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Debris-flow events often comprise a sequence of surges, sometimes termed “roll waves.” The reason for this surging behavior is still a matter of debate. Explanations include the growth of hydraulic instabilities, periodic sediment deposition and release, or grain size sorting. High-resolution field measurements together with triggering rainfall characteristics are rare. We present results for 3 years of monitoring debris-flow events at Lattenbach Creek in the western part of Austria. The monitoring system includes a weather station in the headwaters of the creek, radar sensors for measuring flow depth at different locations along the channel, as well as a two-dimensional rotational laser sensor installed over a fixed cross section that yields a threedimensional surface model of the passing debris-flow event. We find that the debris flows at Lattenbach Creek were all triggered by rainstorms of less than 2 hours and exhibited surges for each observed event. The velocities of the surges were up to twice as high as the front velocity. Often, the first surges that included boulders and woody debris had the highest flow depth and discharge and showed an irregular geometry. The shape of the surges in the second half of the flow, which carried smaller grain sizes and less woody debris, were rather regular and showed a striking geometric similarity, but still high velocities. The results of our monitoring efforts aim to improve our understanding of the surging behavior of debris flows and provide data for model testing for the scientific community. [ABSTRACT FROM AUTHOR]

The mathematical model of inhomogeneous fluid motion in a Hele–Shaw cell is proposed. Based on this model the equations for describing two-layer flows and development of roll waves at the interface are derived. Conditions of roll waves existence are formulated in terms of Whitham criterion. Numerical calculations of the interface position are provided. It is shown that small perturbations of the interface in the inlet section of the channel lead to the roll waves for certain parameters of the flow. Two-parametric class of exact solutions corresponding to the roll waves regime is obtained. Diagrams of critical depths of roll waves development are constructed. [ABSTRACT FROM AUTHOR]

A laminar flow of a thin layer of mud down an inclined plane under the action of gravity is considered. The instability of a film flow and the formation of finite amplitude waves are studied within the framework of both two-dimensional governing equations of a power-law fluid and its depth-averaged hyperbolic simplification. The conditions of the existence of roll waves for these models are formulated in terms of the Whitham criterion. A free surface evolution and the development of roll waves are numerically calculated. The amplitude of roll waves obtained by the 2D equations is slightly larger than that for the 1D model. Moreover, for certain flow parameters, the small perturbations of the basic solution grow for the 2D equations and decay for the depth-averaged model. A two-parameter class of exact piecewise-smooth solutions of the 1D model is obtained and a comparison with a numerical solution is made. In the region of these parameters, diagrams of the roll waves existence are constructed. • A nonlinear analysis of the stability of film flows of a power-law fluid is carried out. • The difference in the flow stability criteria for 2D and 1D models is established. • Numerical calculations of the roll waves development are performed. • Diagrams of the existence of roll waves are constructed. [ABSTRACT FROM AUTHOR]