Erosion–deposition waves in shallow granular free-surface flows

2014 ◽  
Vol 762 ◽  
pp. 35-67 ◽  
Author(s):  
A. N. Edwards ◽  
J. M. N. T. Gray
Keyword(s):  
Travelling Waves ◽  
Static Friction ◽  
Quantitative Agreement ◽  
Free Surface Flows ◽  
Small Scale ◽  
Erosion And Deposition ◽  
Roll Waves ◽  
Minimum Depth ◽  
Coarsening Dynamics ◽  
The Waves

AbstractDebris flows can spontaneously develop regular large-amplitude surge waves that are interspersed by periods in which the channel fill is completely stationary. These are important because each individual surge is much more destructive than a steady uniform flow with the same mass flux. In this paper small-scale experiments that exhibit similar behaviour are described. The flow consists of carborundum particles that flow down a rough inclined chute covered with a static erodible layer of the same grains. For inflow conditions close to the minimum depth required for steady uniform flows to exist, small disturbances are unstable, creating waves that rapidly coarsen and grow in size. As the waves become sufficiently large, the troughs between the wave crests drop below a critical thickness and come to rest. A series of steadily travelling waves develop which erode the static layer of particles in front of them and deposit grains behind them, to form a layer that is again stationary. This is, in turn, re-eroded and deposited by the next wave. We term these waves granular erosion–deposition waves. Although erosion and deposition problems are notoriously difficult, a simple model is developed which uses a depth-averaged version of the ${\it\mu}(I)$-rheology and Pouliquen and Forterre’s extended friction law. The viscous dissipation combines with dynamic, intermediate and static friction regimes to generate finite-length waves with static and mobile regions. The existence of stationary layers fundamentally distinguishes erosion–deposition waves from granular roll waves, which form in slightly deeper flows and are always completely mobilized. Numerical simulations show that the system of equations is able to model both erosion–deposition waves and granular roll waves. Moreover, the computed wave amplitude, wavespeed and coarsening dynamics are in good quantitative agreement with experiments.

scholarly journals The kinematics of bidisperse granular roll waves

2018 ◽  
Vol 848 ◽  
pp. 836-875 ◽  
Author(s):  
S. Viroulet ◽  
J. L. Baker ◽  
F. M. Rocha ◽  
C. G. Johnson ◽  
B. P. Kokelaar ◽  
...  
Keyword(s):  
Particle Concentration ◽  
Wave Crest ◽  
Small Scale ◽  
Size Segregation ◽  
Chute Flow ◽  
Glass Spheres ◽  
Roll Waves ◽  
Low Concentrations ◽  
Large Particles ◽  
The Waves

Small perturbations to a steady uniform granular chute flow can grow as the material moves downslope and develop into a series of surface waves that travel faster than the bulk flow. This roll wave instability has important implications for the mitigation of hazards due to geophysical mass flows, such as snow avalanches, debris flows and landslides, because the resulting waves tend to merge and become much deeper and more destructive than the uniform flow from which they form. Natural flows are usually highly polydisperse and their dynamics is significantly complicated by the particle size segregation that occurs within them. This study investigates the kinematics of such flows theoretically and through small-scale experiments that use a mixture of large and small glass spheres. It is shown that large particles, which segregate to the surface of the flow, are always concentrated near the crests of roll waves. There are different mechanisms for this depending on the relative speed of the waves, compared to the speed of particles at the free surface, as well as on the particle concentration. If all particles at the surface travel more slowly than the waves, the large particles become concentrated as the shock-like wavefronts pass them. This is due to a concertina-like effect in the frame of the moving wave, in which large particles move slowly backwards through the crest, but travel quickly in the troughs between the crests. If, instead, some particles on the surface travel more quickly than the wave and some move slower, then, at low concentrations, large particles can move towards the wave crest from both the forward and rearward sides. This results in isolated regions of large particles that are trapped at the crest of each wave, separated by regions where the flow is thinner and free of large particles. There is also a third regime arising when all surface particles travel faster than the waves, which has large particles present everywhere but with a sharp increase in their concentration towards the wave fronts. In all cases, the significantly enhanced large particle concentration at wave crests means that such flows in nature can be especially destructive and thus particularly hazardous.

