Development Of Roll Waves Research Articles

Formation and evolution of roll waves in a shallow free surface flow of a power-law fluid down an inclined plane

A laminar flow of a thin layer of mud down an inclined plane under the action of gravity is considered. The instability of a film flow and the formation of finite amplitude waves are studied within the framework of both two-dimensional governing equations of a power-law fluid and its depth-averaged hyperbolic simplification. The conditions of the existence of roll waves for these models are formulated in terms of the Whitham criterion. A free surface evolution and the development of roll waves are numerically calculated. The amplitude of roll waves obtained by the 2D equations is slightly larger than that for the 1D model. Moreover, for certain flow parameters, the small perturbations of the basic solution grow for the 2D equations and decay for the depth-averaged model. A two-parameter class of exact piecewise-smooth solutions of the 1D model is obtained and a comparison with a numerical solution is made. In the region of these parameters, diagrams of the roll waves existence are constructed.

Roll waves structure in two-layer Hele–Shaw flows

The mathematical model of inhomogeneous fluid motion in a Hele–Shaw cell is proposed. Based on this model the equations for describing two-layer flows and development of roll waves at the interface are derived. Conditions of roll waves existence are formulated in terms of Whitham criterion. Numerical calculations of the interface position are provided. It is shown that small perturbations of the interface in the inlet section of the channel lead to the roll waves for certain parameters of the flow. Two-parametric class of exact solutions corresponding to the roll waves regime is obtained. Diagrams of critical depths of roll waves development are constructed.

Development of roll-waves in power-law fluids with non-uniform initial conditions

ABSTRACTThis paper investigates the spatial evolution of a disturbance in an open-channel flow of a power-law fluid at non-uniform accelerated and decelerated initial profiles, up to the occurrence of roll-waves in mild and steep slope channels. Both theoretical and numerical analyses are applied to the depth-averaged continuity and momentum conservation equations, deduced from the von Kármán's integral method. For the theoretical investigation, the nonlinear near-front expansion technique was applied. Then, the full nonlinear problem in its conservative formulation was numerically solved. Independently of the rheology of the flowing medium, non-uniform initial conditions strongly influence the perturbation celerity, the disturbance evolution and the roll-wave development. For mild slope channels, an initially decelerated profile of shear-thinning fluids has a stabilizing effect, while the opposite is found for accelerated profiles. For shear-thickening fluids, only the stabilizing effect caused by a decelerated profile is observed. In steep slope channels, independently of the fluid rheology, decelerated initial conditions promote roll-wave occurrence, while accelerated conditions inhibit the perturbation growth. Although experimental verifications are needed, the present results have to be properly accounted for in defining roll-wave prediction methods and in assigning appropriate boundary conditions to enhance or to reduce their formation.

Occurrence conditions of roll waves for three grain–fluid models and comparison with results from experiments and field observation

For the flow and deposition behaviour of debris flows, phenomena like particle sorting, levee formation and the development of roll waves are expected to be important processes. However, these processes are not well understood and hardly implemented in modelling approaches. In this study, we focus on the development of roll waves and derive advanced criteria separating stable and instable flow regimes for three debris flowmodels. These criteria are expressed using critical Froude numbers. Each of these simple flow models reflect different sources of flow resistance: laminar-viscous stress (Bingham type), dispersive stress due to particle collision (Bagnold type), and a model combining turbulent and dispersive stresses. Subsequently, we compare the predictions from these models with results from laboratory experiments with grain–fluid mixtures in a straight flume and with observations from a debris flow monitoring site at the Lattenbach creek in Austria. The experimental flows match with a turbulent flow model including particle collisions. For the natural flows the connection between models and observations is not clear due to limited field data. The results of our study contribute to an improved determination of critical flow conditions and provide data for model testing.

Influence of Relative Roughness and Reynolds Number on the Roll-Waves Spatial Evolution

The paper investigates the influence of the resistance coefficient variability onto the spatial development of roll-waves. Two models, based on time-asymptotic solutions of the linearized St. Venant equations, subject to either impulsive or oscillating perturbation, have been modified by including the dependence of the resistance coefficient on flow conditions, wall roughness, and fluid viscosity. Independently of the perturbation type, it has been shown that the hypothesis of constant resistance coefficient leads to underestimate the disturbance spatial growth. Theoretical predictions are finally compared with results of a fully nonlinear model and with literature experimental data for several combinations of Froude and Reynolds numbers and relative roughness values. The representation of variability of the resistance coefficient fundamentally improves the performance of minimum channel length criteria, whereas its neglect may lead to noncautious channel design.

