以二維有限元素形貌動力模式探討渠道強制效應對自由沙洲之影響

Abstract

本研究利用二維有限元素河川形貌動力模式，探討自由沙洲受變寬渠強制效應之影響。本研究所發展數值模式具有兩個特色：第一是使用流線曲率項來修正底床拖移載受到水流二次流影響後的運動方向。第二是以流線上風演算法處理泥沙連續方程式，使數值模式具有模擬強制沙洲(兩側沙洲、中央沙洲)與自由沙洲共存之能力。數值模擬發現強制沙洲與自由沙洲共存狀態屬於疊加，因此可將自由沙洲之演變取出討論。研究結果顯示自由沙洲之發展到達平衡狀態時，其波高、波長與波速受到渠寬變化所影響，會產生穩定的周期性波動，其週期平均值會隨變寬渠之振幅與波數增大而減小，本研究進一步將變寬渠之振幅與波數整合為一強制因子，對自由沙洲之影響效應進行量化分析，證明自由沙洲會受渠寬變化影響而被壓抑。

In this study a two-dimensional finite-element (2D FE) morphodynamic model is developed to investigate the forcing effects of periodic width variation on free bars. Two features of the proposed model include: (1) The streamline curvature are used to correct the bed load direction effected by secondary flows. (2) The streamline upwind Petrov-Galerkin (SUPG) scheme is applied to solve the sediment continuity equation, which makes it possible to simulate the coexistence of free bars and forced bars (such as side bars and central bars). It is found that the coexistence of free and forced bars is a superposition of the two types of bedform. Thus the free-bar component can be extracted for our study. The results reveal that the bar height, wavelength and celerity of free bars affected by the effect of width variation lead to a periodic wavy pattern when the development of free bars reach the equilibrium state. The mean components of free bars in a cycle of channels with variable-width are inverse proportioned to the amplitude and wave number of width variation. We further derive a forcing factor by combining the amplitude with wave number of width variation and quantitatively prove that the free bars are suppressed by the forcing factor of channels with variable width.