Roll waves in a non-regular inclined channel

2004 ◽  
Vol 15 (3) ◽  
pp. 257-271 ◽  
Author(s):  
A. BOUDLAL ◽  
V. YU. LIAPIDEVSKII
Keyword(s):  
Hyperbolic Equations ◽  
Travelling Waves ◽  
Arbitrary Cross Section ◽  
Nonlinear Hyperbolic Equations ◽  
Pressure Function ◽  
Flow Acceleration ◽  
Roll Waves ◽  
Dynamic Type ◽  
The Waves

For nonlinear hyperbolic equations of a gas dynamic type with flow acceleration and friction terms, the classification of a special class of periodic travelling waves, which are known as roll waves, is given. As an illustration, the shallow water equations for the inclined channels of an arbitrary cross-section are considered. The analysis shows that the flow patterns depend upon the sign of the second derivative of the pressure function. The roll waves in regular channels with the convex pressure have the same structure as the waves described in Dressler [6]. For a nonconvex pressure function, the multi-jump configuration of roll waves is found.

A new model of roll waves: comparison with Brock’s experiments

2012 ◽  
Vol 698 ◽  
pp. 374-405 ◽  
Author(s):  
G. L. Richard ◽  
S. L. Gavrilyuk
Keyword(s):  
Euler Equations ◽  
Large Scale ◽  
Stationary Solutions ◽  
Small Scale ◽  
Roll Waves ◽  
Averaged Equations ◽  
Isentropic Euler Equations ◽  
The Waves ◽  
Shock Thickness

AbstractWe derive a mathematical model of shear flows of shallow water down an inclined plane. The non-dissipative part of the model is obtained by averaging the incompressible Euler equations over the fluid depth. The averaged equations are simplified in the case of weakly sheared flows. They are reminiscent of the compressible non-isentropic Euler equations where the flow enstrophy plays the role of entropy. Two types of enstrophies are distinguished: a small-scale enstrophy generated near the wall, and a large-scale enstrophy corresponding to the flow in the roller region near the free surface. The dissipation is then added in accordance with basic physical principles. The model is hyperbolic, the corresponding ‘sound velocity’ depends on the flow enstrophies. Periodic stationary solutions to this model describing roll waves were obtained. The solutions are in good agreement with the experimental profiles of roll waves measured in Brock’s experiments. In particular, the height of the vertical front of the waves, the shock thickness and the wave amplitude are well captured by the model.

scholarly journals A broadbanded pressure differential wave energy converter based on dielectric elastomer generators

2021 ◽  
Author(s):  
Michele Righi ◽  
Giacomo Moretti ◽  
David Forehand ◽  
Lorenzo Agostini ◽  
Rocco Vertechy ◽  
...  
Keyword(s):  
Wave Energy ◽  
Large Deformations ◽  
Dielectric Elastomer ◽  
Wave Energy Converter ◽  
Pressure Differential ◽  
Design Stage ◽  
Small Scale ◽  
Energy Converter ◽  
Wide Range ◽  
The Waves

AbstractDielectric elastomer generators (DEGs) are a promising option for the implementation of affordable and reliable sea wave energy converters (WECs), as they show considerable promise in replacing expensive and inefficient power take-off systems with cheap direct-drive generators. This paper introduces a concept of a pressure differential wave energy converter, equipped with a DEG power take-off operating in direct contact with sea water. The device consists of a closed submerged air chamber, with a fluid-directing duct and a deformable DEG power take-off mounted on its top surface. The DEG is cyclically deformed by wave-induced pressure, thus acting both as the power take-off and as a deformable interface with the waves. This layout allows the partial balancing of the stiffness due to the DEG’s elasticity with the negative hydrostatic stiffness contribution associated with the displacement of the water column on top of the DEG. This feature makes it possible to design devices in which the DEG exhibits large deformations over a wide range of excitation frequencies, potentially achieving large power capture in a wide range of sea states. We propose a modelling approach for the system that relies on potential-flow theory and electroelasticity theory. This model makes it possible to predict the system dynamic response in different operational conditions and it is computationally efficient to perform iterative and repeated simulations, which are required at the design stage of a new WEC. We performed tests on a small-scale prototype in a wave tank with the aim of investigating the fluid–structure interaction between the DEG membrane and the waves in dynamical conditions and validating the numerical model. The experimental results proved that the device exhibits large deformations of the DEG power take-off over a broad range of monochromatic and panchromatic sea states. The proposed model demonstrates good agreement with the experimental data, hence proving its suitability and effectiveness as a design and prediction tool.

