基于流量函数的海水交换数值模拟研究

水体交换能力只与水体的流动性有关，目前有关水交换的研究大多是通过指示物质浓度来计算水体交换率以及交换时间，其结果不能准确地体现海水交换能力。本文以一个T形区域为例，提出基于流量函数的一种水体交换计算方法。在三维连续方程沿水深方向积分的基础上得到水深平均的二维浅水方程，求解得到流速、水深等数据；进而对二维浅水方程积分引入流量函数；做出流量函数对应的等值线分布图。等值线分布图中显示模拟区域内一半以上的水体能被交换至域外，计算模型前、后半周期的海水交换率分别为0.6396和0.6465。结果表明:采用基于流量函数的数值模拟方法评价某区域的水体交换能力简单而可行，通过流量函数等值线分布图能够直观的反映出区域水体的水交换能力。

Numerical simulation of seawater exchange based on flow function

The water exchange capacity is only related to the fluidity of water.At present, most of the researches on water exchange rely on the concentration of indicator material to calculate water exchange rate and exchange time.But the results cannot reflect the exchange capacity of seawater accurately.Taking a T-shaped region as an example, the paper proposes a calculation method of water exchange based on the flow function.First, obtaining a two-dimensional shallow water equation with the average depth of water based on the integral of the three-dimensional continuous equation along the water depth.By solving the equation, data such as the velocity and depth are obtained.Then making contour map corresponding to flow function, which is obtained by integrating the two-dimensional shallow water equation.It can be clearly seen from the contour map that more than half of the water in the simulated area can be exchanged out of the area.Respectively, it is calculated that in the front and back half of the model the seawater exchange rates are 0.6396 and 0.6465.The result shows that it is simple and feasible to evaluate the water exchange capacity of a certain area by using the numerical simulation method based on the flow function.The contour map can directly reflect the water exchange capacity.