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We consider the propagation of plane waves in an ideal gas in the presence of external sources of energy inflow and dissipation. Using the Whitham criterion, we obtain conditions under which small perturbations of a constant solution are transformed into nonlinear quasiperiodic wave packets of finite amplitude that move in opposite directions. The structure of these wave packets is shown to be similar to roll waves in inclined open channels. We perform numerical calculations of the development of self-oscillations and the nonlinear interaction of waves. The calculations show that under a small harmonic perturbation of the initial equilibrium state, two types of wave structures can develop: roll waves and periodic two-peak standing waves. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical and numerical analysis of the length required for roll waves to become stationary in a free-surface laminar flow of a Newtonian fluid. Two types of stability analysis are brought to verify flow stability and obtain parameters for wave growth rate in a Saint-Venant like system. Then, numerical simulations are performed of the free-surface laminar transient flow of glycerin. The Navier-Stokes equations were solved using the finite volumes method, Euler schemes and PIMPLE, and the VoF technique to solve the interface. Boundary conditions were specified to obtain a steady and uniform regime given a Froude number. Then, a sinusoidal perturbation with controllable properties was applied to the inlet velocity. From the numerical results, the spatial development of the roll waves was evaluated, focusing on the establishment length as a function of the Froude number and the perturbation amplitude. The analyses performed allowed the verification of the influence of flow hydraulic regime over the establishment length, and it was possible to obtain a new equation as a function of the perturbation amplitude. [ABSTRACT FROM AUTHOR]

A survey is given of the forces at work inside traveling roll waves and monoclinal flood waves in dry granular matter. By numerically solving the generalized Saint-Venant equations for shallow granular flow, we find a hierarchy of pairwise near-balancing forces, which together are responsible for sustaining the shape of the nonlinear waves in question. The leading force pair is gravity vs. friction, followed by inertia vs. pressure, while the minor imbalance left by the aforementioned pairs is settled by a (small though essential) diffusive force. [Display omitted] • The balance of forces in granular roll waves and monoclinal flood waves is explored. • The forces turn out to balance each other very nearly pairwise. • The dominant force pair is that of gravity and friction. • The second pair is comprised of pressure and inertia. • The small imbalance left by the former force pairs is settled by a diffusive force. [ABSTRACT FROM AUTHOR]

• An experimental methodology to measure a non-Newtonian fluid flow with free surface. • Photometric and ultrasonic systems providing similar amplitude of roll wave. • An absorbance photometric technique to measure the steep front of the roll wave with high precision. This work aims to measure forced steady roll waves evolving non-Newtonian fluid flow by using absorbance photometric technique. Instabilities on the free surface of the uniform flow were induced by controlled air pulses, generating roll waves under specific conditions of Froude number and disturbance frequency. A systematic procedure was presented to clarify a compromise between the aqueous concentrations of Carbopol (with adequate viscosity) and methylene blue dye (avoiding optical opacity), providing both sensitivity and resolution for absorbance measurements. Roll waves amplitudes were also measured using an ultrasonic sensor in order to compare the results with the absorbance photometric technique. Given a channel inclination, six scenarios defined by different flow rates were tested, which allowed us to observe the generation of roll waves as a succession of shocks. The measured profiles showed a better precision (maximum error of 0.11 mm against 1.37 mm, for pump rotation equal to 475 RPM) using the absorbance photometric technique compared to the ultrasonic system, respectively. [ABSTRACT FROM AUTHOR]

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.

Debris-flow events often comprise a sequence of surges, sometimes termed "roll waves." The reason for this surging behavior is still a matter of debate. Explanations include the growth of hydraulic instabilities, periodic sediment deposition and release, or grain size sorting. High-resolution field measurements together with triggering rainfall characteristics are rare. We present results for 3 years of monitoring debris-flow events at Lattenbach Creek in the western part of Austria. The monitoring system includes a weather station in the headwaters of the creek, radar sensors for measuring flow depth at different locations along the channel, as well as a two-dimensional rotational laser sensor installed over a fixed cross section that yields a threedimensional surface model of the passing debris-flow event. We find that the debris flows at Lattenbach Creek were all triggered by rainstorms of less than 2 hours and exhibited surges for each observed event. The velocities of the surges were up to twice as high as the front velocity. Often, the first surges that included boulders and woody debris had the highest flow depth and discharge and showed an irregular geometry. The shape of the surges in the second half of the flow, which carried smaller grain sizes and less woody debris, were rather regular and showed a striking geometric similarity, but still high velocities. The results of our monitoring efforts aim to improve our understanding of the surging behavior of debris flows and provide data for model testing for the scientific community. [ABSTRACT FROM AUTHOR]