Measurements of the Static Friction Coefficient Between Tin Surfaces and Comparison to a Theoretical Model

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Rebecca D. Ibrahim Dickey ◽  
Robert L. Jackson ◽  
George T. Flowers
Keyword(s):  
Theoretical Model ◽  
Friction Coefficient ◽  
Human Error ◽  
Surface Profile ◽  
Static Friction ◽  
Quantitative Agreement ◽  
High Plasticity ◽  
Static Friction Coefficient ◽  
Experimental Apparatus ◽  
Rough Surface Contact

A new experimental apparatus is used to measure the static friction between tin surfaces under various loads. After the data is collected it is then compared to an existing theoretical model. The experiment uses the classical physics technique of increasing the incline of a plane and block until the block slides. The angle at the initiation of sliding is used to find the static friction coefficient. The experiment utilizes an automated apparatus to minimize human error. The finite element based statistical rough surface contact model for static friction under full stick by Li, Etsion, and Talke (2010, “Contact Area and Static Friction of Rough Surfaces with High Plasticity Index,” ASME Journal of Tribology, 132(3), p. 031401) is used to make predictions of the friction coefficient using surface profile data from the experiment. Comparison of the computational and experimental methods shows similar qualitative trends, and even some quantitative agreement. After adjusting the results for the possible effect of the native tin oxide film, the theoretical and experimental results can be brought into reasonable qualitative and quantitative agreement.

scholarly journals Brittle Fracture Theory Describes the Onset of Frictional Motion

2019 ◽  
Vol 10 (1) ◽  
pp. 253-273 ◽  
Author(s):  
Ilya Svetlizky ◽  
Elsa Bayart ◽  
Jay Fineberg
Keyword(s):  
Friction Coefficient ◽  
Brittle Fracture ◽  
Static Friction ◽  
Quantitative Agreement ◽  
Interface Fracture ◽  
Earthquake Dynamics ◽  
Rupture Dynamics ◽  
Static Friction Coefficient ◽  
Fracture Theory ◽  
Macroscopic Motion

Contacting bodies subjected to sufficiently large applied shear will undergo frictional sliding. The onset of this motion is mediated by dynamically propagating fronts, akin to earthquakes, that rupture the discrete contacts that form the interface separating the bodies. Macroscopic motion commences only after these ruptures have traversed the entire interface. Comparison of measured rupture dynamics with the detailed predictions of fracture mechanics reveals that the propagation dynamics, dissipative properties, radiation, and arrest of these “laboratory earthquakes” are in excellent quantitative agreement with the predictions of the theory of brittle fracture. Thus, interface fracture replaces the idea of a characteristic static friction coefficient as a description of the onset of friction. This fracture-based description of friction additionally provides a fundamental description of earthquake dynamics and arrest.

On the Static-Kinetic Friction Transition in Dry Contact of Rough Surfaces

2011 ◽  
Author(s):  
K. Farhang ◽  
D. Segalman ◽  
M. Starr
Keyword(s):  
Large Scale ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Static Friction ◽  
Partial Slip ◽  
Small Scale ◽  
Asperity Contact ◽  
Kinetic Friction ◽  
Tangential Load ◽  
Asperity Contacts

