scholarly journals Production and decay of random kinetic energy in granular snow avalanches

2009 ◽  
Vol 55 (189) ◽  
pp. 3-12 ◽  
Author(s):  
Othmar Buser ◽  
Perry Bartelt
Keyword(s):  
Kinetic Energy ◽  
Velocity Profiles ◽  
Random Motion ◽  
Particle Interactions ◽  
Snow Avalanches ◽  
Random Energy ◽  
Consistency Problem ◽  
Self Consistency ◽  
Real Scale

AbstractAny model of snow avalanches must be able to reproduce velocity profiles. This is a key problem in avalanche science because the profiles are the result of a multitude of snow/ice particle interactions that, in the fend, define the rheology of flowing snow. Recent measurements on real-scale avalanches show that the velocity profiles change from a highly sheared profile at the avalanche front to a plug-like profile at the avalanche tail, preventing the application of a single, simple rheology to the avalanche problem. In this paper, we model not only the velocity profiles but also the evolution of the velocity profiles, by taking into account the production and decay of the kinetic energy of the random motion of the snow granules. We find that the generation of this random energy depends on the distribution of viscous shearing within the avalanche. Conversely, the viscous shearing depends on the magnitude of the random energy and therefore its collisional dissipation. Thus, there is a self–consistency problem that must be resolved in order to predict the amount of random energy and therefore the velocity profiles. We solve this problem by stating equations that describe the production and decay of random energy in avalanches. An important guide to the form of these equations is that the generation of random energy is irreversible. We show that our approach successfully accounts for measured profiles in natural avalanches.

Consistent Theoretical Model of Mean Diameter and Size Distribution by Liquid Sheet Atomization

2012 ◽  
Author(s):  
Chihiro Inoue ◽  
Toshinori Watanabe ◽  
Takehiro Himeno ◽  
Seiji Uzawa ◽  
Mitsuo Koshi
Keyword(s):  
Theoretical Model ◽  
Kinetic Energy ◽  
Droplet Diameter ◽  
Velocity Profiles ◽  
Liquid Sheet ◽  
Estimation Methods ◽  
Liquid Jets ◽  
Injection Velocity ◽  
Size Distributions ◽  
Mean Diameter

A consistent theoretical model is proposed and validated for calculating droplet diameters and size distributions. The model is derived based on the energy conservation law including the surface free energy and the Laplace pressure. Under several hypotheses, the law derives an equation indicating that atomization results from kinetic energy loss. Thus, once the amount of loss is determined, the droplet diameter is able to be calculated without the use of experimental parameters. When the effects of ambient gas are negligible, injection velocity profiles of liquid jets are the essential cause of the reduction of kinetic energy. The minimum Sauter mean diameter produced by liquid sheet atomization is inversely proportional to the injection Weber number when the injection velocity profiles are laminar or turbulent. A non-dimensional distribution function is also derived from the mean diameter model and Nukiyama-Tanasawa’s function. The new estimation methods are favorably validated by comparing with corresponding mean diameters and the size distributions, which are experimentally measured under atmospheric pressure.

scholarly journals Experimental study of dense snow avalanches: velocity profiles in steady and fully developed flows

2004 ◽  
Vol 38 ◽  
pp. 30-34 ◽  
Author(s):  
Alexi Bouchet ◽  
Mohamed Naaim ◽  
Hervé Bellot ◽  
Frédéric Ousset
Keyword(s):  
Experimental Study ◽  
Feeding Rate ◽  
Velocity Profiles ◽  
Normal Stresses ◽  
Snow Avalanches ◽  
Ski Resort ◽  
Highly Active ◽  
Scale Experiment ◽  
Long Channel ◽  
High Pass

AbstractIn order to study channelled snow flows over rough surfaces, a laboratory-scale experiment was installed at the “Col du Lac Blanc”, a 2800 m high pass in the French Alps, near the Alpe d’Huez ski resort. It consists of a 0.2 mwide, 10 m long channel fed with snow by a motorized hopper. Both the slope of the channel and the feeding rate of the hopper can be modified. Sensors in the channel provide measurements of the velocity profile, the flow height and the shear and normal stresses at the bottom of the flow. Velocity profiles for different slopes are presented in this paper. Results indicate the presence of a highly active layer at the bottom. This layer is mainly responsible for the avalanche velocity, while the upper layer has a much smaller velocity gradient. A first interpretation of both layers is given.

scholarly journals Frictional relaxation in avalanches

2010 ◽  
Vol 51 (54) ◽  
pp. 98-104 ◽  
Author(s):  
Perry Bartelt ◽  
Othmar Buser
Keyword(s):  
Kinetic Energy ◽  
Energy Levels ◽  
Full Range ◽  
Test Site ◽  
Friction Model ◽  
Random Motion ◽  
Avalanche Dynamics ◽  
Avalanche Flow ◽  
Friction Parameters ◽  
Steep Slopes

