McNair, J.N., J.D. Newbold, and D.D. Hart. 1997. Journal of Theoretical Biology 188:29–52.
Turbulence plays an important role in the transport of particles in many aquatic systems. In addition to various types of inorganic sediment (silt, sand, etc.), these particles typically include bacteria, algae, invertebrates, and fine organic debris. In this paper, we focus on one aspect of turbulent particle transport; namely, the average time required for a suspended particle to reach the bottom of a waterbody from a specified initial elevation. This is the mean hitting-time problem, and it is important in determining, for example, the effect of turbulence on downstream transport of organic particles, dispersal times and dispersal propagules. We approach this problem by developing a stochastic diffusion model of particle transport called the Local Exchange Model, which is an extension of a model posed by Denny & Shibata (1989) in an earlier study of the same problem. We show how the mean hitting-time of the Local Exchange Model varies with factors such as a particle’s fall velocity an the shape of the vertical profile in turbulent mixing. We also show how the mean hitting-time is related to both the vertical profile in current velocity and the vertical profile in concentration of suspended particles, and how these relationships can be exploited in testing the model. Among other things, our results predict that, with the sole exception of neutrally buoyant particles that do not swim downward, there is always a region of the water-column in which turbulence increases rather than decreases the mean hitting-time. We discuss the significance of this and other results for dispersal by benthic organisms.