scholarly journals Bulbous head formation in bidisperse shallow granular flow over an inclined plane

2019 ◽  
Vol 866 ◽  
pp. 263-297 ◽  
Author(s):  
I. F. C. Denissen ◽  
T. Weinhart ◽  
A. Te Voortwis ◽  
S. Luding ◽  
J. M. N. T. Gray ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Pyroclastic Flows ◽  
Surface Velocity ◽  
Small Scale ◽  
Efficient Computation ◽  
Flow Front ◽  
Mean Velocity ◽  
Discrete Particle ◽  
Large Particles ◽  
Particle Simulations

Rapid shallow granular flows over inclined planes are often seen in nature in the form of avalanches, landslides and pyroclastic flows. In these situations the flow develops an inversely graded (large at the top) particle-size distribution perpendicular to the plane. As the surface velocity of such flows is larger than the mean velocity, the larger material is transported to the flow front. This causes size segregation in the downstream direction, resulting in a flow front composed of large particles. Since the large particles are often more frictional than the small, the mobility of the flow front is reduced, resulting in a so-called bulbous head. This study focuses on the formation and evolution of this bulbous head, which we show to emerge in both a depth-averaged continuum framework and discrete particle simulations. Furthermore, our numerical solutions of the continuum model converge to a travelling wave solution, which allows for a very efficient computation of the long-time behaviour of the flow. We use small-scale periodic discrete particle simulations to calibrate (close) our continuum framework, and validate the simple one-dimensional (1-D) model with full-scale 3-D discrete particle simulations. The comparison shows that there are conditions under which the model works surprisingly well given the strong approximations made; for example, instantaneous vertical segregation.

scholarly journals Segregation-induced fingering instabilities in granular free-surface flows

2012 ◽  
Vol 709 ◽  
pp. 543-580 ◽  
Author(s):  
M. J. Woodhouse ◽  
A. R. Thornton ◽  
C. G. Johnson ◽  
B. P. Kokelaar ◽  
J. M. N. T. Gray
Keyword(s):  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
Free Surface Flows ◽  
Numerical Results ◽  
Small Scale ◽  
Size Segregation ◽  
Numerical Resolution ◽  
Bulk Motion ◽  
Large Particles ◽  
Ill Posed

AbstractParticle-size segregation can have a significant feedback on the bulk motion of granular avalanches when the larger grains experience greater resistance to motion than the fine grains. When such segregation-mobility feedback effects occur the flow may form digitate lobate fingers or spontaneously self-channelize to form lateral levees that enhance run-out distance. This is particularly important in geophysical mass flows, such as pyroclastic currents, snow avalanches and debris flows, where run-out distance is of crucial importance in hazards assessment. A model for finger formation in a bidisperse granular avalanche is developed by coupling a depth-averaged description of the preferential transport of large particles towards the front with an established avalanche model. The coupling is achieved through a concentration-dependent friction coefficient, which results in a system of non-strictly hyperbolic equations. We compute numerical solutions to the flow of a bidisperse mixture of small mobile particles and larger more resistive grains down an inclined chute. The numerical results demonstrate that our model is able to describe the formation of a front rich in large particles, the instability of this front and the subsequent evolution of elongated fingers bounded by large-rich lateral levees, as observed in small-scale laboratory experiments. However, our numerical results are grid dependent, with the number of fingers increasing as the numerical resolution is increased. We investigate this pathology by examining the linear stability of a steady uniform flow, which shows that arbitrarily small wavelength perturbations grow exponentially quickly. Furthermore, we find that on a curve in parameter space the growth rate is unbounded above as the wavelength of perturbations is decreased and so the system of equations on this curve is ill-posed. This indicates that the model captures the physical mechanisms that drive the instability, but additional dissipation mechanisms, such as those considered in the realm of flow rheology, are required to set the length scale of the fingers that develop.

scholarly journals Monitoring Lakes Surface Water Velocity with SAR: A Feasibility Study on Lake Garda, Italy

