Roll waves and their generation criteria

Abstract

Pulsating waves (also known as roll waves) might occur on the free surface of extreme events like mud and debris flows, among others, usually intensifying the caused damage. This technical note aims to inform about the roll wave phenomenon developing in a free-surface laminar flow, and analyze its generation criteria, centered on the concepts of Froude number and disturbance frequency. The complete linear stability analysis of the new depth-averaged model was proven a useful theoretical tool in determining new generation criteria for roll waves developing in non-Newtonian fluids. The results showed that the roll wave generation depends on two criteria: the first is associated to the minimum Froude number, and the second is related to the cut-off frequency. In addition, we have confirmed that the new generation criteria can be verified via numerical simulation based on a second model with full equations (Fluent software). Globally, the emergence of roll waves is favored by the non-Newtonian properties of the flowing fluid and the fact that the cut-off frequency decreases along with the minimum Froude number. Lastly, both generation criteria were tested in order to examine a case study involving the occurrence of roll waves in a watershed.

Nonlinear evolution of viscoplastic film flows down an inclined plane

“…4(a)). Theses observations are qualitatively in agreement with the simulations of viscoplastic fluid [11,26] and power-law fluid [23].…”

“…Fig. 5(a) shows for two different flow configurations a good agreement between the experimental data and this model concerning the decrease of the wave finite amplitude as a function of the frequency, as observed in a numerical model in [11]. Fig.…”

“…Numerical and theoretical studies have been carried out on non-Newtonian fluids. De Oliveira Ferreira et al [11] found that the roll wave amplitudes and lengths decreased along with the disturbance frequency in viscoplastic fluids, and this seems to be also the case for granular matter [12]. The main experimental focus has been for now on the linear instability threshold, which has been notably measured for granular flows [13], shear-thinning fluids [14], viscoplastic fluids [15][16][17][18] and shear-thickening fluids [19], as well as on the shape and form of the fully developed roll wave in viscoplastic fluid [20].…”