地下水海水入侵之研究

Abstract

對於傳統地下水具明顯交界的海水入侵之流體力學，係將明顯交界面視為固體邊界且無回流機制，故本研究發展一套有別於傳統的全新理論。先令壓力與流速為穩態(steady)與非穩態(unsteady)的線性組合，首先吾人釐清了傳統交界蓋本-赫茲方程式(Ghyben-Herzberg eq.)的來源，接著以黑姆赫茲(Helmholtz)拆解流速為非旋性(irrotational)部分與旋性(rotational)部分，代入布林克曼方程式(Brinkman eq.)方程式，解決傳統不合物理現象及疑惑。 本研究發現(1)海、淡水交界面是流體而不是固體，(2) 海、淡水交界面的流動呈邊界層現象，使海水產生回流，(3) 海、淡水交界面的趾部(toe)是停滯點，不會不合理地無限延伸。此外，吾人亦提出海水入流之基底流概念，透過質量守恆求得且基底流將驅動海、淡水交界面之下的海水流動。 本研究使用邊界積分法分別解出非旋性部分海、淡水之流況，再以邊界層方程式解出海、淡水交界面旋性部分的流場。此外，根據邊界海水波浪擾動案例模擬結果顯示擾動越大邊界層厚度越厚，海淡水交界面位置移動顯著。 最後，為使本研究落實現場地下水計算應用，將利用數條地質斷面找尋基底流，再透過內插方式而得到海水入流邊界條件，結合地下水計算 座標轉換，疊代求解出三維海水入侵問題。本研究以屏東平原的初步資料且簡化地質條件作為應用案例，成功完成屏東平原地下水海水入侵問題的初步計算。

In the literatures, saltwater intrusion has been studied for long time. However, since the lack of boundary conditions at saltwater intrusion areas, or considering freshwater-saltwater interfaces as solid boundary and assuming there is no stagnation point for saltwater intrusion, those models are insufficient for explanations of real world. First, we clarified Gheben-Herzberg equation, and Helmholtz theory is applied to sparate the irrotational potential flow and rotational viscous boundary layer flow. Last, Brinkman equation is applied to calculate boundary layer. The study found phenomena that (1) freshwater-saltwater interfaces as fluid boundary; (2) saltwater could reflux because of the boundary layer effect; (3) there is stagnation point for saltwater intrusion. This allows us to understand the mechanism of saltwater intrusion which includes the fluctuations of boundary layer effect. On the other hand, we propose the conceptual of saltwater base flow, using the law of conservation of matter, the amount of saltwater injection must equal to the amount of fresh water outflow. The concept of saltwater base flow can provide simulated boundary condition to handle the correct flow condition at simulated area when the real boundary condition is absent. Utilizing mathematical formulation, boundary layer effect and the base flow of saltwater to construct the saltwater intrusion mechanisms. In the earlier stage of the study, we propose a new idea for two-dimensional seawater intrusion. In order to utilize the theory, we extend the study to three-dimension and provide a more reasonable method. First, we plan to construct the seawater intrusion mechanisms by interpolating and deriving the boundary conditions of saltwater base flow. Moreover, we extend the groundwater model for irregular boundary (Wang(2013)) to simulate seawater intrusion mechanisms. By using mathematical theories, boundary effect, conceptual of seawater base flow and intrusion mechanism The calculation of groundwater seawater intrusion in Pingtung Plain was successfully completed.