Explaining the formation of debris flow surges

Ongoing improvements in monitoring are increasingly documenting the presence of quasi-regular trains of surge waves in debris flows. These phenomena exacerbate hazards associated with these events, since they can grow to reach depths and discharges greater than anywhere else in the flow. Using data from Illgraben, Switzerland, we track the development of these surges from small undulations on the free surface to waves with amplitudes of a metre or more. From this, we argue that the waves arise from a flow instability analogous to the classical 'roll wave' instability that occurs in flows of turbulent water. A complementary theoretical model is presented, which uses a basal drag parametrisation informed by the observational data. When initiated with measured upstream fluxes, the model develops waves that mature from small perturbations to large waves that are in excellent agreement with the field data. The underlying mathematics that governs the instability can be used to explain why waves are observed in some flows, but not others. Contributing factors include the bulk flow discharge and the shape of the channel.