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A stochastic model for sand sorting in a wind-tunnel

Published online by Cambridge University Press:  01 July 2016

O. Barndorff-Nielsen  and
J. N. Darroch
O. Barndorff-Nielsen*
Affiliation:
Aarhus University
J. N. Darroch*
Affiliation:
Flinders University
*
∗Postal address: Afdeling for Teoretisk Statistik, Matematisk Institut, Aarhus Universitet, DK-8000 Aarhus, Denmark.
∗∗Postal address: School of Mathematical Sciences, Flinders University of South Australia, Bedford Park, South Australia 5042, Australia.
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Abstract

The wind exerts a sorting effect on particles of sands and, under certain stable conditions that occur frequently but whose nature is little understood, the sorting results in log-size distributions of the hyperbolic form, first noted by R. A. Bagnold. Here, for wind-tunnel experiments a stochastic model is constructed which exhibits a sorting effect deriving from the dependence of distance travelled on the size of the single particle. Under rather specific, experimentally testable assumptions the model reproduces log-size distributions which are of the hyperbolic type and show a variation with distance along the wind tunnel that accords with experimental findings of R. A. Bagnold.

Keywords

COMPOUND POISSON PROCESSGENERALISED INVERSE GAUSSIANHYPERBOLIC DISTRIBUTIONSIZE DISTRIBUTIONS OF SAND GRAINSVELOCITY OF SAND GRAINS
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 2 , June 1981 , pp. 282 - 297
Copyright
Copyright © Applied Probability Trust 1981 

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References

Bagnold, R. A. (1941) The Physics of Blown Sands and Desert Dunes. Methuen, London.Google Scholar
Bagnold, R. A. (1978) Sediment transport by wind and water. Nordic Hydrology 10, 309–322.Google Scholar
Bagnold, R. A. and Barndorff-Nielsen, O. (1979) The pattern of natural size distributions. Sedimentology 27, 199–207.Google Scholar
Barndorff-Nielsen, O. (1977) Exponentially decreasing distributions for the logarithm of particle size. Proc. R. Soc. London A353, 401–419.Google Scholar
Barndorff-Nielsen, O. (1978) Hyperbolic distributions and distributions on hyperbolae. Scand. J. Statist. 5, 151–157.Google Scholar
Barndorff-Nielsen, O. (1979) Models for non-Gaussian variation; with applications to turbulence. Proc. R. Soc. London A368, 501–520.Google Scholar
Barndorff-Nielsen, O., Dalsgaard, K., Halgreen, C., Kuhlman, H., Møller, J. T., and Schou, G. (1980) Variation in particle size distribution over a small dune. Research Report No. 51, Dept. Theor. Statist., Aarhus University.Google Scholar
Blæsild, P. (1978) On the two-dimensional hyperbolic distribution and some related distributions; with an application to Johannsen's bean data. Biometrika. Google Scholar
Deigaard, R. and Fredsøe, J. (1978) Longitudinal grain sorting by current in alluvial streams. Nordic Hydrology 9, 7–16.Google Scholar
Engelund, F. and Fredsøe, J. (1976) A sediment transport model for straight alluvial channels. Nordic Hydrology 7, 293–306.Google Scholar
Hung, C. S. and Shen, H. W. (1979) Statistical analysis of sediment motions on dunes. J. Hydraul. Div. 105, 213–227.Google Scholar