2021 ◽  
Vol 13 (12) ◽  
pp. 2293
Author(s):  
Marina Amadori ◽  
Virginia Zamparelli ◽  
Giacomo De Carolis ◽  
Gianfranco Fornaro ◽  
Marco Toffolon ◽  
...  
Keyword(s):  
Surface Water ◽  
Wind Waves ◽  
Test Site ◽  
Water Velocity ◽  
Surface Velocity ◽  
Medium Size ◽  
Small Scale ◽  
Lake Garda ◽  
Marine Applications

The SAR Doppler frequencies are directly related to the motion of the scatterers in the illuminated area and have already been used in marine applications to monitor moving water surfaces. Here we investigate the possibility of retrieving surface water velocity from SAR Doppler analysis in medium-size lakes. ENVISAT images of the test site (Lake Garda) are processed and the Doppler Centroid Anomaly technique is adopted. The resulting surface velocity maps are compared with the outputs of a hydrodynamic model specifically validated for the case study. Thermal images from MODIS Terra are used in support of the modeling results. The surface velocity retrieved from SAR is found to overestimate the numerical results and the existence of a bias is investigated. In marine applications, such bias is traditionally removed through Geophysical Model Functions (GMFs) by ascribing it to a fully developed wind waves spectrum. We found that such an assumption is not supported in our case study, due to the small-scale variations of topography and wind. The role of wind intensity and duration on the results from SAR is evaluated, and the inclusion of lake bathymetry and the SAR backscatter gradient is recommended for the future development of GMFs suitable for lake environments.

scholarly journals Surface kinetic energy transfer in surface quasi-geostrophic flows

2008 ◽  
Vol 604 ◽  
pp. 165-174 ◽  
Author(s):  
XAVIER CAPET ◽  
PATRICE KLEIN ◽  
BACH LIEN HUA ◽  
GUILLAUME LAPEYRE ◽  
JAMES C. MCWILLIAMS
Keyword(s):  
Kinetic Energy ◽  
Surface Velocity ◽  
Small Scale ◽  
Surface Dynamics ◽  
Spectral Flux ◽  
Advection Term ◽  
Wide Range ◽  
Geostrophic Flows ◽  
Scale Range ◽  
Density Variance

The relevance of surface quasi-geostrophic dynamics (SQG) to the upper ocean and the atmospheric tropopause has been recently demonstrated in a wide range of conditions. Within this context, the properties of SQG in terms of kinetic energy (KE) transfers at the surface are revisited and further explored. Two well-known and important properties of SQG characterize the surface dynamics: (i) the identity between surface velocity and density spectra (when appropriately scaled) and (ii) the existence of a forward cascade for surface density variance. Here we show numerically and analytically that (i) and (ii) do not imply a forward cascade of surface KE (through the advection term in the KE budget). On the contrary, advection by the geostrophic flow primarily induces an inverse cascade of surface KE on a large range of scales. This spectral flux is locally compensated by a KE source that is related to surface frontogenesis. The subsequent spectral budget resembles those exhibited by more complex systems (primitive equations or Boussinesq models) and observations, which strengthens the relevance of SQG for the description of ocean/atmosphere dynamics near vertical boundaries. The main weakness of SQG however is in the small-scale range (scales smaller than 20–30 km in the ocean) where it poorly represents the forward KE cascade observed in non-QG numerical simulations.

Discrete particle simulations of an electric-field enhanced fluidized bed

2008 ◽  
Vol 183 (2) ◽  
pp. 196-206 ◽  
Author(s):  
F. Kleijn van Willigen ◽  
B. Demirbas ◽  
N.G. Deen ◽  
J.A.M. Kuipers ◽  
J.R. van Ommen
Keyword(s):  
Electric Field ◽  
Fluidized Bed ◽  
Discrete Particle ◽  
Particle Simulations

