Occurrence conditions of roll waves for three grain–fluid models and comparison with results from experiments and field observation

Abstract

For the flow and deposition behaviour of debris flows, phenomena like particle sorting, levee formation and the development of roll waves are expected to be important processes. However, these processes are not well understood and hardly implemented in modelling approaches. In this study, we focus on the development of roll waves and derive advanced criteria separating stable and instable flow regimes for three debris flow models. These criteria are expressed using critical Froude numbers. Each of these simple flow models reflect different sources of flow resistance: laminar-viscous stress (Bingham type), dispersive stress due to particle collision (Bagnold type), and a model combining turbulent and dispersive stresses. Subsequently, we compare the predictions from these models with results from laboratory experiments with grain-fluid mixtures in a straight flume and with observations from a debris flow monitoring site at the Lattenbach creek in Austria. The experimental flows match with a turbulent flow model including particle collisions. For the natural flows the connection between models and observations is not clear due to limited field data. The results of our study contribute to an improved determination of critical flow conditions and provide data for model testing.

Effects of coarse grain size distribution and fine particle content on pore fluid pressure and shear behavior in experimental debris flows

“…We infer length and mean velocity of debris flow surges in alpine regions from hydrographs reported by Arai et al . [] with 100–500 m and 5–10 m/s, respectively, and calculate an upper bound of T fc,DF ~ 10 1 s, which is 1 order of magnitude longer than in our experiments.…”

Debris-flow velocities and superelevation in a curved laboratory channel

“…Observations from debris-flow monitoring stations, like at Lattenbach (Arai et al 2013), Illgraben (Rickenmann et al 2001;Hürlimann et al 2003), the Moscardo torrent (Marchi et al 2002) or Chalk Cliffs (McCoy et al 2011), lack superelevation data. Mizuyama and Uehara (1981) as well as Ikeya and Uehara (1982) first analysed the application of the forced vortex equation for debris-flow velocity estimates, based on the results of small-scale laboratory experiments.…”

Response of roll wave to suspended load and hydraulics of overland flow on steep slope

“…Critical Froude number is widely used as the criteria separating the existence of the roll wave or not (Arai et al, 2013;Jeffreys, 1925;Smith et al, 2011;Thual, 2013). Several researchers, among them Ishihara et al (1954), Benjamin (1957), Yih (1963Yih ( , 1977 and Ferreira et al (2015) indicated that for laminar flow down an inclined plane, the roll waves tended to form when the Froude number was greater than 0.58.…”