Application of Micro-continuum Approach in the Estimation of Snow Drift Density, Velocity and Mass Transport in Hilly Bound Cold Regions

Authors: Mahmoud Zarrini, R. N. Pralhad

Abstract:

We estimate snow velocity and snow drift density on hilly terrain under the assumption that the drifting snow mass can be represented using a micro-continuum approach (i.e. using a nonclassical mechanics approach assuming a class of fluids for which basic equations of mass, momentum and energy have been derived). In our model, the theory of coupled stress fluids proposed by Stokes [1] has been employed for the computation of flow parameters. Analyses of bulk drift velocity, drift density, drift transport and mass transport of snow particles have been carried out and computations made, considering various parametric effects. Results are compared with those of classical mechanics (logarithmic wind profile). The results indicate that particle size affects the flow characteristics significantly.

Keywords: Snow velocity, snow drift density, mass transport of snow particles, snow avalanche.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1060417

References:

[1] V.K. Stokes, Couple stresses in Fluids. Phys Fluids 9, 1710-15, 1966.
[2] R.A. Bagnold, The physics of blown sand and desert dunes. William morrow and company, 1941.
[3] W. Budd, R. Dingle and W. Radok, Byrd snow drift project . , 1966.
[4] R. Kawamura, Study on sand moment by wind. , 1951.
[5] G.H. Liljequist, Energy Exchange of an Antarctic Snowfield, Wind Structure in the Low Layer, "Norwegian-British-Swedish Antarctic Expedition, 1949-52". scientific Results, Vol. 2, part 1C, 187-233, 1957.
[6] M. Mellor, Blowing snow U.S. Cold Regions Research and Engineering Laboratory. Cold regions science and Engineering Hanover, N.H., pt. III, section A3c, 1965.
[7] M. Mellor, A drift review of snow drifts research. Technical Report CRSE III-A3d, Cold Regions Research Engineering Laboratory, 1974.
[8] R.A. Schmidt, Wind Flow over Alpine ridges, Ph.D. dissertation. (USA), 1967.
[9] Paul M.B. Fohn, Snow Transport over mountain crests. Journal of Glaciology vol. 26, No. 94, 1980.
[10] D. Kobayashi, Studies of Snow transport in low level drifting snow. contributions from the Institute of low temperature science, series A, No. 24, 1971.
[11] Y.C. Fung, A First course in continuum mechanics. Prentice Hall, 1993.
[12] S.C. Cowin, The theory of polar fluids. Adv. In Appl. Mech. 14, 279- 347, 1974.
[13] A.C. Eringan, Theory of micro polar fluids. J. Math. Mech. 16, 1-18, 1966.
[14] F.M. White, Fluid Mechanics. Mc-Graw-Hill, 2003.
[15] D.M. McClung, Derivation of Voellmy-s maximum speed and run-out estimates from a centre of mass model. Journal of Glaciology, 29(102), 1983.