Thermal Elastohydrodynamic Lubrication Analysis for Point Contact Transmission

2009 ◽  
Author(s):  
Hai-zhou Huang ◽  
Xi-chuan Niu ◽  
Xiao-yang Yuan
Keyword(s):  
Film Thickness ◽  
Numerical Solutions ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Surface Velocity ◽  
Squeeze Film ◽  
Elastic Displacement ◽  
Circular Arc ◽  
Tooth Width ◽  
Contact Transmission

To investigate the thermal EHL (elastohydrodynamic lubrication) in point contact transmission, a model considering the two-dimensional surface velocity of tooth face and the running-in is proposed. The numerical solutions for pressure, temperature and film thickness distribution in the contact zone are obtained by solving equations including the Reynolds, Energy and the elastic displacement with variable dimension meshing method. The model was used to study the point contact transmission of the circular arc gear in a windlass. The main results show that it is pure rolling along the direction of tooth width, and the rolling speed plays a leading role in improving the lubricating performance and transmission efficiency of circular arc gear. The squeeze film effect makes the pressure peak tend to be gentle and the film thickness increase slightly.

The Fully Developed Wake of a Circular Cylinder

1949 ◽  
Vol 2 (4) ◽  
pp. 451 ◽  
Author(s):  
AA Townsend
Keyword(s):  
Circular Cylinder ◽  
Diffusion Coefficients ◽  
Large Scale ◽  
Turbulent Transport ◽  
Turbulent Energy ◽  
Small Scale ◽  
Mean Velocity ◽  
Turbulent Fluid ◽  
Air Stream ◽  
Scale Motion

Extending previous work on turbulent diffusion in the wake of a circular-cylinder, a series of measurements have been made of the turbulent transport of mean stream momentum, turbulent energy, and heat in the wake of a cylinder of 0.169 cm. diameter, placed in an air-stream of velocity 1280 cm. sec.-1. It has been possible to extend the measurements to 960 diameters down-stream from the cylinder, and it 1s found that, at distances in excess of 600 diameters, the requirements of dynamical similarity are very nearly satisfied. To account for the observed rates of transport of turbulent energy and heat, it is necessary that only part of this transport be due to bulk convection by the slow large-scale motion of the jets of turbulent fluid emitted by the central, fully turbulent core of the wake, which had been supposed previously to perform most of the transport. The remainder of the transport is carried out by the small-scale diffusive motion of the turbulent eddies within the jets, and may be described by assigning diffusion coefficients to the turbulent fluid. It is found that the diffusion coefficients for momentum and heat are approximately equal, but that for turbulent energy is considerably smaller. On the basis of these hypotheses, it is possible to calculate $he form of the mean velocity distribution in good agreement with experiment, and to give a qualitative explanation of the apparently more rapid diffusion of heat.

scholarly journals On the structure of the self-sustaining cycle in separating and reattaching flows

2018 ◽  
Vol 857 ◽  
pp. 907-936 ◽  
Author(s):  
A. Cimarelli ◽  
A. Leonforte ◽  
D. Angeli
Keyword(s):  
Shear Layer ◽  
Rectangular Plate ◽  
Large Scale ◽  
Reverse Flow ◽  
Leading Edge ◽  
Streamwise Velocity ◽  
The Self ◽  
Small Scale ◽  
Spectral Evolution ◽  
Mean Velocity

The separating and reattaching flows and the wake of a finite rectangular plate are studied by means of direct numerical simulation data. The large amount of information provided by the numerical approach is exploited here to address the multi-scale features of the flow and to assess the self-sustaining mechanisms that form the basis of the main unsteadinesses of the flows. We first analyse the statistically dominant flow structures by means of three-dimensional spatial correlation functions. The developed flow is found to be statistically dominated by quasi-streamwise vortices and streamwise velocity streaks as a result of flow motions induced by hairpin-like structures. On the other hand, the reverse flow within the separated region is found to be characterized by spanwise vortices. We then study the spectral properties of the flow. Given the strongly inhomogeneous nature of the flow, the spectral analysis has been conducted along two selected streamtraces of the mean velocity field. This approach allows us to study the spectral evolution of the flow along its paths. Two well-separated characteristic scales are identified in the near-wall reverse flow and in the leading-edge shear layer. The first is recognized to represent trains of small-scale structures triggering the leading-edge shear layer, whereas the second is found to be related to a very large-scale phenomenon that embraces the entire flow field. A picture of the self-sustaining mechanisms of the flow is then derived. It is shown that very-large-scale fluctuations of the pressure field alternate between promoting and suppressing the reverse flow within the separation region. Driven by these large-scale dynamics, packages of small-scale motions trigger the leading-edge shear layers, which in turn created them, alternating in the top and bottom sides of the rectangular plate with a relatively long period of inversion, thus closing the self-sustaining cycle.

