Turbulent Transport of Suspended Particles and Dispersing Benthic Organisms: The Hitting-time Distribution for the Local Exchange Model

Abstract

Fine particles suspended in turbulent water exhibit highly irregular trajectories as they are buffeted by fluid eddies. The Local Exchange Model provides a stochastic diffusion approximation to the randomlike motion of such particles (e.g. dispersing benthic organisms in a stream). McNair et al. (1997, J. theor. Biol.188, 29) used this model to derive equations governing the mean hitting time, which is the expected time until a particle hits bottom for the first time from a given initial elevation. The present paper derives equations governing the probability distribution of the hitting time, then studies the distribution's dependence on a particle's initial elevation and two dimensionless parameters. The results show that for fine particles suspended in moderately to highly turbulent water, the hitting-time distribution is strongly skewed to the right, with mode<median<mean. Because of the distribution's thick upper tail, there is a significant probability that a particle's hitting time will greatly exceed the mean. The results also show that the position of the mode depends strongly on a particle's initial elevation but, compared to the median or mean, is relatively insensitive to the particle's fall velocity.