Dispersal by randomly varying currents

Abstract

The long-term oceanic dispersal of persistent contaminants is approached as a problem in turbulent diffusion, with tidal, wind-driven, and other variable currents relegated to turbulence. The mean advection velocity in this problem is typically small compared with the r.m.s. fluctuation. Therefore, close to a continuous concentrated source, puffs of contaminant of all ages are present and have significant effects. Old puffs, i.e. those released a long time previously, give rise to a background concentration field. Young puffs affect the local contaminant concentration p.d.f. according to the probability of their presence, quantified by the visitation frequency.The behaviour of young puffs is governed by variable advection and may be described approximately in terms of probability distributions obtainable from current-meter data. The visitation frequency can be calculated from the distribution of escape probability density, a Lagrangian equivalent of flux. A long-term effect of variable advection is the distribution of the contaminant over an ‘extended’ source, which serves as a starting point for the random walk of old puffs. The conventional approach of using the diffusion equation to describe this random walk is therefore valid as a description of the near-source background concentration field, provided that the extended source is used in place of the physical source.A sample calculation for a typical open coastal case shows that the background concentration plume becomes wide compared with source dimensions, of order KH/U, with KH horizontal (eddy and shear) diffusivity, U mean advection velocity. The near-source value of the background concentration is correspondingly low, of order m/hKn, with m the mass-release rate and h the water depth. Visitation frequencies calculated with the aid of current statistics drop rapidly with distance from the source, especially in the cross-shore direction. The typical cross-shore diameter of the extended source region is a few kilometres.