An experimental approach to examine the instabilities present on free surfaces of non-Newtonian fluid flow occurring in inclined channels is presented. When these flows occur in favorable conditions of inclination and discharge, it is observed that the propagation of instabilities can evolve into a specific type of wave, known as roll waves. The experimental apparatus developed allows simulation of stabilized roll waves in many scenarios for Newtonian and non-Newtonian rheology fluids, thereby constituting a highly useful approach for the understanding and control of roll waves. The fluid test for the non-Newtonian case used a gel rheometrically representative of the muddy material presented in natural disasters, such as mudflows. A low-cost, high-performance, and nonintrusive level measurement system (ultrasonic transducer) is proposed. A comparison between the experimental results obtained and a one-dimensional (1D) mathematical model exhibited good amplitude and wave-period estimations.

In an attempt to develop risk-assessment engineering tools, a method is presented that involves the application of a simplified model that represents periodic permanent roll waves in Herschel–Bulkley laminar fluid flows. Using data from in situ sparse measurements during the August 1998 event at Acquabona Creek in the Dolomites (Eastern Italian Alps) previously, the missing rheological properties of the fluid and dynamical characteristics of the flow were estimated in order to perform a case study of the Acquabona site to explore the validity of the proposed model. The use of roll-wave theory to predict the flow properties during such events was considered. The mathematical model for roll waves was able to estimate the characteristics of the waves under the given flow conditions. The proposed model was also used to study of the influence of rheological properties on the waves’ characteristics. The results show the importance of the rheological properties and roll-waves theory to predict the flow height. Finally, the model’s potential to be a tool for risk assessment was tested and its usefulness demonstrated.

This article aims to determine roll waves generation criteria for mudflow events. A representative system of equations to mudflows is reached through Cauchy’s equations (mass and momentum conservation) with proper stress tensor (non-Newtonian fluid) in shallow water conditions. Linear stability analysis is then applied to the system and two roll waves generation criteria are found: one related to Froude number and another related to flow disturbance frequency. Numerical simulations for both Newtonian and non-Newtonian fluids were carried. Good agreement was observed between numerical results and theoretical criteria.