Most simulation findings regarding granular roll waves are based on the analysis of steady uniform flows with an initial artificial perturbation. The difference in the scenario used in our study is that roll waves are generated by applying a zero-mean fluctuant flux inflow condition over the upstream boundary. Only the upstream section of the inclined chute is covered with a sheet of granules with no supplementary application of a boundary condition. Starting with the depth-averaged governing framework, the μ (Fr,h)-dynamic basal friction law, and the μ(I) -rheology-based second-order viscous terms, and adopting a second-order shock-capturing total variation diminishing–MacCormack scheme, we captured self-destabilized roll waves generated in an unsteady granular chute flow. In the simulated unsteady flow, three stages—wave spreading, wave forming and wave-collapse—are identified and discussed. The simulation results are confirmed by observations in laboratory granular flow experiment and natural avalanches from other literatures. • Spontaneous roll waves emerged though Froude number below the instability threshold. • Wave spreading, wave forming and wave collapse stages are identified. • Roll waves decreased with increasing coefficient of the depth-averaged viscosity. [ABSTRACT FROM AUTHOR]

We extend the model of Needham, et al. (2008, The development of slugging in two-layer hydraulic flows, IMA J. Appl. Math. 73, 274–322)—a hydraulic model for turbulent, two-layer, gas–liquid flow with gas velocity much greater than liquid velocity, in a horizontal channel—to include the effect of a small, spatially varying inclination. This allows us to consider the effect of non-horizontal topography of the channel on slug formation. The stratified flow of gas–liquid mixtures is important in many industries, in particular, oil and gas, where the formation of slugs is usually undesirable. We show that, in channels of constant inclination, for sufficiently downhill flows there is a unique spatially uniform steady state. However, as the pipe inclination increases, there are two bifurcations: the first leads to the existence of a second steady state, while the second, a saddle-node bifurcation, means that there are no uniform steady-state solutions for sufficiently uphill flow. The steady state with the thicker liquid layer is unstable except for a very small range of flow rates, while the other steady state is unstable for sufficiently downhill flows and for sufficiently high liquid flow rate. We also study roll waves (periodic travelling wave solutions) and determine the form of these solutions numerically. Finally, we study an initial value problem driven by noise at the inlet of channels with, firstly, constant, and secondly, sinusoidally-varying inclinations. We provide numerical evidence for the likely formation of slugs at points where the inclination of the pipe is anywhere equal to the saddle-node bifurcation angle. [ABSTRACT FROM AUTHOR]

We derive a model for Bingham fluid flows down an inclined plane with a consistent asymptotic method in the shallow-flow approximation. The variables are expanded up to the first order of accuracy both in the sheared and pseudo-plug layers. The divergence of the strain rate, which is obtained in classical approaches, is here avoided by a specific regularization of the rheology allowing to implement a regular perturbation method in the whole fluid domain. Unlike classical regularization methods, the material is here characterized by a true yield stress. Below the yield point, the behavior is perfectly rigid. An alternative tensor expression of the constitutive law is proposed. In particular, the assumption of an alignment between the yield-stress tensor and the strain-rate tensor is removed. The model is derived by averaging the mass, momentum and energy balance equations over the depth. This yields a hyperbolic model of three equations for the fluid depth, the average velocity and a third variable, called enstrophy, related to the variance of the velocity. The model features new relaxation source terms and admits an exact balance energy equation. The velocity field in the depth is consistently reconstructed using only the variables of the depth-averaged model without any derivative. The physical relevance of the enstrophy is related to the shape of the velocity profile. The linear stability of a uniform solution is investigated for this model, showing a stabilizing effect of the plasticity. Roll waves are simulated numerically using a classical Godunov's scheme. The model for a Newtonian fluid is presented as a particular case. • A consistent three-equation shallow-flow model for Bingham fluids is derived. • Smooth asymptotic velocity profiles can be reconstructed from the model. • An alternative tensorial extension of the Bingham constitutive law is proposed. • Roll waves in viscoplastic fluid are computed. [ABSTRACT FROM AUTHOR]

