice-Covered Channels

Jiao Zhang,Zhanbin Li,Wen Wang,Zhaohui Xia,Hunan Qiu,Qian Li,Ya Zhong

doi:10.3390/w13081107

Abstract

Ice cover in an open channel can influence the flow structure, such as the flow velocity, Reynolds stress and turbulence intensity. This study analyzes the vertical distributions of velocity, Reynolds stress and turbulence intensity in fully and partially ice-covered channels by theoretical methods and laboratory experiments. According to the experimental data, the vertical profile of longitudinal velocities follows an approximately symmetry form. Different from the open channel flow, the maximum value of longitudinal velocity occurs near the middle of the water depth, which is close to the channel bed with a smoother boundary roughness compared to the ice cover. The measured Reynolds stress has a linear distribution along the vertical axis, and the vertical distribution of measured turbulence intensity follows an exponential law. Theoretically, a two-power-law function is presented to obtain the analytical formula of the longitudinal velocity. In addition, the vertical profile of Reynolds stress is obtained by the simplified momentum equation and the vertical profile of turbulence intensity is investigated by an improved exponential model. The predicted data from the analytical models agree well with the experimental ones, thereby confirming that the analytical models are feasible to predict the vertical distribution of velocity, Reynolds stress and turbulence intensity in ice-covered channels. The proposed models can offer an important theoretical reference for future study about the sediment transport and contaminant dispersion in ice-covered channels.

Highlights

Most rivers at high altitude in cold northern regions always freeze in the winter and form ice sheets
The analytical results were consistent with the experimental velocities, so the proposed model and corresponding parameters are reasonable and reliable to be used to predict the velocity profile in the straight open channel flow covered by the ice cover
We here proposed theoretical models to describe the vertical distribution of longitudinal velocity, shear stress and turbulence intensity

Summary

Introduction

Most rivers at high altitude in cold northern regions always freeze in the winter and form ice sheets. The wetted perimeter of the cross section and flow resistance in ice-covered flows increases with the presence of the ice sheet, which significantly affects the hydraulic characteristics of river and topographical features and greatly change the flow velocity distribution, flow transport capacity and sediment transport rate [2,3,4,5,6,7,8,9,10,11]. Unlike the open channel flow, flows in the ice-covered channel have asymmetric forms. The presence of the ice sheet makes the maximum streamwise velocity appear at the inner center of the flow, and the location of the maximum velocity is generally considered the division point in the asymmetrically distributed flow [12,13]. Previous studies have shown that the main effects of the ice sheets on alluvial channels can be summarized as: they increase the water level (compared to open channels at the same flow rate), reduce

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Conclusion