Turbulent transport of suspended particles and dispersing benthic organisms: the hitting-distance problem for the local exchange model

The local exchange model developed by McNair et al. (1997) provides a stochastic diffusion approximation to the random-like motion of fine particles suspended in turbulent water. Based on this model, McNair (2000) derived equations governing the probability distribution and moments of the hitting time, which is the time until a particle hits the bottom for the first time from a given initial elevation. In the present paper, we derive the corresponding equations for the probability distribution and moments of the hitting distance, which is the longitudinal distance a particle has traveled when it hits the bottom for the first time. We study the dependence of the distribution and moments on a particle's initial elevation and on two dimensionless parameters: an inverse Reynolds number M (a measure of the importance of viscous mixing compared to turbulent mixing of water) and the Rouse number ŝ(a measure of the importance of deterministic gravitational sinking compared to stochastic turbulent mixing in governing the vertical motion of a particle). We also compute predicted hitting-distance distributions for two published data sets. The results show that for fine particles suspended in moderately to highly turbulent water, the hitting-distance distribution is strongly skewed to the right, with mode