AbstractWe use velocity profile measurements captured at the Vallée de la Sionne test site, Switzerland, to find experimental evidence for the value of extreme, Voellmy-type runout parameters for snow avalanche flow. We apply a constitutive relation that adjusts the internal shear stress as a function of the kinetic energy associated with random motion of the snow granules, R. We then show how the Voellmy dry-Coulomb and velocity-squared friction parameters change (relax) as a function of an increase in R. Since the avalanche head is characterized by high random energy levels, friction decreases significantly, leading to rapidly moving and far-reaching avalanches. The relaxed friction parameters are near to values recommended by the Swiss avalanche dynamics guidelines. As the random kinetic energy decreases towards the tail, friction increases, causing avalanches to deposit mass and stop even on steep slopes. Our results suggest that the Voellmy friction model can be effectively applied to predict maximum avalanche velocities and maximum runout distances. However, it cannot be applied to model the full range of avalanche behaviour, especially to find the distribution of mass in the runout zone. We answer a series of questions concerning the role of R in avalanche dynamics.

Maximum kinetic energy dissipation and the stability of turbulent Poiseuille flow

2015 ◽  
Vol 767 ◽  
pp. 342-363 ◽  
Author(s):  
J. Bertram
Keyword(s):  
Reynolds Number ◽  
Energy Dissipation ◽  
Kinetic Energy ◽  
Viscous Dissipation ◽  
Velocity Profiles ◽  
Mean Flow ◽  
Mean Velocity ◽  
Statistical Stability ◽  
The Stability ◽  
Principle Of Maximum

AbstractFollowing Malkus’s (J. Fluid Mech., vol. 1, 1956, pp. 521–539) proposal that turbulent Poiseuille channel flow maximises total viscous dissipation $D$, a variety of variational procedures have been explored involving the maximisation of different flow quantities under different constraints. However, the physical justification for these variational procedures has remained unclear. Here we address more recent claims that mean flow viscous dissipation $D_{m}$ should be maximised on the basis of a statistical stability argument, and that maximising $D_{m}$ yields realistic mean velocity profiles (Malkus, J. Fluid Mech., vol. 489, 2003, pp. 185–198). We clarify the connection between maximising $D_{m}$ and other flow quantities, verify Malkus & Smith’s, (J. Fluid Mech., vol. 208, 1989, pp. 479–507) claim that maximising the ‘efficiency’ yields realistic profiles and show that, in contrast, maximising $D_{m}$ does not yield realistic mean velocity profiles as recently claimed. This leads us to revisit Malkus’s statistical stability argument for maximising $D_{m}$ and to address some of its limitations. We propose an alternative statistical stability argument leading to a principle of minimum kinetic energy for fixed pressure gradient, which suggests a principle of maximum $D$ for fixed Reynolds number under certain conditions. We discuss possible ways to reconcile these conflicting results, focusing on the choice of constraints.

scholarly journals Measurements of Velocity Profiles in Natural Debris Flows: A View behind the Muddy Curtain

2020 ◽  
Vol 27 (1) ◽  
pp. 87-94
Author(s):  
Georg Nagl ◽  
Johannes Hübl ◽  
Roland Kaitna
Keyword(s):  
Debris Flow ◽  
Debris Flows ◽  
Model Development ◽  
Fluid Pressure ◽  
Velocity Profiles ◽  
Flow Parameters ◽  
Internal Deformation ◽  
Debris Flow Hazard ◽  
Real Scale

ABSTRACT The internal deformation behavior of natural debris flows is of interest for model development and model testing for debris-flow hazard mitigation. Up to now, only a few attempts have been made to measure velocity profiles in natural debris flows due to the low predictability and high destructive power of these flows. In this contribution, we present recent advances to measure in-situ velocity profiles together with flow parameters like flow height, basal normal stress, and pore fluid pressure. This was accomplished by constructing a fin-shaped monitoring barrier with an array of paired conductivity sensors in the middle of Gadria Creek, Italy. We present results from two natural debris-flow events. Compared to the first event on July 10, 2017, the second event on August 19, 2017, was visually more liquid. Both debris flows exhibited significant longitudinal changes of flow properties like flow height and density. The liquefaction ratios reached values up to unity in some sections of the flows. Velocity profiles for the July event were mostly concave-up, while the profiles for the more liquid event in August were linear to convex. These measurements provide new insights into the dynamics of real-scale debris flows.

