海湾、近岸海域水交换研究的关联矩阵方法及应用
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摘要
水交换是海湾、近岸海域的重要水动力学特性,是研究海湾、近岸海域环境容量的基础。目前,对水交换问题的研究主要有两类方法:一是在假定研究海域内水体充分混合的前提下,根据水量守恒和指标物质(通常为盐分)守恒,利用实测到的湾内外及湾口指标物质浓度差,计算海水交换率、交换时间,进而建立简单的水质预测模型,这类方法适用于小海湾。二是,直接用数值模拟方法模拟特定海域水体的运动过程,得出水交换时间尺度的分布。
本文针对大型海湾、近岸海域水交换的特点,在数值模拟的基础上,提出了用关联矩阵研究水交换的方法。关联矩阵的概念是,将研究海域划分为多个海区,用关联矩阵中的元素表示一定时刻某海区中来自其它海区的海水权重,整个矩阵描述了研究区域各海区间的水体交换关系。关联矩阵可由数值模拟结果统计而得,是对数值模拟结果中水体交换特征的提炼和归纳。
利用关联矩阵的矩阵运算可以预测在初始浓度或源项作用下的水质变化。利用矩阵运算预测水质变化是一种简单的水质预测模型,计算简单、速度较快,是对复杂数值模拟方法的一种补充。在进行水质预测的过程中,由于引入了交换浓度的概念,故放宽了对“海区内混合充分”假定的要求。
应用关联矩阵将驻留时间概念扩展到矩阵形式,用以表示各海区海水相互影响的时间尺度。推导出了各时间尺度与关联矩阵之间的关系。指出驻留过程和更新过程分别是以拉格朗日观点和欧拉观点描述水交换特征。
建立了用于模拟海湾、近岸海域水交换的水动力学数学模型和对流扩散数学模型,通过解析解和实测资料对本文所建立的数学模型进行了检验和验证。针对数值模拟中缓坡浅海海域宽阔潮间带上的动边界处理问题,提出了一种基于“预估水深”的新的干湿判断方法,并应用多个算例对所提出的干湿判断方法进行了验证。结果显示,本文的干湿判断方法无明显的数值振荡产生,且可以较准确的估计浅水处水体的蓄留能力。
通过典型算例,对所提出的用关联矩阵研究水交换的方法进行了检验。并将其应用于渤海、渤海湾和天津近岸海域的水交换研究当中。
Water exchange is an important hydrodynamic character of sea bay and coastal water, and it is the basis to study the environmental capacity of the water body. There are two main approaches to the study of water exchange. Firstly, based on the assumption that the studied bay is mixing sufficiently, the whole exchange rate or time is calculated by the measured concentration in the bay, out of the bay and at the mouth of the bay, according to the conservation of the water body and the index substance (the salinity is used usually). This method is effective for the bay with small area. Secondly, the distribution of the character time scales of water exchange can be obtained by numerical simulation of water motion.
In this dissertation, based on the numerical simulation, the relation matrix is introduced to study the water exchange of sea bay or coastal water with large area. With the study area divided into sub-areas, the element of relation matrix is used to represent the water weighting of certain sub-area contributed by another sub-area, while the relation matrix describe the water exchange relationship among sub-areas. This matrix can be calculated by the results of numerical simulation, and can be considered as the extraction and conclusion of the water exchange character.
Variation of water quality due to initial field and source can be predicted by the operation of relation matrix. This method is a simplified model for water quality prediction with simply computation and rapid speed, so it is an effective complement to the complex numerical simulation. In the water quality prediction by relation matrix, the assumption of sufficient mixing is relaxed due to the introduction of the exchange concentration.
The conception of residence time is extended from single value to the matrix form which is used to express the time scales of the interaction of water body in the sub-areas. The relation formula of the time scales and the relation matrix is educed. It is pointed out that the residence process and the flushing process characterize the water exchange in Lagrangian viewpoint and Eulerian viewpoint respectively.
The hydrodynamic model and the advection-diffusion model are set up to simulate the water exchange. The models are verified by cases with exact solutions and validated against the measured data. In the numerical simulation, a new wetting and drying method based on the“predicted water depth”is developed to deal with the moving boundary due to tidal waves at the tidal flat. In order to validate the new method, test cases are performed. The results show that the new method leads to no excessive numerical wiggles and results in effective estimation of retention volume in each cell with shallow water.
