On the size distribution of sand

Abstract

A model is presented of the development of the size distribution of sand while it is transported from a source to a deposit. The model provides a possible explanation of the log-hyperbolic shape that is frequently found in unimodal grain size distributions in natural sand deposits, as pointed out by Bagnold and confirmed in numerous empirical studies. The model implies that the size distribution of a sand deposit is a logarithmic normal-inverse Gaussian (NIG) distribution, which is one of the generalized hyperbolic distributions. The model modifies a previous model, which implied a log-normal size-distribution, by taking into account that individual grains do not have the same travel time from the source to the deposit. The travel time is assumed to be random so that the wear on the individual grains vary randomly. The model provides an interpretation of the parameters of the NIG-distribution, and relates the mean, variance and skewness of the log-size distribution to the physical parameters of the model. The results might be useful when comparing empirical size-distributions from different deposits. It is argued that size-distributions with the same general shape as the NIG-distributions can be obtained also when some of the model assumptions are relaxed.