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

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.