Advection-diffusion in reversing and oscillating flows .2. Flows with multiple reversals

The dispersion of a passive tracer from a continuous point source in an estuary is modelled by a two-dimensional advection-diffusion equation with a time-varying, unidirectional velocity. Asymptotic solutions obtained by Kay (1990, IMA J. Appl. Math., 45, 115-37) for a constant-acceleration flow are generalized to take account of arbitrary velocity variations, and a new solution is presented for the case of rapidly varying acceleration around a time of flow reversal. A procedure for building up the total concentration distribution by linear superposition of the various types of solution is described. This is applied to the case of an estuarine flow, considered to consist of a constant river flow superimposed on tidal oscillations. Depending on the relative size of these two components, the concentration distribution may include prominent peaks, with concentrations which are many times higher than those in nearby waters. The effect of allowing the diffusion coefficient to vary proportionally to the flow speed is shown to be small except close to the tracer source.