The mathematical model of shear shallow water flows of constant density is studied. This is a 2 D hyperbolic non-conservative system of equations that is mathematically equivalent to the Reynolds-averaged model of barotropic turbulent flows. The model has three families of characteristics corresponding to the propagation of surface waves, shear waves and average flow (contact characteristics). The system is non-conservative: for six unknowns (the fluid depth, two components of the depth averaged horizontal velocity, and three independent components of the symmetric Reynolds stress tensor) one has only five conservation laws (conservation of mass, momentum, energy and mathematical ‘entropy’). A splitting procedure for solving such a system is proposed allowing us to define a weak solution. Each split subsystem contains only one family of waves (either surface or shear waves) and contact characteristics. The accuracy of such an approach is tested on 2 D analytical solutions describing the flow with linear with respect to the space variables velocity, and on the solutions describing 1 D roll waves. The capacity of the model to describe the full transition scenario as commonly seen in the formation of roll waves: from uniform flow to 1 D roll waves, and, finally, to 2 D transverse ‘fingering’ of the wave profiles, is shown. [ABSTRACT FROM AUTHOR]

Huge waves are periodic interfacial structures which are observed in vertical co-current gas-liquid two-phase flow under churn and the transition between churn and annular flows. Published data examining vertical gas-liquid flow indicate that a huge wave has either a continuous gas core surrounded by a large-scale interfacial wave or a core with a highly-agitated mixture of gas and liquid. Employing a Wire-Mesh Sensor (WMS), the spatio/temporal investigation of high flow rate horizontal air-water flow divulged some recurrent liquid structures (one may call pseudo-slugs) analogous to huge waves of (vertical) churn flow. In both cases, the blow-through (penetration of gas into the liquid structure) was the most manifest feature. Different qualitative and quantitative methods were employed to compare the behavior of pseudo-slug to churn flow. The quantitative measures included Probability Density Function analysis (PDF), distribution coefficient in drift flux model, structural velocity, core average velocity, interfacial friction factor, and slippage number. Both flow regimes demonstrated similar behavior. [ABSTRACT FROM AUTHOR]

In this note, we announce a complete classification of the stability of periodic roll-wave solutions of the viscous shallow water equations, from their onset at Froude number F ≈ 2 up to the infinite Froude limit. For intermediate Froude numbers, we obtain numerically a particularly simple power-law relation between F and the boundaries of the region of stable periods, which appears potentially useful in hydraulic engineering applications. In the asymptotic regime F → 2 (onset), we provide an analytic expression of the stability boundaries, whereas in the limit F → ∞ , we show that roll waves are always unstable. [ABSTRACT FROM AUTHOR]

Gravity-driven geophysical mass flows often consist of fluid-sediment mixtures. The contemporary presence of a fluid and a granular phase determines a complicated fluid-like and solid-like behaviour. The present paper adopts the mixture theory to incorporate the two phases and describe their respective movements. For the granular phase, a Mohr-Coulomb plasticity is employed to describe the relationship between normal and shear stresses, while for the fluid phase, the viscous Newtonian fluid is taken into account. At the basal topography, a Coulomb sliding condition for the solid phase and a Navier's sliding condition for the fluid phase are satisfied, while the top free surface is traction-free for both the phases. For the interactive forces between the phases, the buoyancy force and viscous drag force are included. The established governing equations are expressed in a curvilinear coordinate system embedded in a curvilinear reference basal surface, above which an arbitrary shallow basal topography is permitted. Taking into account the typical length characteristics of such geophysical mass flows, the 'thin-layer' approximation is assumed, so that a depth integration can be performed to simplify the governing equations. The resulting strongly nonlinear partial differential equations (PDEs) are first simplified and then analysed for a steady state in a travelling coordinate system. We find the current model can reproduce the characteristic shape of some flow fronts. Additionally, a stability analysis for steady uniform flows is performed to demonstrate the development of roll waves that means instabilities grow up and become clearly distinguishable waves. Furthermore, we numerically solve the resulting PDEs to investigate general unsteady flows down a curved surface by means of a high-resolution non-oscillatory central difference scheme with the total variation diminishing property. The dynamic behaviours of the granular and fluid phases, especially, the effects of the drag force and the fluid bed friction are discussed. These investigations can enhance the understanding of physics behind natural debris flows. [ABSTRACT FROM AUTHOR]