The method of relation matrix is verified by a series of typical cases. And it is applied to the water exchange of the Bohai Sea, the Bohai Bay and the Tianjin Coastal Water.
本文针对大型海湾、近岸海域水交换的特点,在数值模拟的基础上,提出了用关联矩阵研究水交换的方法。关联矩阵的概念是,将研究海域划分为多个海区,用关联矩阵中的元素表示一定时刻某海区中来自其它海区的海水权重,整个矩阵描述了研究区域各海区间的水体交换关系。关联矩阵可由数值模拟结果统计而得,是对数值模拟结果中水体交换特征的提炼和归纳。
利用关联矩阵的矩阵运算可以预测在初始浓度或源项作用下的水质变化。利用矩阵运算预测水质变化是一种简单的水质预测模型,计算简单、速度较快,是对复杂数值模拟方法的一种补充。在进行水质预测的过程中,由于引入了交换浓度的概念,故放宽了对“海区内混合充分”假定的要求。
应用关联矩阵将驻留时间概念扩展到矩阵形式,用以表示各海区海水相互影响的时间尺度。推导出了各时间尺度与关联矩阵之间的关系。指出驻留过程和更新过程分别是以拉格朗日观点和欧拉观点描述水交换特征。
建立了用于模拟海湾、近岸海域水交换的水动力学数学模型和对流扩散数学模型,通过解析解和实测资料对本文所建立的数学模型进行了检验和验证。针对数值模拟中缓坡浅海海域宽阔潮间带上的动边界处理问题,提出了一种基于“预估水深”的新的干湿判断方法,并应用多个算例对所提出的干湿判断方法进行了验证。结果显示,本文的干湿判断方法无明显的数值振荡产生,且可以较准确的估计浅水处水体的蓄留能力。
通过典型算例,对所提出的用关联矩阵研究水交换的方法进行了检验。并将其应用于渤海、渤海湾和天津近岸海域的水交换研究当中。
Water exchange is an important hydrodynamic character of sea bay and coastal water, and it is the basis to study the environmental capacity of the water body. There are two main approaches to the study of water exchange. Firstly, based on the assumption that the studied bay is mixing sufficiently, the whole exchange rate or time is calculated by the measured concentration in the bay, out of the bay and at the mouth of the bay, according to the conservation of the water body and the index substance (the salinity is used usually). This method is effective for the bay with small area. Secondly, the distribution of the character time scales of water exchange can be obtained by numerical simulation of water motion.
In this dissertation, based on the numerical simulation, the relation matrix is introduced to study the water exchange of sea bay or coastal water with large area. With the study area divided into sub-areas, the element of relation matrix is used to represent the water weighting of certain sub-area contributed by another sub-area, while the relation matrix describe the water exchange relationship among sub-areas. This matrix can be calculated by the results of numerical simulation, and can be considered as the extraction and conclusion of the water exchange character.
Variation of water quality due to initial field and source can be predicted by the operation of relation matrix. This method is a simplified model for water quality prediction with simply computation and rapid speed, so it is an effective complement to the complex numerical simulation. In the water quality prediction by relation matrix, the assumption of sufficient mixing is relaxed due to the introduction of the exchange concentration.
The conception of residence time is extended from single value to the matrix form which is used to express the time scales of the interaction of water body in the sub-areas. The relation formula of the time scales and the relation matrix is educed. It is pointed out that the residence process and the flushing process characterize the water exchange in Lagrangian viewpoint and Eulerian viewpoint respectively.
The hydrodynamic model and the advection-diffusion model are set up to simulate the water exchange. The models are verified by cases with exact solutions and validated against the measured data. In the numerical simulation, a new wetting and drying method based on the“predicted water depth”is developed to deal with the moving boundary due to tidal waves at the tidal flat. In order to validate the new method, test cases are performed. The results show that the new method leads to no excessive numerical wiggles and results in effective estimation of retention volume in each cell with shallow water.
The method of relation matrix is verified by a series of typical cases. And it is applied to the water exchange of the Bohai Sea, the Bohai Bay and the Tianjin Coastal Water.
引文
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