scholarly journals The influence of vertical density and velocity distributions on snow avalanche runout

2010 ◽  
Vol 51 (54) ◽  
pp. 200-206 ◽  
Author(s):  
Ashok K. Keshari ◽  
Deba P. Satapathy ◽  
Amod Kumar
Keyword(s):  
Flux Distribution ◽  
Numerical Solutions ◽  
Model Parameters ◽  
Dynamics Model ◽  
Turbulent Friction ◽  
One Dimensional ◽  
Variation Diminishing ◽  
Flow Features ◽  
Vertical Density ◽  
Two Fluid

AbstractA one-dimensional avalanche dynamics model accounting for vertical density and velocity distributions is presented. Mass and momentum flux distribution factors are derived to incorporate the effect of density and velocity variations within the framework of depth-integrated models. Using experiments of avalanche flows on an inclined snow chute at Dhundhi, Manali, India, we conceptualize snow flow rheology as a Voellmy fluid where the distribution of internal shearing is given by a Newtonian fluid (NF) or Criminale–Ericksen–Filbey fluid (CEFF). Then the generalized mass and momentum distribution factors are computed for these two fluid models for different density stratifications. Numerical solutions are obtained using a total variation diminishing Lax–Friedrichs (TVDLF) finite-difference method. The model is validated with the experimental results. We find that the flow features of the chute experiments are simulated well by the model. The velocities and runout distances are obtained for the Voellmy model with both NF and CEFF extensions for various input volumes, and the optimum values of the model parameters, namely, coefficients of dynamic and turbulent friction, are determined.

scholarly journals Determination of Avalanche Dynamics Friction Coefficients from Measured Speeds

1983 ◽  
Vol 4 ◽  
pp. 170-173 ◽  
Author(s):  
D. M. McClung ◽  
P. A. Schaerer
Keyword(s):  
Complex Terrain ◽  
Sliding Friction ◽  
Numerical Solutions ◽  
Analytic Solutions ◽  
Dynamics Model ◽  
Friction Coefficients ◽  
Turbulent Friction ◽  
Constant Friction ◽  
Avalanche Dynamics

An avalanche dynamics model, appropriate for complex terrain, for real avalanche paths was developed by Perla, Cheng and McClung in 1980. The model has two friction terms, one for sliding friction which is independent of speed, and one for turbulent friction which is proportional to V2, where V is the centre-of-mass speed along the incline. By introducing speed maxima for avalanches, along with start and stop reference positions, it is possible to determine the the two constant friction coefficients for the model. When this is done, it is found that speed data often exceed a model speed limit implied by the application of V = 0 at the start and stop positions. This effect is illustrated by analytic solutions of the relevant equations, as well as numerical solutions for actual avalanche paths. Some limitations and properties of the fundamental modelling are outlined and suggestions given for future use of such models.

scholarly journals Determination of Avalanche Dynamics Friction Coefficients from Measured Speeds

1983 ◽  
Vol 4 ◽  
pp. 170-173 ◽  
Author(s):  
D. M. McClung ◽  
P. A. Schaerer
Keyword(s):  
Complex Terrain ◽  
Sliding Friction ◽  
Numerical Solutions ◽  
Analytic Solutions ◽  
Dynamics Model ◽  
Friction Coefficients ◽  
Turbulent Friction ◽  
Constant Friction ◽  
Avalanche Dynamics

An avalanche dynamics model, appropriate for complex terrain, for real avalanche paths was developed by Perla, Cheng and McClung in 1980. The model has two friction terms, one for sliding friction which is independent of speed, and one for turbulent friction which is proportional to V2, where V is the centre-of-mass speed along the incline. By introducing speed maxima for avalanches, along with start and stop reference positions, it is possible to determine the the two constant friction coefficients for the model. When this is done, it is found that speed data often exceed a model speed limit implied by the application of V = 0 at the start and stop positions. This effect is illustrated by analytic solutions of the relevant equations, as well as numerical solutions for actual avalanche paths. Some limitations and properties of the fundamental modelling are outlined and suggestions given for future use of such models.

