scholarly journals Comments on avalanche flow models based on the concept of random kinetic energy

2017 ◽  
Vol 64 (243) ◽  
pp. 148-164 ◽  
Author(s):  
DIETER ISSLER ◽  
JAMES T. JENKINS ◽  
JIM N. McELWAINE
Keyword(s):  
Kinetic Energy ◽  
Mathematical Formulation ◽  
Variable Density ◽  
Constant Density ◽  
Third Order ◽  
Flow Models ◽  
Suspension Layer ◽  
Avalanche Flow ◽  
Friction Parameters ◽  
Single Constant

ABSTRACTIn a series of papers, Bartelt and co-workers developed novel snow-avalanche models in which random kinetic energy (RKE) RK (a.k.a. granular temperature) is a key concept. The earliest models were for a single, constant density layer, using a Voellmy model but with RK-dependent friction parameters. This was then extended to variable density, and finally a suspension layer (powder-snow cloud) was added. The physical basis and mathematical formulation of these models are critically reviewed here, with the following main findings: (i) Key assumptions in the original RKE model differ substantially from established results on dense granular flows; in particular, the effective friction coefficient decreases to zero with velocity in the RKE model. (ii) In the variable-density model, non-canonical interpretation of the energy balance leads to a third-order evolution equation for the flow depth or density, whereas the stated assumptions imply a first-order equation. (iii) The model for the suspension layer neglects gravity and disregards well-established theoretical and experimental results on particulate gravity currents. Some options for improving these aspects are discussed.

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.

Les travaux sur la turbulence : les origines, Toucans, Cost-ES0905 et influence de l'entropie

2021 ◽  
pp. 079
Author(s):  
Ivan Bašták Ďurán ◽  
Pascal Marquet
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Richardson Number ◽  
Stable Stratification ◽  
Turbulence Energy ◽  
Third Order ◽  
Length Scales ◽  
Gradient Richardson Number ◽  
Turbulence Length ◽  
Consistent Treatment

Le schéma de turbulence Toucans est utilisé dans la configuration opérationnelle Alaro du modèle Aladin depuis début 2015. Son développement a été initié, guidé et en grande partie conçu par Jean-François Geleyn. Ce développement a commencé avec le prédécesseur du schéma Toucans, le schéma « pseudo-pronostique » en énergie cinétique turbulente, lui-même basé sur l'ancien schéma de turbulence de Louis, mais étendu dans Toucans à un schéma pronostique. Le schéma Toucans a pour objectif de traiter de manière cohérente les fonctions qui dépendent de la stabilité verticale de l'atmosphère, de l'influence de l'humidité et des échelles de longueur de la turbulence (de mélange et de dissipation). De plus, de nouvelles caractéristiques ont été ajoutées : une représentation améliorée pour les stratifications très stables (absence de nombre de Richardson critique), une meilleure représentation de l'anisotropie, un paramétrage unifié de la turbulence et des nuages par l'ajout d'une deuxième énergie turbulente pronostique et la paramétrisation des moments du troisième ordre. The Toucans turbulence scheme is a turbulence scheme that is used in the operational Alaro configuration of the Aladin model since early 2015. Its development was initiated, guided and to a large extend authored by Jean-François Geleyn. The development started with the predecessor of the Toucans scheme, the "pseudo-prognostic" turbulent kinetic energy scheme which itself was built on the "Louis" turbulence scheme, but extended to a prognostic scheme. The Toucans scheme aims for a consistent treatment of stability dependency functions, influence of moisture, and turbulence length scales. Additionally, new features were added to the turbulence scheme: improved representation of turbulence in very stable stratification (absence of critical gradient Richardson number), better representation of anisotropy, unified parameterization of turbulence and clouds via addition of second prognostic turbulence energy, and parameterization of third order moments.

scholarly journals Assessment of heat sources on the control of fast flow of Vestfonna ice cap, Svalbard

2014 ◽  
Vol 8 (5) ◽  
pp. 1951-1973 ◽  
Author(s):  
M. Schäfer ◽  
F. Gillet-Chaulet ◽  
R. Gladstone ◽  
R. Pettersson ◽  
V. A. Pohjola ◽  
...  
Keyword(s):  
Latent Heat ◽  
Temperature Record ◽  
Heat Sources ◽  
Ice Flow ◽  
Outlet Glacier ◽  
Flow Models ◽  
Ice Cap ◽  
Melt Water ◽  
Friction Parameters ◽  
Fast Flow

Abstract. Understanding the response of fast flowing ice streams or outlet glaciers to changing climate is crucial in order to make reliable projections of sea level change over the coming decades. Motion of fast outlet glaciers occurs largely through basal motion governed by physical processes at the glacier bed, which are not yet fully understood. Various subglacial mechanisms have been suggested for fast flow but common to most of the suggested processes is the requirement of presence of liquid water, and thus temperate conditions. We use a combination of modelling, field, and remote observations in order to study links between different heat sources, the thermal regime and basal sliding in fast flowing areas on Vestfonna ice cap. A special emphasis lies on Franklinbreen, a fast flowing outlet glacier which has been observed to accelerate recently. We use the ice flow model Elmer/Ice including a Weertman type sliding law and a Robin inverse method to infer basal friction parameters from observed surface velocities. Firn heating, i.e. latent heat release through percolation of melt water, is included in our model; its parameterisation is calibrated with the temperature record of a deep borehole. We found that strain heating is negligible, whereas friction heating is identified as one possible trigger for the onset of fast flow. Firn heating is a significant heat source in the central thick and slow flowing area of the ice cap and the essential driver behind the ongoing fast flow in all outlets. Our findings suggest a possible scenario of the onset and maintenance of fast flow on the Vestfonna ice cap based on thermal processes and emphasise the role of latent heat released through refreezing of percolating melt water for fast flow. However, these processes cannot yet be captured in a temporally evolving sliding law. In order to simulate correctly fast flowing outlet glaciers, ice flow models not only need to account fully for all heat sources, but also need to incorporate a sliding law that is not solely based on the basal temperature, but also on hydrology and/or sediment physics.

