An experimental assessment of roll waves evolution in mud-like fluids flowing down steep slopes

The free-surface behavior prediction is conditioned by the appearance of hydrodynamic instabilities, which may arise at the interface when flow presents sufficient conditions for developing and stabilizing small-scale disturbances. One typical wave that may develop is known as a roll wave. The study of these waves examines the necessary conditions for appearance, propagation, and amplification, i.e., how such instabilities develop in time and space. In this sense, this paper presents an experimental work that was carried out to observe and quantify the development of these waves in a laminar free-surface flow of non-Newtonian Herschel–Bulkley-type fluid regarding the flow height. Experiments were carried out in a rectangular channel, 3.00 m long and 0.30 m wide, applying inclinations varying from 13∘ to 20∘ and discharge rate from 0.88 to 1.07×10-3 m3/s. The experimental apparatus allowed the production of stabilized roll waves in a narrow Froude numbers range, thus constituting a beneficial database for understanding and controlling these waves. The test fluid used was a Carbopol-based gel, a fluid that exhibits yield stress, a property also present in natural muddy materials. After a controlled disturbance was applied, the variation of the free-surface interface was measured using an ultrasonic system at different points along the channel length. It was observed that the stabilized waves present as long waves, validating the mathematical assumptions normally used in shallow water-type flows, even for non-Newtonian fluids. The generation criterion usually employed regarding the Froude number and the cutoff frequency was also assured. Furthermore, it was noted that, in some cases, the spatial evolution of roll waves could follow an asymptotic behavior as a function of the distance traveled and present stabilization after traveling three wavelengths. However, even for controlled laboratory tests, it was shown that the slight variation of parameters could harshly affect the prediction of wave evolution. Comparison against available formulations for the roll wave establishment lengths showed insufficient to predict their evolution for laminar non-Newtonian fluid flow.