A Theoretical Analysis of CO2 Absorption in Sun Versus Shade Leaves

1978 ◽  
Vol 100 (1) ◽  
pp. 20-24 ◽  
Author(s):  
R. H. Rand
Keyword(s):  
Experimental Data ◽  
Quantitative Estimate ◽  
Geometric Model ◽  
Model Parameters ◽  
Co2 Absorption ◽  
Temperature Model ◽  
Spongy Mesophyll ◽  
One Dimensional ◽  
Mesophyll Tissue ◽  
Shade Leaves

A one-dimensional, steady-state, constant temperature model of diffusion and absorption of CO2 in the intercellular air spaces of a leaf is presented. The model includes two geometrically distinct regions of the leaf interior, corresponding to palisade and spongy mesophyll tissue, respectively. Sun, shade, and intermediate light leaves are modeled by varying the thicknesses of these two regions. Values of the geometric model parameters are obtained by comparing geometric properties of the model with experimental data of other investigators found from dissection of real leaves. The model provides a quantitative estimate of the extent to which the concentration of gaseous CO2 varies locally within the leaf interior.

A Physically Based, One-Dimensional Two-Fluid Model for Direct Contact Condensation of Steam Jets Submerged in Subcooled Water

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
David Heinze ◽  
Thomas Schulenberg ◽  
Lars Behnke
Keyword(s):  
Direct Contact ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Interfacial Area ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional ◽  
Two Fluid Model ◽  
Contact Condensation ◽  
Two Fluid

A simulation model for the direct contact condensation of steam in subcooled water is presented that allows determination of major parameters of the process, such as the jet penetration length. Entrainment of water by the steam jet is modeled based on the Kelvin–Helmholtz and Rayleigh–Taylor instability theories. Primary atomization due to acceleration of interfacial waves and secondary atomization due to aerodynamic forces account for the initial size of entrained droplets. The resulting steam-water two-phase flow is simulated based on a one-dimensional two-fluid model. An interfacial area transport equation is used to track changes of the interfacial area density due to droplet entrainment and steam condensation. Interfacial heat and mass transfer rates during condensation are calculated using the two-resistance model. The resulting two-phase flow equations constitute a system of ordinary differential equations, which is solved by means of the explicit Runge–Kutta–Fehlberg algorithm. The simulation results are in good qualitative agreement with published experimental data over a wide range of pool temperatures and mass flow rates.

scholarly journals Tornado-type stationary vortex with nonlinear term due to moisture transport

2010 ◽  
Vol 4 (1) ◽  
pp. 77-82 ◽  
Author(s):  
P. B. Rutkevich ◽  
P. P. Rutkevych
Keyword(s):  
Tropical Cyclones ◽  
Shooting Method ◽  
Nonlinear Term ◽  
Numerical Solutions ◽  
Variable Temperature ◽  
Slow Rotation ◽  
Nonlinear Phenomenon ◽  
One Dimensional ◽  
Stationary Vortex ◽  
General Possibility

Abstract. Tornado vortex is believed to be essentially nonlinear phenomenon; and the puzzle to choose the nonlinear term(s) responsible for its formation is still unresolved. In the present work we consider the nonlinear term associated with atmosphere humidity, by introducing variable temperature gradient depending on the vertical velocity of the fluid. Such term is able to yield energy to the system and is very suitable for such a problem. Other nonlinear terms are neglected, assuming slow rotation, or in other words a "weak" tornado approximation. We consider one-dimensional radial boundary problem, and use a modificaiton of shooting method to satisfy boundary conditions at large radii. Obtained numerical solutions of the nonlinear differential equation qualitatively agree with the observed atmosphere vortices (tornados, tropical cyclones). The obtained results show general possibility of existence of unstable motion even in convectively stable atmosphere stratification.

Diffusion-Limited Cell Dehydration: Analytical and Numerical Solutions for a Planar Model

1999 ◽  
Author(s):  
Alexander V. Kasharin ◽  
Jens O. M. Karlsson
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Planar System ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Constant Diffusivity ◽  
A Cell ◽  
Cell Dehydration ◽  
The One

Abstract The process of diffusion-limited cell dehydration is modeled for a planar system by writing the one-dimensional diffusion-equation for a cell with moving, semipermeable boundaries. For the simplifying case of isothermal dehydration with constant diffusivity, an approximate analytical solution is obtained by linearizing the governing partial differential equations. The general problem must be solved numerically. The Forward Time Center Space (FTCS) and Crank-Nicholson differencing schemes are implemented, and evaluated by comparison with the analytical solution. Putative stability criteria for the two algorithms are proposed based on numerical experiments, and the Crank-Nicholson method is shown to be accurate for a mesh with as few as six nodes.

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