The dynamics of biofouled particles in vortical flows.

When using mathematical models to predict the pathways of biofouled microplastic in the ocean, it is necessary to parametrise the impact of turbulence on their motions. In this paper, statistics on particle motion have been computed from simulations of small, spherical particles with time-dependent mass in cellular flow fields. The cellular flows are a prototype for Langmuir circulation and flows dominated by vortical motion. Upwelling regions lead to particle suspension and particles fall out at different times. The uncertainty of fallout time and a particle's vertical position is quantified across a range of parameters. A slight increase in settling velocities, for short times, is observed for particles with inertia due to clustering in fast downwelling regions for steady, background flow. For particles in time-dependent, chaotic flows, uncertainty is significantly reduced and we observe no significant increase in the average settling rates due to inertial effects.

Deceleration of one-dimensional mixing by discontinuous mappings.

We present a computational study of a simple one-dimensional map with dynamics composed of stretching, permutations of equally sized cells, and diffusion. We observe that the combination of the aforementioned dynamics results in eigenmodes with long-time exponential decay rates. The decay rate of the eigenmodes is shown to be dependent on the choice of permutation and changes nonmonotonically with the diffusion coefficient for many of the permutations. The global mixing rate of the map M in the limit of vanishing diffusivity approximates well the decay rates of the eigenmodes for small diffusivity, however this global mixing rate does not bound the rates for all values of the diffusion coefficient. This counterintuitively predicts a deceleration in the asymptotic mixing rate with an increasing diffusivity rate. The implications of the results on finite time mixing are discussed.