Abstract
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.
Highlights
Roll waves are waves that propagate with constant amplitude, length and velocity, modeled as a wave train, under the action of weight and viscous forces, wall resistances, and surface tensions
The aim of this work is to revisit a roll wave mathematical model based on depth-averaged equations, for a laminar flow of non-Newtonian fluid (Maciel et al, 2013), focusing on two generation criteria for the phenomenon: the minimum Froude number, determined with basis on the temporal linear stability analysis, and the cut-off frequency, defined as the maximum frequency below which roll waves would occur, and above which they would be dampened (Ferreira, 2013)
Our work aims to verify if the new generation criteria established for flows of non-Newtonians fluids can be confirmed through numerical simulations performed by a second model with full equations (Fluent software)
Summary
Roll waves are waves that propagate with constant amplitude, length and velocity, modeled as a wave train, under the action of weight and viscous forces, wall resistances, and surface tensions. There is a propitious domain for the phenomenon to occur in the ambit of “natural” disasters (landslides, mudflows, avalanches, volcanic lavas, superficial flows), depending on topographic, physical (viscosity, for instance) and dynamic factors (like the discharge). It depends on the flow Froude (Fr > Frmin) and Reynolds numbers (Coussot, 1994; Ng & Mei, 1994; Balmforth & Liu, 2004; Maciel et al, 2013) and, at the same level, on the involved disturbance frequencies, being all parameters intimately related to the flowing fluid rheology
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