自由沙洲與強制沙洲之非線性解析

Nonlinear Analyses on Free and Forced Bars

葉子豪(Tzu-Hao Yeh)

指導教授 ： 吳富春

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.00919

摘要

本研究包含兩部分。在第一部份，我們以奇異擾動法進行自由沙洲的非線性解析。在先前Colombini et al. (1987) 的研究中，其模式藉由給定的沙洲波數來預測相對應的沙洲高度。在此，我們將其研究加以延伸，並在四個可解析條件同時成立的情況下，得到自由沙洲的波數與高度解析解。透過與釵h前人實驗結果的比較，我們發現本模式會高估實際波數並且低估實際高度。本研究建議未來可納入其他的物理現象（例如懸浮載及二次流現象等）再進一步提高模式的精確度。
在第二部分，我們探討在變寬渠道中強制沙洲的非線性解析。基於數學推導複雜度與模式精確度的考量，我們在此引用一般擾動法。由非線性的解析中，我們發現了在線性解析中所未見的二次床形，因而驗證了前人實驗結果。透過兩者細部的比較，我們發現非線性的解析比線性解析更能適切的描述河床的形貌。然而，在本研究實驗條件下，線性與非線性解趨於一致，表示渠寬的變化微小時，可忽略非線性的效果。

關鍵字

變寬渠道 ； 沙洲 ； 擾動法 ； 河川形貌 ； 河床侵蝕與淤積

並列摘要

This study consists of two parts. In Part I, a nonlinear analysis of free bars in straight channels is made using a singular perturbation method. We followed the work of Colombini et al. (1987) and discovered the self-generating feature of the alternate bar wavenumber and bar height by imposing all four solvability conditions. In contrast to the previous model which predicts only alternate bar height given alternate bar wavenumber, the present model enables us to obtain both features characterizing alternates bars under specified flow and sediment conditions. Comparisons between the predicted and experimental results show that the model tends to give an overall overestimation of the wavenumber and an underestimation of the bar height. Further incorporation of other effects such as suspended load and secondary flow is suggested to eliminate such tendencies.
In Part II, we deal with the problem of forced bars in channels with variable width. A regular perturbation method is used for the nonlinear analysis of the problem to balance the derivation complexity and model accuracy. Bedforms obtained from the nonlinear analysis exhibit secondary features including a secondary trough and a secondary peak which are previously neglected in the linear analysis. In comparison with previous experimental results, the existence of such secondary bedforms is found as that described exhibit better agreement than linear solutions. The resemblance of the solutions given by the linear and nonlinear theories when applied to our experiments further implies that the nonlinear effects are negligible when the amplitude of width variation is small, however, significant errors may be produced when that is large.

並列關鍵字

bars ； perturbation method ； river geomorphology

參考文獻

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