scholarly journals Nonlinear feedback in a six-dimensional Lorenz Model: impact of an additional heating term

2015 ◽  
Vol 2 (2) ◽  
pp. 475-512
Author(s):  
B.-W. Shen
Keyword(s):  
Rayleigh Number ◽  
Numerical Solutions ◽  
Critical Rayleigh Number ◽  
Critical Value ◽  
Small Scale ◽  
Solution Stability ◽  
Nonlinear Feedback ◽  
Lorenz Model ◽  
Additional Heating ◽  
The Impact

Abstract. In this study, a six-dimensional Lorenz model (6DLM) is derived, based on a recent study using a five-dimensional (5-D) Lorenz model (LM), in order to examine the impact of an additional mode and its accompanying heating term on solution stability. The new mode added to improve the representation of the steamfunction is referred to as a secondary streamfunction mode, while the two additional modes, that appear in both the 6DLM and 5DLM but not in the original LM, are referred to as secondary temperature modes. Two energy conservation relationships of the 6DLM are first derived in the dissipationless limit. The impact of three additional modes on solution stability is examined by comparing numerical solutions and ensemble Lyapunov exponents of the 6DLM and 5DLM as well as the original LM. For the onset of chaos, the critical value of the normalized Rayleigh number (rc) is determined to be 41.1. The critical value is larger than that in the 3DLM (rc ~ 24.74), but slightly smaller than the one in the 5DLM (rc ~ 42.9). A stability analysis and numerical experiments obtained using generalized LMs, with or without simplifications, suggest the following: (1) negative nonlinear feedback in association with the secondary temperature modes, as first identified using the 5DLM, plays a dominant role in providing feedback for improving the solution's stability of the 6DLM, (2) the additional heating term in association with the secondary streamfunction mode may destabilize the solution, and (3) overall feedback due to the secondary streamfunction mode is much smaller than the feedback due to the secondary temperature modes; therefore, the critical Rayleigh number of the 6DLM is comparable to that of the 5DLM. The 5DLM and 6DLM collectively suggest different roles for small-scale processes (i.e., stabilization vs. destabilization), consistent with the following statement by Lorenz (1972): If the flap of a butterfly's wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado. The implications of this and previous work, as well as future work, are also discussed.

Tracking of velocity variations at depth in the presence of surface velocity fluctuations

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. U1-U8 ◽  
Author(s):  
Benoit de Cacqueray ◽  
Philippe Roux ◽  
Michel Campillo ◽  
Stefan Catheline
Keyword(s):  
Surface Waves ◽  
Body Waves ◽  
Surface Velocity ◽  
Small Scale ◽  
Beam Forming ◽  
Near Surface ◽  
Velocity Fluctuations ◽  
Wave Separation ◽  
Double Beam ◽  
Velocity Variations

We tested a small-scale experiment that is dedicated to the study of the wave separation algorithm and to the velocity variations monitoring problem itself. It handles the case in which velocity variations at depth are hidden by near-surface velocity fluctuations. Using an acquisition system that combines an array of sources and an array of receivers, coupled with controlled velocity variations, we tested the ability of beam-forming techniques to track velocity variations separately for body waves and surface waves. After wave separation through double beam forming, the arrival time variations of the different waves were measured through the phase difference between the extracted wavelets. Finally, a method was tested to estimate near-surface velocity variations using surface waves or shallow reflection and compute a correction to isolate target velocity variations at depth.

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