海域流場與其延散係數之數值模擬研究

Abstract

摘要 本研究主要分為兩個部份，第一部份是以二維水深平均(Depth Average)方程式，利用有限差分法(Finite Difference Method)之顯性差分(Explicit Scheme)模擬一個二維不可壓縮黏性流之海域流場，且不考慮風和科氏力的影響。研究區域為介於嘉義東石以南至台南將軍以北之海域。以兩種不同邊界條件分別討論一個潮汐週期十二小時的流況，並找出合理的邊界條件假設，再根據此邊界條件，針對不同的渦流黏滯係數及曼寧係數作討論，並找出流場的渦流黏滯係數值與曼寧係數值。 第二部份是根據所模擬的流場，在不同區域，以不同質點數的浮標群，探討浮標群在不同區域所產生的相對位置變化，並依此關係推求出二維的相對延散係數。另外更深入探討在不同格網大小及不同水深的情況下，對流場之影響及對質點浮標群所產生的相對延散情形。由本文所推求出的延散係數顯示，由於未考慮到風的影響，因此所求出的延散係數會比較小，但大致上均符合三分之四定理。

Abstract This research includes two parts. First, using two-dimensional depth-average governing equation with finite difference method of explicit scheme to solve a coastal flow which is incompressible, viscous, and do not consider the effects of the wind and Coriolis forces. The modeling region in this research is from Dong-Shi, Chia-Yie to Chiang-Chung, Tainan. To model a coastal flow during a tidal period 12 hours, we compare two different boundary conditions in the flow ,and then find the reasonable one. According to the condition, we make a further discussion in different eddy viscousity coefficients and manning coefficients, and then find the suitable ones. Second, according to the coast flow we have made, we discuss the relative variations of position of the groups of particles in different regions, and then estimate the relative dispersion coefficients by the relations of the groups of particles. In the other sides, we also discuss the situation of relative dispersion of the groups of particles by shortening grid size and non-uniform depth so as to know the further situation of groups of particles in the shortening grid size and non-uniform depth. According to dispersion coefficients we have estimated, the coefficients is smaller because we do not consider the effects of the wind, but they mostly still corresponding to the theory Fourth-three .