scholarly journals Dispersive pressure and density variations in snow avalanches

2011 ◽  
Vol 57 (205) ◽  
pp. 857-860 ◽  
Author(s):  
Othmar Buser ◽  
Perry Bartelt
Keyword(s):  
Kinetic Energy ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Random Fluctuation ◽  
Flow Density ◽  
Snow Avalanches ◽  
Mean Velocity ◽  
The Mean ◽  
Dispersive Pressure ◽  
Fluctuation Energy

AbstractSnow avalanches possess two types of kinetic energy: the kinetic energy associated with the mean velocity in the downhill direction and the kinetic energy associated with individual particle velocities that vary from the mean. The mean kinetic energy is directional; the kinetic energy associated with the velocity fluctuations is non-directional in the sense that it is connected to random particle movements. However, the rigid, basal boundary directs the random fluctuation energy into the avalanche. Thus, the random energy flux is converted to free mechanical energy which lifts and dilates the avalanche flow mass, changing the flow density and increasing the normal (dispersive) pressure and, as a consequence, changing the flow resistance. In this paper we derive macroscopic relations that link the production of the random kinetic energy to the perpendicular acceleration of the avalanche’s center of mass. We show that a single burst of fluctuation energy will produce pressures that oscillate around the hydrostatic pressure. Because we do not include a damping process, the oscillations of the center of mass remain, even if the production of random kinetic energy stops. We formulate relationships that can be used within the framework of depth-averaged mass and momentum equations that are often used to simulate snow avalanches in realistic terrain.

scholarly journals R fluids

2008 ◽  
pp. 23-35 ◽  
Author(s):  
R. Caimmi
Keyword(s):  
Kinetic Energy ◽  
Velocity Component ◽  
Axial Velocity ◽  
Tangential Velocity ◽  
Random Motion ◽  
Moment Of Inertia ◽  
Random Velocity ◽  
Principal Axes ◽  
The Moment ◽  
Figure Rotation

A theory of collisionless fluids is developed in a unified picture, where nonrotating (?f1 = ?f2 = ?f3 = 0) figures with some given random velocity component distributions, and rotating (?f1 = ?f2 = ?f3 ) figures with a different random velocity component distributions, make adjoint configurations to the same system. R fluids are defined as ideal, self-gravitating fluids satisfying the virial theorem assumptions, in presence of systematic rotation around each of the principal axes of inertia. To this aim, mean and rms angular velocities and mean and rms tangential velocity components are expressed, by weighting on the moment of inertia and the mass, respectively. The figure rotation is defined as the mean angular velocity, weighted on the moment of inertia, with respect to a selected axis. The generalized tensor virial equations (Caimmi and Marmo 2005) are formulated for R fluids and further attention is devoted to axisymmetric configurations where, for selected coordinate axes, a variation in figure rotation has to be counterbalanced by a variation in anisotropy excess and vice versa. A microscopical analysis of systematic and random motions is performed under a few general hypotheses, by reversing the sign of tangential or axial velocity components of an assigned fraction of particles, leaving the distribution function and other parameters unchanged (Meza 2002). The application of the reversion process to tangential velocity components is found to imply the conversion of random motion rotation kinetic energy into systematic motion rotation kinetic energy. The application of the reversion process to axial velocity components is found to imply the conversion of random motion translation kinetic energy into systematic motion translation kinetic energy, and the loss related to a change of reference frame is expressed in terms of systematic motion (imaginary) rotation kinetic energy. A number of special situations are investigated in greater detail. It is found that an R fluid always admits an adjoint configuration where figure rotation occurs around only one principal axis of inertia (R3 fluid), which implies that all the results related to R3 fluids (Caimmi 2007) may be ex- tended to R fluids. Finally, a procedure is sketched for deriving the spin parameter distribution (including imaginary rotation) from a sample of observed or simulated large-scale collisionless fluids i.e. galaxies and galaxy clusters.

Depth-integrated equations for entraining granular flows in narrow channels

2015 ◽  
Vol 765 ◽  
Author(s):  
H. Capart ◽  
C.-Y. Hung ◽  
C. P. Stark
Keyword(s):  
Kinetic Energy ◽  
Granular Flows ◽  
Velocity Profiles ◽  
Narrow Channels ◽  
Granular Rheology ◽  
Bed Material ◽  
Erodible Beds ◽  
Non Equilibrium

AbstractFlowing over erodible beds, channelized granular avalanches can alter their volume by entraining or detraining basal grains. In detail, entrainment results from a gradual adjustment of stress and velocity profiles over depth, bringing bed material past yield (and vice versa for detrainment). To capture this process, we propose new depth-integrated equations that balance kinetic energy in addition to mass and momentum. The equations require a local granular rheology, assumed viscoplastic, but no extra erosion law. Entrainment rates are instead deduced from the depth-integrated layer dynamics. To check the approach, we obtain solutions for non-equilibrium heap flows, and compare them with experiments conducted in a seesaw channel.

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