支流堰塞湖演變分析：實驗與數值方法

Experimental and numerical study of evolving tributary-dammed lakes

翁琬晴(Wan-Ching Weng)

指導教授 ： 卡艾瑋

國立臺灣大學/工學院/土木工程學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.01829

摘要

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。

關鍵字

河床演變 ； 支流堰塞湖 ； HLL ； 特徵結構 ； 一維淺水方程模式 ； 二階精度

並列摘要

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.

並列關鍵字

Fluvial geomorphology evolution ； Tributary-dammed lake ； HLL ； Eigenstructure ； One dimensional shallow-water model ； Second-order accuracy

參考文獻

[3] Capart, H., Hsu, J. P., Lai, S. Y., & Hsieh, M. L. (2010). Formation and decay of a tributary‐dammed lake, Laonong River, Taiwan. Water Resources Research, 46(11).

[8] Dong, J.-J., Li, Y.-S., Kuo, C.-Y., Sung, R.-T., Li, M.-H., Lee, C.-T., Chen, C.-C, Lee, W.-R. (2011). The formation and breach of a short-lived landslide dam at Hsiaolin village, Taiwan—part I: post-event reconstruction of dam geometry. Engineering Geology, 123(1), 40-59.

[9] Fraccarollo, L., Capart, H., and Zech, Y. (2003). A Godunov method for the computation of erosional shallow water transients. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 41, 951–976.

[10] Fraccarollo, L., and Capart, H. (2002). Riemann wave description of erosional dam-break flows. Journal of Fluid Mechanics, 461, 183-228.

[11] Harten, A., Lax, P. D., and Leer, B. (1983). On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM review, 25, 35-61.