1 AIT Asian Institute of Technology

Linear stability analysis of the generation of roll waves in water flows and debris flows

AuthorNguyen Huy Phuong
Call NumberAIT Thesis no. WM-00-07
Subject(s)Debris avalanches
NoteA thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Engineering and Technology
PublisherAsian Institute of Technology
AbstractThe debris flow is a flowage of mixture of all sizes of sediment. It is frequently observed that debris flows, especially mudflows, consist of waves or successive surges. While it is known that a number of large rocks gather at the surge front, which causes strong, destructive power of debris flows, the mechanism of the wave or surge formation has not been completely clarified. In this study, a mathematical model to describe the surge formation is presented based on the idea that the debris flow surges are physically identical to the roll waves observed in water flows. Roll waves are commonly observed in sheet flows on comparatively steep slopes. The roll waves are characterized by a series of waves each of which has a strongly discontinuous surge front and the subsequent mildly-varied portion. The generation of roll waves has been described by the linear stability analysis with the use of the long wave approximation and the depth-averaged shallow water equations. According to the existing theory, however, the characteristic wavenumber associated with the maximum growth rate of disturbance turned out to be infinitely large; thus, infinitely small wavelengths should be dominant in waves. In this study, a new theo1y with the use of non-depth-averaged flow equations is presented to explain the generation of roll waves. The theory is, then, extended to apply to the fonnation of debris flow surges with the use of the Newtonian fluid formulation. In the analysis of roll waves in water, it is found that the critical Froude number beyond which uniform flows destabilized to evolve into a series of waves takes a value between 1.2 and 2.4 dependently on the condition of bottom friction. It is also found that the uniform flow is stabilized against the waves with wavenumbers larger than 1.0-5.0. The angular frequency derived from the theo1y is found to agree well with experimental results. In the analysis of debris flows, the critical Froude number is found to be 0-1.0, which is considerably smaller than the case of water. Theory shows that the largest possible wavenumber beyond which waves do not appear is 1.0-5.0. The relation between angular frequency and wavenumber (dispersion relation) is found to be explained by the present the01y reasonably well. This strongly suggests that the debris flow surges are generated due to the same instability that causes roll waves in water.
Year2001
TypeThesis
SchoolSchool of Engineering and Technology (SET)
DepartmentDepartment of Civil and Infrastucture Engineering (DCIE)
Academic Program/FoSWater Engineering and Management (WM)
Chairperson(s)Izumi, Norihiro
Examination Committee(s)Gupta, Ashim Das ;Babel, Mukand Singh ;Sutat Weesakul
Scholarship Donor(s)Swedish International Development Cooperation Agency
DegreeThesis (M.Eng.) - Asian Institute of Technology, 2001


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