基于分形理论的冰下水流流速垂线分布研究  

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

作　　者：罗红春 冀鸿兰[1] 郜国明[2] 张宝森[2] 牟献友[1] LUO Hongchun;JI Honglan;GAO Guoming;ZHANG Baosen;MOU Xianyou(College of Water Conservancy and Civil Engineering,Inner Mongolia Agricultural University,Hohhot 010018,China;Yellow River Institute of Hydraulic Research,Zhengzhou 450003,China)

机构地区：[1]内蒙古农业大学水利与土木建筑工程学院,内蒙古呼和浩特010018 [2]黄河水利科学研究院,河南郑州450003

出　　处：《水利学报》2020年第1期102-111,共10页Journal of Hydraulic Engineering

基　　金：国家重点研发计划项目(2018YFC1508401);国家自然科学基金项目(51969020,51569020);2018自治区应用技术研究与开发资金项目(201802104)。

摘　　要：冰下水流流速分布是冰凌生消、泥沙输移、河床演变及冰期输水的重要参考依据,基于分形理论,在前人的研究基础上,研究了冰下水流流速垂线分布规律。结果表明,依托明渠水流的若干成果,从分形理论出发,基于Einstein假定,可推出已有冰下不同形式的流速垂线分布公式;理论分析认为,冰下分区水流流速分布近似镜像,均具有分形特征,可用双对数公式表达,实测结果证明,对于弯曲河道,水流核心区流速分布均匀,并不服从对数分布,公式在运用时需考虑适用性或引入因子项;稳封期,冰盖区水流流速分布的分维值大于河床区,流速分布更均匀,而在弯道卡冰区域,由于弯道冰下水流结构的复杂性,河床区水流流速分布的分维值无规律。对冰下水流流速的研究,拓展了分形理论在水流流速垂线分布研究方面的应用成果,概化的冰下水流结构,对工程运用有一定借鉴意义。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 ver⁃tical distribution law of flow velocity under ice is studied.The results show that,based on the fractal theo⁃ry and Einstein hypothesis,different existing vertical distribution formulas of velocity under ice can be de⁃rived 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 characteris⁃tics,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 logarith⁃mic 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 frac⁃tal theory in the research on the vertical distribution of flow velocity,the generalized structure of subgla⁃cial flow has certain reference significance for engineering application.

关 键 词：分形理论 冰盖 水流 流速 垂线分布 

分 类 号：TV133[水利工程—水力学及河流动力学]