Roll waves create unstable and turbulent behaviour in channels and chutes and also change the behaviour of water entering the energy dissipater structures. In the present study, the free surface of water in the chute is simulated by numerical models. The roll waves' occurrence is investigated in the numerical model for the discharge up to 30 m3/s, the longitudinal slope varying from 17 to 20% and the width of chute varying from 3.4 to 4.0 m. The ratios of the hydraulic depth to the chute width and also the minimum velocity to the maximum velocity are calculated along the chute length for different discharges, widths and longitudinal slopes of the chute. Results indicated that for the chutes in which the ratio of hydraulic depth to the chute width less than 0.16 the ratio of minimum to maximum velocity is less than 0.75, the formation of roll waves is inevitable. [ABSTRACT FROM AUTHOR]

A mathematical model of the flow of a thin layer of heavy liquid under an elastic shell filled with gas is constructed. By means of mass exchange with the environment, the gas phase is active and maintains self-organized wave motion in the liquid layer. The conditions under which small perturbations are transformed into quasiperiodic wave packets of finite amplitude which move in the same direction are found. It is shown that the structure of the waves is similar to that of roll waves in open channels. [ABSTRACT FROM AUTHOR]

Experimental studies on open channel flows are explored mostly because of their importance in validating analytical and numerical models. Although steady flows are usually measured and explored, difficulties arise in the precise execution of this task when the free surface becomes oscillatory. This paper presents a methodology for measuring a particular non-stationary phenomenon that occurs under specific conditions, namely, roll waves. Limited data exists in literature on roll waves. The objective of this work is to contribute to this database and to describe a useful experimental method for measuring roll waves. Based on some well-known literature experiments, an experimental setup was designed to achieve the free surface flow of a viscous fluid in a steady and uniform configuration. The flow was set to generate roll waves and controlled disturbances were applied at the inlet to develop roll waves. These waves were then measured using a photometric device based on a light absorption technique. The wave profiles for different flow configurations are presented. Experimental results were compared with numerical simulations to assess the validity of the measurements taken. [ABSTRACT FROM AUTHOR]

As in Newtonian fluids, unconfined yield stress fluid slender flows are prone to become unstable and host travelling waves. We propose a non-local dimensionless numberψ, obtained from a physical order-of-magnitude analysis, to predict, for the first time, the transition that marks the onset of roll waves in unconfined discharges of bentonite, whose rheology was assumed as a Bingham plastic. Involved variables include the discharge volume flow, Bingham viscosity, mixture density, gravity acceleration, plane inclination and yield stress. Experimental verification considering various discharge flow-plane inclinations and concentrations of the mixture indicate that for values ofψexceeding the unity, single or multiple roll waves appear. [ABSTRACT FROM AUTHOR]

Abstract: The investigation of thin liquid film flowing down a vertical wall in the roll-wave regime in presence of heat and mass transfer through the free surface is presented. The roll-wave equation taking into account heat and mass transfer through the liquid–vapor interface has been derived. The self-similar solutions of the progressive-wave type for film thickness have been obtained. The families of discontinuous solutions have been constructed, where the progressive waves are conjugated with each other or with “residual” film thickness through the strong discontinuity. As an example, the calculations of the condensate water film flowing down a vertical surface are presented. [Copyright &y& Elsevier]

