| Summary: | 碩士 === 國立臺灣大學 === 生物環境系統工程學研究所 === 92 === 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.
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