A stochastic model of dispersion of sediment particles released from a continuous source

Recent interest in bed sediment as a pollutant and as a carrier of various pollutants has emphasized the need for better understanding the dispersion process of bed sediment. Unfortunately, the existing mathematical models were constructed to describe longitudinal dispersion of a set of bed sediment particles simultaneously released in a flow from a line or a point source. In this paper, stochastic models are proposed for description of the longitudinal dispersion of a set of bed sediment particles released in a flow over a certain interval of time at a given rate α ( u ). Two particular cases are considered separately. First, the release occurs during a finite time interval, say, [0, t ]. Second, the release occurs during [0, ∞). provided that certain regularity conditions hold, it is shown that both dispersion models are obtained by means of a simple integral transformation of the model for instantaneous release.