Abstract: This paper is about the free surface instabilities of granular flows, usually called roll waves. A shallow layer of shear-thickening fluid ( with ) is considered to study finite-amplitude permanent roll waves down a slope, simplified by Karman’s momentum integral approach. The existence of conditions of a periodic discontinuous solution is derived, as smooth profiles with depth increasing monotonically between periodic shocks. Energy dissipation in the body of the stream and in the discontinuity is analysed and discussed. Two conditions are derived. The first is related to the physically acceptable shape of the smooth profiles, and the second is related to positive energy loss across the shock. These conditions can be converted into a limiting discharge, viewed in the fixed frame, and in a limiting flow thickness (or limiting Froude number), for the permanent periodic roll wave to exist without further conditions. A minimum-length roll wave (MLRW) is defined as the periodic permanent roll waves with zero energy dissipation in the shock. The MLRW also requires a limiting value of the Froude number to exist. [ABSTRACT FROM AUTHOR]

Abstract: Due to the similarities between large amplitude roll waves and slug flow in two-phase gas–liquid pipe flow, a slug tracking scheme is presented with the addition of a simplified model for roll waves. The waves are treated in a similar way to slugs, modelled as objects moving at the wave velocity and with a pressure variation across them. The two-fluid model is solved on a stationary staggered grid in stratified sections between moving waves and slugs. The model is dynamic meaning that the growth and decay of waves and slugs can be simulated. The wave model implementation within the tracking scheme is discussed and demonstrated in comparison to existing experimental data on wave velocities and averaged pressure drops. The results from the tracking scheme compared well to the experiments when waves were initiated with the experimental frequency. Wave initiation remains as a modelling challenge. [Copyright &y& Elsevier]

Abstract: This paper examines the effects of small upward inclinations on the formation of roll waves and the properties of fully developed roll waves at high pressure conditions. A total of 984 experiments were conducted at six positive pipe inclinations θ =0.00°, 0.10°, 0.25°, 1.00°, 2.50° and 5.00° using a 25m long 10cm i.d. pipe. Sulfur hexafluoride (SF6) was used at 8 bara giving a gas density of 50kg/m3. Two independent mechanisms for the formation of roll waves were identified; (1) interaction between 2D shallow water waves and (2) a visible long wavelength instability of the stratified layer. Viscous long wavelength linear stability analysis predicted the critical liquid flow rate and liquid height for the initiation of roll waves when roll waves were formed due to the second mechanism. A simple equation from shallow water wave theory agreed with measurements for critical liquid flow rate when roll waves were formed due to the first mechanism. Shallow water wave speed agreed with critical wave speeds at transition and nonlinear wave speeds for fully developed roll waves in certain cases. The increase in interfacial friction due to the presence of large waves was compared with models from the literature. [Copyright &y& Elsevier]

Abstract: Many improvements of the Wallis correlation for the interfacial friction in annular flow have been proposed in the literature. These improvements give in general a better fit to data, however, their physical basis is not always justified. In this work, we present a physical approach to predict the interfacial shear-stress, based on the theory on roughness in single-phase turbulent pipe flows. Using measured interfacial shear-stress data and measured data on roll waves, which provide most of the contribution to the liquid film roughness, we show that the interfacial shear-stress in vertical annular flow is in very close agreement with the theory. We show that the sand-grain roughness of the liquid film is not equal to four times the mean film thickness, as it is assumed in the Wallis correlation. Instead, the sand-grain roughness is proportional to the wave height, and the proportionality constant can be predicted accurately using the roughness density (or solidity). Furthermore, we show that our annular flow, which is in similar conditions to others in the literature, is fully rough. Hence, the bulk Reynolds number should not appear in the prediction of the interfacial friction coefficient, as is often done in the improvements of the Wallis correlation proposed in the literature. [Copyright &y& Elsevier]

The article discusses an experiment regarding the problem of transport of suspended sediment after the rupture of a dam. The study showed that the numerical technique was validated by comparison with available data and analytical solutions. In addition, the formation of roll waves were found to be near the water front, and is said to significantly affect the transport of sediments due to the production of spatial oscillations. Also, the validity of the dilute sediment approach as a function of the bed slope and sediment properties was also characterized. It is concluded that the numerical solutions can be used to check numerical results from future formulations.

