基于涡黏度模型的冰封河道纵向时均流速垂向分布解析解

Analytical solution for the vertical distribution of the longitudinal time-averaged velocityin ice-covered channel based on the eddy viscosity model

冰盖的存在显著改变了河道水流结构,使流速垂向分布关于零切应力平抛物线面呈型。考虑到准确预测冰盖下水流流速分布是计算冰封河道流量、泥沙输移率和河床演变预估的基础,本文应用双层假定和冰盖流涡黏度模型,推导出一个物理意义明确且速度梯度连续的冰封河道纵向时均流速垂向分布解析解,并明确常见的冰盖流对数流速公式和双幂律流速公式的应用条件。采用水槽实测数据和原型实验数据,对比分析所提出的解析解与现有对数公式和双幂律公式的有效性和精确性,并基于本文解析解探究了纵向时均流速垂向分布对各物理特征参数的敏感性。结果表明,该解析解的流速计算值与实测值吻合较好且较现有对数公式和双幂律公式具有较高精度;雷诺数的较小变化并不会引起纵向时均流速垂向分布的较大改变,但流速分布对冰盖糙率与河床糙率的相对值比较敏感,且纵向时均流速的最大值偏向于较光滑边界一侧,该结论与以往基于k-ε湍流模型所得到的数值结果是一致的,再次证实了本文解析解的有效性。

The existence of ice cover significantly changes the flow structure of the river,wherein the vertical distribution of the streamwise velocity is parabola with respect to the zero shear stress plane.Given that accurately predicting the velocity distribution is the basis of calculating the flow discharge,the sediment transport rate,and the bed evolution for ice-covered channels,an analytical solution for the vertical distribution of the longitudinal time-averaged velocity in ice-covered channels,which has a clear physical meaning and continuous velocity gradient,was derived by applying the two-layer hypothesis and the eddy viscosity model.Meanwhile,the application conditions of the frequently used log-law velocity formula and two-power law velocity formula were clarified.By using available experimental data and field data reported in the literature,the validity and accuracy of the analytical formula presented here were then compared with that of the existing log-law velocity formula and two-power law velocity formula.Based on the validated analytical formula,the sensitivity of the vertical distribution of the longitudinal time-averaged velocity to the physical characteristic parameters was also explored.The results show that the calculated values of the streamwise velocity by the presented analytical formula are in good agreement with the measured data and have higher accuracy than that of the log-law formula and the two-power law formula.Sensitivity analysis displays that the Reynolds number has little influence on the vertical distribution of the longitudinal time-averaged velocity,whereas the vertical distribution of the velocity is sensitive to the relative value of the ice cover roughness and the channel bed roughness.The maximum value of the longitudinal time-averaged velocity tends to the smooth boundary.These results are consistent with previous numerical results obtained by the k-εturbulence model,which again confirms the validity of the presented analytical solution.