Nonlinear stability analysis of unimodal and multimodal sand bars | |
| Author | Adichai Pornprommin |
| Call Number | AIT Thesis no.WM-00-15 |
| Subject(s) | River channels--Mathematical models Geomorphology Sediment transport |
| Note | A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Engineering and Technology |
| Publisher | Asian Institute of Technology |
| Abstract | River morphology is self-fo1med through the interaction between the movements of water and sediment. The fact that the self-adjusting boundaries of alluvial rivers encompass a variety of parameters renders river morphology and river mechanics complex subjects. The bar is largescale topography appeared on riverbeds when the aspect ratio (width/depth) is sufficiently large. It is known that the bar formation is caused by the instability of erodible beds, and that there exists alternate and multiple bars depending on the mode, the number of bars laterally contained in a channel. It is known that channels with large aspect ratios commonly show complex bed topography composed of more than two different modes of bars. The objectives of this study are to present a nonlinear analyses for the bar formation and the interaction between two different modes of bars. Firstly, a two-dimensional nonlinear stability analysis of unimodal, alternate and multiple bars is performed with the use of the sediment transp01i formula including the effect of stream wise slope and the amplitude expansion method. The characteristic wavelength and the equilibrium amplitude are derived theoretically from the analysis. It is found that the characteristic wavelength is significantly shifted to larger wavelengths due to the effect of streamwise slope. The results for alternate bars are tested and show satisfactory agreement with experimental data. The theory shows that multiple bars with higher modes have smaller equilibrium amplitude in the vicinity of neutral stability curves. Secondly, two different cases of multimodal analyses, the interaction between the original mode and the non-propagating mode, and the interaction between the original mode and the higher mode, are performed with the use of the amplitude expansion method. In the case of the interaction between the original mode and the non-propagating mode, only a very narrow region is found to exist up to the second order, which does not explain real phenomena well. In the case of the interaction between the original mode and the higher mode, the equilibrium state is found in the third order solutions. Periodic, limit cycle solutions in both different modes are found to appear. The multimodal solutions show two interesting features that do not appear in the unimodal solutions: one is that the higher mode can be activated by the original mode even when the higher mode is in the decaying regime, and the other is that some irregularity which cannot be seen in the unimodal analysis appear due to the interaction of multimodal bars. |
| Year | 2001 |
| Type | Thesis |
| School | School of Engineering and Technology (SET) |
| Department | Department of Civil and Infrastucture Engineering (DCIE) |
| Academic Program/FoS | Water Engineering and Management (WM) |
| Chairperson(s) | Izumi, Norihiro |
| Examination Committee(s) | Tawatchai Tingsanchali ;Mark, Ole ;Sutat Weesakul |
| Scholarship Donor(s) | The Government of Denmark (Danida) |
| Degree | Thesis (M.Eng.) - Asian Institute of Technology, 2001 |