A hierarchy of theoretical and numerical models for the dispersion of discrete floating tracers on lakes and oceans is presented. Central to these models is the role of Langmuir circulations, which concentrate tracers into narrow windrows this inhibiting tracer dispersion. But time-dependent Langmuir circulations cause the rows of tracers to wander and so split, by local time dependence and by downwind advection, thus promoting dispersion. Accordingly, the Langmuir circulations generally render the smaller-scale background turbulence irrelevant for direct estimates of surface dispersion.
Analytical models includes: 1) a theory of tracers in a linear mean-flow convergence plus homogeneous turbulence, this theory being applicable to the width of windrows; and 2) a model with a spatially periodic mean flow and a periodic small-scale eddy diffusion coefficient that allows an estimate of the Langmuir-scale dispersivity for steady parallel cells.
Random-flight calculations for a model of complex time-dependent and downwind dependent Langmuir circulations have led to the explicit prediction K = 0.5TC*−½ where Kast; and TC* are the nondimensional dispersivity and cellular time scale, respectively.