In this paper, we develop a hydraulic theory to describe the occurrence and structure of slugging in a confined two-layer gas–liquid flow generated by prescribed, constant, upstream volumetric flow rates in each layer. A linearized theory for the uniform flow is established, after which we use bifurcation theory to study fully non-linear periodic travelling wave structures. We find that a two-parameter family of such travelling wave solutions exists. Under given conditions, the volumetric flow rate constraint provides a relation between these two parameters. To select a unique periodic travelling wave solution, we require a further relation. We first investigate the conjecture that the periodic travelling wave solution selected in the initial value problem has the same wavelength as the linearly most temporally unstable mode. To do this, we solve the initial value problem numerically on a periodic domain. We find that the separation of the liquid slugs that form is much longer than the wavelength of the most unstable temporal mode. We then develop a different conjecture based on the convective instability of the long ‘tails’ of the available periodic travelling wave solutions, which leads to a better understanding of the wavelength selection process. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper we investigate the effect of a prescribed superficial shear stress on the generation and structure of roll waves developing from infinitesimal disturbances on the surface of a power-law fluid layer flowing down an incline. The unsteady equations of motion are depth integrated according to the von Kármán momentum integral method to obtain a non-homogeneous system of nonlinear hyperbolic conservation laws governing the average flow rate and the thickness of the fluid layer. By conducting a linear stability analysis we obtain an analytical formula for the critical conditions for the onset of instability of a uniform and steady flow in terms of the prescribed surface shear stress. A nonlinear analysis is performed by numerically calculating the nonlinear evolution of a perturbed flow. The calculation is carried out using a high-resolution finite volume scheme. The source term is handled by implementing the quasi-steady wave propagation algorithm. Conclusions are drawn regarding the effect of the applied surface shear stress parameter and flow conditions on the development and characteristics of the roll waves arising from the instability. For a Newtonian flow subjected to a prescribed superficial shear stress, using an analytical theory, we show that the nonlinear governing equations do not admit roll waves solutions under conditions when the uniform and steady flow is linearly stable. For the case of a general power-law fluid flow with zero shear stress applied at the surface, the analytical investigation leads to a procedure for calculating the characteristics of a roll waves flow. These results are compared with those yielded by the numerical procedure. [Copyright &y& Elsevier]

Abstract: We develop a theoretical tool to examine the properties of numerical schemes for advection equations. To magnify the defects of a scheme we consider a convection-reaction equationIt is shown that, if a numerical scheme for the advection part is performed with a splitting method, the intrinsic properties of the scheme are magnified and observed easily. From this test we observe that numerical solutions based on the Lax–Friedrichs, the MacCormack and the Lax–Wendroff break down easily. These quite unexpected results indicate that certain undesirable defects of a scheme may grow and destroy the numerical solution completely and hence one need to pay extra caution to deal with reaction dominant systems. On the other hand, some other schemes including WENO, NT and Godunov are more stable and one can obtain more detailed features of them using the test. This phenomenon is also similarly observed under other methods for the reaction part. [Copyright &y& Elsevier]

Abstract: In this paper we investigate the generation and structure of roll waves developing on the surface of a power-law fluid layer flowing down a porous incline. The unsteady equations of motion for the power-law fluid layer are depth integrated according to the von Kármán momentum integral method accounting for the variation of the velocity distribution with depth. The slip boundary condition at the interface between the fluid layer and the porous plane is based on the assumption that the flow through the porous medium is governed by the modified Darcy’s law, and that the characteristic length scale of the pore space is much smaller than the depth of the fluid layer above. An analytical theory of permanent roll waves is employed to determine under what flow conditions roll waves can exist and to calculate the wavelength, wave height, and speed of the roll waves. The nonlinear stability analysis is also carried out by numerically solving the time dependent governing equations and calculating the nonlinear evolution of infinitesimal disturbances imposed on the uniform and steady flow. Conclusions are drawn regarding the effect of the permeability of the porous medium and flow conditions on the development and characteristics of roll waves arising from the instability of the uniform flow. [Copyright &y& Elsevier]

