Modeling One and Two Dimensional Evolution of Straight Channels after Dam Removal

本研究基於Exner方程式進一步探討壩體移除後底床變動的一維及平面二維現象，主要為輸砂率變動對底床變動的影響。在一維渠道方面，藉由均勻流及定流量且忽略泥砂啟動剪應力的假設，可以將Exner方程式化簡成擴散方程式，並可以利用傅立葉轉換方法求得解析解，同時，可以使用有限差分法求此擴散方程式之數值解，藉以驗證解析解的正確性；而在二維渠道方面，假設固定邊壁且無二次流效應之直線河床，其控制方程式具有非線性項，較難以一般方法求得解析解，故本研究同樣沿用一維情條件之假設，使用有限差分法解出此二維渠道變動之數值解。 在一維解析解中，庫區淤砂的沖蝕速度將隨時間遞減，顯示拆壩初期的泥砂運移會比較強烈；至於二維結果，可以發現在本研究之假設條件下，河道兩側泥砂會向河道中心填滿，進而成為一近似於一維之渠道，而沒有在二維方向的變化。總的來說，一維河道的沖淤行為最主要由擴散係數所控制，而擴散係數同時是流量的函數，而在二維條件時，主要的控制因子則為一表示水與砂關係的係數，顯示水文條件可能是河道變動的主要因素。This study tries to use the Exner equation to investigate the one dimensional and horizontal two dimensional channel evolution after removal of a dam. The Exner equation considers the difference of sediment transport rate in space to govern the channel evolution. In 1D condition, by assuming uniform flow, no incipient shear stress, and constant flow rate, the Exner equation can be derived as a diffusion equation. In this study, this equation is solved analytically by Fourier transformation method. On the other hand, the Exner equation under a horizontal 2D straight, inerodible banks, and no secondary flow channel can be derived as our governing equation which has the nonlinear terms, and the analytical method might not work to solve the Exner equation under the 2D condition. Hence, we adopt the finite difference method to proceed this work. The result of 1D analytical solution represents that the flushing rate is decreasing as time goes by, and reveals the sediment transport rate is significant in the early stage of the dam removal. On the other hand, the 2D results represent that under our assumptions, the sediment will transport to the center of the channel to become very similar to the 1D phase. In summary, the 1D channel evolution is dominated by the diffusivity which is a function of flow rate, and the 2D channel is dominated by the relationship between sediment and water. Thus, the hydrology condition might be the main factor to control the channel evolution