Termolecular ion–molecule reactions involving C3H5+

1970 ◽  
Vol 48 (22) ◽  
pp. 3549-3553 ◽  
Author(s):  
A. G. Harrison ◽  
A. A. Herod
Keyword(s):  
Kinetic Energy ◽  
Molecular Size ◽  
Order Rate Constant ◽  
Second Order ◽  
Rate Coefficients ◽  
Third Order ◽  
Order Rate ◽  
Ion Molecule Reactions ◽  
Similar Dependence ◽  
Ion Kinetic Energy

The reaction of C3H5+ with C2D4 to produce C5H5D4+ is shown to be second order in C2D4. The rate coefficients are in the range 10−24 to 10−25 cm6 molecule−2 s−1 but decrease markedly with increasing ion kinetic energy. This decrease reflects the effect of the ion kinetic energy on the lifetime of the initial collision complex. Small differences in rate coefficients are observed depending on the source of the C3H5+ ion but these are insufficient to distinguish between possibly different ionic structures. The reaction of C3H5+ with C2H3F forms C5H7+ in a reaction second order in C2H3F. The rate coefficients are also in the range 10−24 to 10−25 cm6 molecule−1 s−1 and show a similar dependence on ion kinetic energy. These high third order rate constants are compared with data for other termolecular reactions and are shown to be consistent with the effect of molecular size on the third order rate constant.

Turbulent flow normal to a triangular cylinder

1997 ◽  
Vol 331 ◽  
pp. 107-125 ◽  
Author(s):  
D. K. HEIST ◽  
F. C. GOULDIN
Keyword(s):  
Energy Balance ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
High Speed ◽  
Turbulent Transport ◽  
Low Frequency ◽  
Recirculation Region ◽  
Constant Density ◽  
Energy Balances

Laser Doppler Velocimetry (LDV) measurements are presented for a nominally two-dimensional constant-density flow over a surface-mounted triangular cylinder. The thickness of the boundary layer approaching the triangular cylinder is much less than the height of the triangle. Momentum and turbulent kinetic energy balances are presented and comparisons are made with other separated and reattaching flows. Also, time domain information is presented in the form of autocorrelations and spectra. From the energy balances, the importance of the pressure transport term at the high-speed edge of the shear layer is seen. Observations of the relationships between the shapes of the spectra and the details of the energy balance are made. For example, the slope of the velocity spectra varies from the free-stream value of −5/3 to a value of −1 in the middle of the recirculation region. Concurrent with this increase in slope is a decrease in the role of shear production in the turbulent kinetic energy balance and an increase in the role of advection and turbulent transport. From the two-component LDV measurements, a very low-frequency unsteadiness is shown to contribute energy preferentially to different components of the velocity fluctuations depending on the location in the flow.

2.5-D wave equations and high‐frequency asymptotics

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 556-562 ◽  
Author(s):  
John W. Stockwell
Keyword(s):  
Seismic Data ◽  
High Frequency ◽  
Wave Equations ◽  
Maximum Amplitude ◽  
Variable Density ◽  
Constant Density ◽  
Correction Factors ◽  
Wave Operators ◽  
Ray Series ◽  
D Wave

The need for modeling 3-D seismic data in a 2-D setting has motivated investigators to create so‐called 2.5-D modeling methods. One such method proposed by Liner involves the use of an approximate 2.5-D wave operator for constant‐density media. The traveltimes and amplitudes predicted by high‐frequency asymptotic ray series (WKBJ) analysis of the Liner 2.5-D wave equation match those predicted by Bleistein’s 2.5-D ray‐theoretic development in constant wavespeed media. However, high‐frequency analysis indicates that the Liner 2.5-D variable wavespeed equation will have a maximum amplitude error of ±35% in a linear c(z) model where the wavespeed doubles or halves from the beginning to the end of a raypath. These amplitudes are comparable to those produced by converting 2-D data to 2.5-D using correction factors of the type proposed by Emersoy and Oristaglio and Deregowski and Brown, with the exception being that the Liner equation lacks the half derivative waveform correction present in these operators. An alternate method of constructing 2.5-D wave operators based on the WKBJ analysis is proposed. This method permits variable density (acoustic) 2.5-D wave operators to be derived.

scholarly journals Avalanche dynamics by Newton. Reply to comments on avalanche flow models based on the concept of random kinetic energy

2018 ◽  
Vol 64 (243) ◽  
pp. 165-170 ◽  
Author(s):  
PERRY BARTELT ◽  
OTHMAR BUSER
Keyword(s):  
Flow Behavior ◽  
Practical Applications ◽  
Flow Models ◽  
Size Dependent ◽  
Drag Forces ◽  
Gravity Flows ◽  
Wide Range ◽  
Avalanche Dynamics ◽  
Avalanche Flow ◽  
Model Equations

ABSTRACTThe critique by Issler and other (2017) of our avalanche dynamics model maintains that we disregard well-established results of particulate gravity flows. Here we show that the arguments of Issler and others (1) violate Newton's laws of motion in the avalanche core and (2) ignore size-dependent drag forces on snow particles (Stokes law) that lead to the formation of avalanche suspension layers. We explain why we cannot amend our model equations to accommodate their suggestions. The goal of our approach is to describe highly non-stationary processes in the avalanche core that lead to a wide range of avalanche flow types and therefore different flow behavior. This is important for practical applications.

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