支流堰塞湖演變分析：實驗與數值方法

Abstract

本篇論文結合實驗與數值計算模擬支流大量供砂下河床變化之情形。實驗渠道為長312公分，寬1.2公分的小尺度實驗，以上游流量與供砂量達動床平衡作為初始條件，在渠道中游提供三種供砂量，並藉此使河川形貌動力產生不同的現象，經由影像處理自動捕捉底床與水面的變化，再透過淺水方程式 (Shallow water equation)，艾克納方程式 (Exner equation)以及邊界特徵結構分析 (Eigenstructure analysis)，並根據HLL與LHLL和有限體積法建立一維雙層地貌數值模式。本文中亦延伸該模式至二階精度以探討不同階數次序的模擬差異，最後透過實驗結果以檢核數值模擬的表現。

In this study, one-dimension laboratory experiments and mathematical descriptions are used to perform the evolution of river influenced by tributary sediment influx. For the small-scale laboratory experiments (312cm long and 1.2 cm width), three tests are conducted to describe the differences of the morphodynamic response of the river bed: tributary-induced cuspate aggradation, tributary-dammed lake and water blocking dam. To simulate the phenomena, the numerical model dividing the flow into two layers, a pure water layer and a sediment transport layer, adopts shallow water equations that govern the evolution of each interface: with appropriate boundaries which depend on characteristics equations. According to the HLL, LHLL scheme and finite volume numerical solver, the model can be extended to both first-order and second-order accurate version. The proposed methods are applied to the laboratory experiments in order to examine the performance of the one dimensional geomorphological model.