Turbulent transport of suspended particles and dispersing benthic organisms: the hitting-time distribution for the local exchange model.
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.
Mcnair
J N
JN
Patrick Center for Environmental Research, Academy of Natural Sciences of Philadelphia, 1900 Benjamin Franklin Parkway, Philadelphia, PA 19103, USA. mcnair@acnatsci.org
D055598:Chemical Phenomena; D002627:Chemistry, Physical; D005618:Fresh Water; D019015:Geologic Sediments; D009038:Motion; D014871:Water Microbiology