This paper shows that the Mindlin problem involving two spheres in contact under the action of oscillating tangential force can lead to the account of static-kinetic friction transition. In Mindlin’s problem two spheres experience partial slip as a result of application of oscillating tangential load. When the problem is extended to multi-sphere contact, i.e. two rough surfaces, the application of tangential oscillating load results in partial slip for some asperity contacts while others experience full slip. Increase in the amplitude of the oscillating tangential force results in more contacts experiencing full slip, thereby decreasing the number of contacts in parial slip. Constitutive relation proposed by Mindlin at small scale, governing asperity interaction, is used to obtain the large scale slip function through a statistical summation of asperity scale events. The slip function establishes the fraction of asperity contact in full slip. The complement of the slip parameter is a fraction of asperities in partial slip. Through slip function it is shown that it is possible to define a slip condition for the entire surface. The derivation of the slip function allows the account of transition between static friction and kinetic friction.

scholarly journals Micro Sand Engine Beach Stabilization Strategy at Puerto Morelos, Mexico

2020 ◽  
Vol 8 (4) ◽  
pp. 247 ◽  
Author(s):  
Mireille Escudero ◽  
Edgar Mendoza ◽  
Rodolfo Silva
Keyword(s):  
Small Scale ◽  
Coastal Protection ◽  
Protection Measure ◽  
Morphological Response ◽  
Protection Measures ◽  
Small Bell ◽  
Waves And Currents ◽  
Maintenance Work ◽  
Negative Impacts ◽  
The Waves

In the last decade, innovative beach nourishment strategies have been developed, driven by the increased worldwide interest in environmentally friendly coastal protection measures. In this context, the massive nourishment project of the Netherlands, known as Sand Engine, begun in 2011, has been hailed as a successful means of beach protection. Continuous monitoring, field campaigns, and numerical modeling have shown that the great volume of sand deployed is gradually transported by the waves and currents along the coastline, avoiding the need for repeated invasive, small scale beach replenishments. A very small, bell-shaped Sand Engine was designed to protect the beachfront at a tourist resort near Puerto Morelos, Mexico. To estimate the morphological response of the beach and the functioning of the micro Sand Engine as a sand reservoir, XBeach numerical modelling was applied to the project. The micro Sand Engine is seen to be a sustainable and eco-friendly coastal protection measure, especially applicable when a large nourishment project is not viable. Maintenance work for the nourishment is cost and time effective, and any negative impacts to sensitive ecosystems nearby can be detected and controlled quickly.

scholarly journals Derivation of Canopy Resistance in Turbulent Flow from First-Order Closure Models

Water ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 1782 ◽  
Author(s):  
Wei-Jie Wang ◽  
Wen-Qi Peng ◽  
Wen-Xin Huai ◽  
Gabriel Katul ◽  
Xiao-Bo Liu ◽  
...  
Keyword(s):  
Friction Factor ◽  
Free Surface Flows ◽  
Hydrodynamic Resistance ◽  
Small Scale ◽  
Length Scale ◽  
Length Scales ◽  
First Order ◽  
Closure Models ◽  
Wide Range ◽  
The Mean

Quantification of roughness effects on free surface flows is unquestionably necessary when describing water and material transport within ecosystems. The conventional hydrodynamic resistance formula empirically shows that the Darcy–Weisbach friction factor f~(r/hw)1/3 describes the energy loss of flowing water caused by small-scale roughness elements characterized by size r (<<hw), where hw is the water depth. When the roughness obstacle size becomes large (but <hw) as may be encountered in flow within canopies covering wetlands or river ecosystem, the f becomes far more complicated. The presence of a canopy introduces additional length scales above and beyond r/hw such as canopy height hv, arrangement density m, frontal element width D, and an adjustment length scale that varies with the canopy drag coefficient Cd. Linking those length scales to the friction factor f frames the scope of this work. By adopting a scaling analysis on the mean momentum equation and closing the turbulent stress with a first-order closure model, the mean velocity profile, its depth-integrated value defining the bulk velocity, as well as f can be determined. The work here showed that f varies with two dimensionless groups that depend on the canopy submergence depth and a canopy length scale. The relation between f and these two length scales was quantified using first-order closure models for a wide range of canopy and depth configurations that span much of the published experiments. Evaluation through experiments suggests that the proposed model can be imminently employed in eco-hydrology or eco-hydraulics when using the De Saint-Venant equations.

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