基于富里哀级数的河段水流模型结构误差研究

According to the problem of the research on flow models for rivers affected by river flow and tide in estuaries, an approach based on Fourier progression is proposed to describe model structure error and analyze the related factors. This work will explore a new way to construct a physical flow model for flow simulation under the combined effects of river flow and tide, which is more effective and practical in comparison with the existing models. Firstly, we establish an ideal model based on Navier-Stokes equations to analyze the feasibility of the usage of the Fourier progression to describe model structure error. This part includes the construction of the ideal model, the rulers for establishing Fourier progression, the expression of the constructed Fourier progression, and the validation with the successive approximation method based on Kalman filtering and gain matrix. Secondly, we use laboratory experiments and prototype observation in rivers with significant turbulent effect to analyze turbulence. The prototype observation is designed in typical reach with good boundary condition and channel geometry. This part includes the design of observation, data collection, validation of the proposed method from ideal model test, analysis of the correlation of changing tendency between the time series of the factors affected turbulence, and construction turbulence model. Thirdly, the proposed methods will be applied in common rivers to validate the performance.

针对河口地区洪潮作用河段水流模型研究中存在的不足,提出基于富里哀级数的模型结构影响因素分析与结构误差描述方法,探索洪潮组合作用水流的模型研究新路径,研究更实用、更有效、更普适性、更物理化的模拟模型。项目研究第一阶段将构建河道水流理想模型,先对理想模型进行方法性探索，分析富里哀级数表达模型结构误差的可行性、富里哀级数确定准则、表达结构与Kalman 增益逼近方法验证；第二阶段将以实验室试验和感潮河段紊动作用较大的水体为重点研究对象，原型观测选择边界条件、河道特征的误差相对较小的典型河段进行强化观测与水流模型研究。这主要包括强化观测方案设计、资料采集、理想模型研究所确定方法的实际水流检验、洪水与潮水及其风暴等众多误差因素影响的误差时间系列趋势关联性分析、水流模型结构误差研究等；第三阶段将基于富里哀级数的模型结构误差分析方法在一般性水流中的应用检验。以使方法与成果具有广泛的代表性。

针对河道水流和感潮河段受紊动影响而使水动力学模型摩阻模拟结构与实际出入大，常导致模型模拟误差大问题，项目提出摩阻结构改进和模拟误差描述方法研究。项目研究过程分为三个阶段。第一阶段以室内实验为基础，探索了河段水流模拟的理想模型构建方法，分析了富里爱级数表达模型误差的可行性;第二阶段选择钱塘江从闸口到之江水文站河段，进行了一个汛期的强化观测，结合第一阶段实验室观测的资料，研究了河段水流水动力学模型结构误差表达方法，提出了以水深和流速微分表达的摩阻公式;第三阶段将提出的摩阻公式和相应的水动力学模型应用于全国七条大中河流（长江、黄河、松辽河、钱塘江、曹娥江、椒江、珠江）43个不同水流特征的河段进行了验证，论证了其结构的合理性和模拟实际水流的有效性。