The special class of periodic travelling waves which is known as roll waves is investigated for nonhomogeneous hyperbolic equations of gas dynamics type. In this Note these equations are applied to shallow water flows in inclined open channels, but the results obtained are more general and far-reaching. The necessary conditions for the existence of a roll wave are derived. It is shown that for a nonconvex pressure term, multi-shock configurations of roll waves of finite amplitude exist. A new type of periodic travelling wave, which corresponds to the slug flow regime in two-layer flows, is found. To cite this article: A. Boudlal, V.Yu. Liapidevskii, C. R. Mecanique 332 (2004). [Copyright &y& Elsevier]

It has recently been shown that a consideration of the stability of a stratified flow and of the stability of a slug has provided accurate predictions of the critical liquid height of a stratified flow for the transition to a slug or plug flow in horizontal and downwardly inclined pipes. Two diameters and viscosities of 1–70 cp were considered. Predictions of the critical superficial liquid velocity are not so accurate. This paper partially examines this issue by presenting measurements of the mean pressure gradient and of the time-varying holdup for air and water flowing in a horizontal 2.54 cm pipe.Important contributions are the use of viscous long wavelength theory to predict the initiations of roll waves and the discovery of a range of liquid flows (in the pseudo-slug regime) at which the liquid holdup of the stratified layer is close to the critical and is not changing strongly with liquid flow. A partial explanation for this behavior is given which recognizes that the liquid layer over which roll waves are propagating is below that required for the stability of a slug. Slugs will appear if conditions are favorable for the coalescence of roll waves. [Copyright &y& Elsevier]

Cloud bands observed over the Arctic sea ice are interpreted in terms of long-wavelength gravity-wave modes trapped between the ground and a vertically-thin over-reflecting layer in the mid-troposphere. The over-reflecting layer is neutrally-stratified and lies between the counter-streaming upper troposphere and lower troposphere in a strong high-pressure system. The Arctic cloud bands appear to share many features with the long-wavelength roll waves observed in more temperate latitudes. [ABSTRACT FROM AUTHOR]

The media have been reporting natural disasters frequently associated with climate change. When it comes to mudflows, the impact is substantial, especially on highly vulnerable communities. Under appropriate conditions (inclination, discharge and rheology), waves with constant amplitude, length and celerity can occur on the free surface of the flow. Such phenomenon is called roll wave, and it generally intensifies the disaster. Researchers usually represent the phenomenon through mathematical models. The present work aims to implement a new roll wave model, by taking into account three situations: the employment of Cauchy equations in a shallow water regime; the study of a Herschel–Bulkley fluid flowing on a channel with porous bottom and non-zero velocity at the bottom, and the analysis of a Darcian flow evolving on a porous medium. Numerical simulations were conducted in order to determine new criteria for roll wave generation and to describe how these parameters interfere with the characteristics of the phenomenon. As an example of the result reached, for a Froude number F r < 1 (with n = 0. 6 and C = 0. 2), the presence of a porous bottom was able to increase the wave amplitude by 20% and the bottom shear stress by 10%, when compared to an impermeable bottom. For a F r ⟶ ∞ , the variation in the wave amplitude reached 80% and the bottom shear stress presented an even more significant increase (¿ 100%), indicating high sensitivity to the porous effect. In non-Newtonian fluids, the domain for roll wave generation is extended and the porous bottom acts basically as an additive element, altering wave properties and its effects on the bottom. The resulting data provided trend curves for the amplitude, the celerity and the wavelength of roll waves, building the basis for a prediction model with potential application in engineering, especially in determining shear stresses on the bottom that allow to infer erosion rates produced by the phenomenon on channels with porous bottom or on wetlands with the presence of cohesive material. • New roll wave model evolving in Herschel–Bulkley fluid on porous bottom. • New criteria for roll wave generation based on linear and phasor analyses. • Rheological parameters and the porosity factor interfere with the wave pattern. • Porosity factor is decisive on the wave amplitude and bottom shear stress. • The resulting data provide trend curves with potential application in engineering. [ABSTRACT FROM AUTHOR]