Free surface instability of non-Newtonian laminar flows

The mechanism of free surface instability of non-Newtonian laminar flows is studied theoretically and experimentally in the paper. Development of surface waves and roll waves of non-Newtonian flow has been reported in many cases, such as the river clogging in the hyperconcentrated flows, intermittent viscous debris flows and fluctuation in mudflows. Theoretical analysis from the equation of motion incorporating the non-Newtonian nature the effects of yield stress and viscosity are calculated and compared for various flows. It is concluded that the free surface is unstable and roll waves of the fluid demonstrated that the free surface instability is essentially caused by the yield stress. Two dimensionless numbers. Sy and Svis, representing may develop even at constant incoming flow rate if Sy is much larger than Svis and is stable if Sy is smaller than Svis. Experiments were conducted to study the phenomena of river clogging, development of a perturbation wave in non-Newtonian laminar flow, and development of roll waves. The results agree well with the theoretical formula showing exponential law of growth of wave height. The growth rate of wave height depends essentially on the parameter Sy If Sy is large enough a series of roll waves develop from stable flow and the larger is the parameter, the higher the waves.

Characteristics and Depositional Processes of Large-scale Gravelly Gilbert-Type Foresets in the Miocene Doumsan Fan Delta, Pohang Basin, Se Korea

ABSTRACT The Doumsan fan delta in the Miocene Pohang Basin (SE Korea) includes large-scale gravelly Gilbert-type foresets that are more than 150 m high and dip at about 20°. The foresets consist of six sedimentary facies: medium- to thick-bedded sandy gravel deposits with variable grading patterns and bed geometries (Facies A), thin- to medium-bedded, commonly inversely graded sandy gravel deposits (Facies B), sheet-like layers, a few grains thick, of pebble gravel (gravel sheets; Facies C), lensoidal layers, a few grains thick, of cobble to boulder gravel (gravel lenses; Facies D), thin-bedded sand with outsized clasts (Facies E), and very thick-bedded (> 10 m thick) disorganized gravel deposits in the toeset area (Facies F). These facies are indicative of deposition from cohesionless ebris flows (Facies A and B), debris falls (Facies C and D), turbulent flows (Facies E), and very thick debris flows that are related to large-scale foreset failure (Facies F). These facies are in close association with one another, except for Facies F, and are either vertically superposed or laterally juxtaposed within single sedimentation units. This suggests that these facies originated from a series of evolving sediment gravity flows. A cohesionless debris flow generated at the topset-foreset boundary or on the middle of the foreset slope segregated its sediments into a pebble-rich lower division and a sandy upper division with sparse cobble-to-boulder clasts by preferential upward drift of large clasts and surface transformation of fine-grained material. The pebbly lower division was emplaced by frictional freezing, forming Facies A beds. On the other hand, the sediments in the upper division continued to move as a sandy turbulent flow and bouldery debris fall, resulting in Facies E and D deposits downslope. The cohesionless debris flow occasionally transformed into a series of thinner flows by development of roll waves along the top of the flow, producing Facies B layers on the margin of a Facies A bed. Otherwise the cohesionless debris flow transformed into grain-assemblage debris fall and single-grain debris fall consecutively by removal of interstitial sand via downward percolation and stripping into ambient water. The debris falls produced gravel sheets (Facies C) and gravel lenses (Facies D). During this flow transformation, cobble- to boulder-size clasts and sandy material were selectively transported farther downslope, resulting in prominent textural bimodality of the prodelta deposits, which comprise isolated large clasts and lensoidal deposits of cobble-to-boulder gravel set in sandy background material.

On Viscous Fluid Flow Down an Inclined Plane and the Development of Roll Waves

We develop a tractable, and mathematically rigorous, asymptotic theory for the development of instability in viscous fluid flow down an inclined plane, at supercritical Reynolds numbers. Our theory involves consideration of an ill posed problem, and provides a new example of the way such problems come up in applied mathematics. We show how one may use additional information, inherent in the problem one really wishes to solve, in order to regularize this improperly posed problem. We discuss several numerical experiments and compare the results with experimental observations of “roll waves” and “slug flows” in inclined channels, at similar slopes and Reynolds numbers.