擾動法概念應用於具明顯交界面海水入侵之研究

近年來，台灣沿海地區包括屏東、嘉義縣布袋、東石及雲林縣一帶，由於養殖業超抽地下水，造成地層下陷、海水入侵貯存淡水的含水層。本研究之海水入侵方式為海水由海岸線入侵。探討海水由海岸線入侵之研究方法約可分成兩大類：其一為假設海水與淡水交界區為明顯交界面（sharp interface），其二為假設海水與淡水可以相混。在本文擬探討的海水入侵問題為具明顯交界面之海水入侵。因淡水與海水的密度差相當微小，故本研究有別於一般研究此問題的方法，應用擾動法概念，先行計算淡水部分之勢能分布，再計算海水擾動部分，最後合成淡水部分及海水擾動部份以求得海水入侵之解，而不進行海水與淡水聯立計算或甚至假設海水處於靜止狀態。本研究於求解三維海水入侵問題時，水平方向採用具有局部解析解與無條件收斂之有限解析法（finite analytic method），而垂直方向則採用二次內插形狀函數，如此不但能同時求解多層含水層問題，亦能模擬垂向水頭變化。本研究方法之特點可歸納如下：1﹒適用於交界面型態為明顯交界面（sharp interface），2﹒不為杜布假設（Dupuit assumption）所限，3﹒海水可流動而非假設為靜止狀態，4﹒不需耦合求解海水及淡水，僅需先計算淡水部分之水頭，再藉擾動法求出微小密度差海水擾動部分之水頭即可。本研究以Wilson and Sa Da Costa（1982）解析解與Strack（1976）、Strack（1989）解析解作檢驗。另外，以圓形海島及不連續土層兩案例之測試展現模式能用於現地複雜地質之運算能力。

關鍵字

明顯交界面；海水入侵；擾動法

並列摘要

Recently, landsubsidence and aquifer pollution due to seawater intrusion caused by groundwater over pumping of farm fishing business have happened in coastal areas of Taiwan such as Ping-dong, Budai, Yunlin, etc. The so-called seawater intrusion in this study is seawater invading from the coastal line. There are two ways to investigate this kind of seawater intrusion：the first way assumes there is a sharp interface between fresh water and seawater, and the second way allows mixing of seawater and fresh water. In this study, we choose the first way. Because the little density difference between seawater and fresh water, other than using conventional methods, we apply perturbation concept to solve our seawater intrusion problem. Neither solving seawater and fresh water simultaneously, nor assuming the seawater stationary（Gyben assumption）, in this study, we compute fresh water potential first, then compute the perturbation part due to density difference of seawater and fresh water, and finally combine both parts to get the completed solution. In our three dimensional computation, the finite analytic method which preserves local analytical solution and unconditional convergence is applied to our horizontal two dimensional computation, while the second order polynomial is used as the vertical interpolation function. Hence we can not only solve problems with multiple layers of aquifers but also obtain vertical variation of water head for each layer. The characteristics of our method can be summarized as follows：1. the method is only valid for seawater intrusion with sharp interface, 2. Duipuit’s assumption is not necessary, 3. Gyben assumption is not necessary（i.e. it is not necessary to assume stationary seawater）, 4. fresh water and seawater perturbation are solved in sequence instead of solved fresh water and seawater simultaneously as conventional method does. The model established in this study is examined by the analytical solutions of Wilson and Sa Da Costa（1982）, Strack（1976）and Strack（1989）. The computation capability of this model is also tested by the cases of a circle island and a discontinuous multiple layered soil.

並列關鍵字

sharp interface ； seawater intrusion ； perturbation method

參考文獻

3.Bear﹐J﹒ and G﹒Dagon﹐〝Some exact solution of interface problem by means of the hydrograph method﹐〞J﹒Geophvs﹒Res﹒69（8）﹐pp﹒1563–1572﹐1964﹒

4.Bear﹐J﹒ and I﹒ Kapular﹐〝A numerical solution for the movement of an interface in a layered coastal aquifer﹐〞Jour﹒of Hydrology﹐50：273–298﹐1981﹒

5.Columbs﹐N﹒〝Viscous models study of sea water intrusion in water table Aquifers﹐〞Water Resour﹒Res﹒﹐Vol﹒1﹐No﹒2﹐313–323﹐1965﹒

6.Essaid（1990）﹐A Multilayered Sharp Interface Model of Coupled Freshwater and Saltwater Flow in Coastal Systems：Model Development and Application﹐Water Resour﹒Res﹒26（7）﹐1431-1454﹐1990﹒

7.Fetter﹐C﹒W﹒﹐〝Position of the saline water interface beneath oceanic island﹐〞Water Resour﹒Res﹒8﹐1307–1314﹐1972﹒

國際替代計量

擾動法概念應用於具明顯交界面海水入侵之研究

全文下載

主題瀏覽