The Interaction of Swimming Microorganisms With Flow: Modelling Motile Phytoplankton in Turbulence
by
Graeme Thorn
Department of Mathematical Sciences, University of Liverpool

The interaction of swimming phytoplankton and typical ocean flow conditions is important to study in order to understand how the spatial distribution evolves due to the dispersive properties of turbulence. Many harmful algal bloom-forming species are motile: one plausible mechanism for the formation of such a bloom is that cells swim into a lower-salinity layer at the top of the water column becoming trapped due to the stratification. Eutrophication of this layer from pollutants in river run-off can cause a population explosion leading to a bloom. A study of the interaction of turbulence with motility will therefore provide insights into how these blooms develop once they are formed. For a gyrotactic microorganism, whose preferred motile behaviour is to swim upwards, the interaction is non-trivial, as turbulence can alter this behaviour due to relatively rapid (compared to the cell’s intrinsic reorientation to the vertical) along its Lagrangian particle path.

As phytoplankton swimming typically occurs on length scales (of the order 1-100 µm) some orders of magnitude below the Kolmogorov scale for ocean turbulence (of the order 1 cm), a model for the swimming behaviour in arbitrarily-oriented simple flows can be used to parameterise the effects of the smallest eddies on the mean swimming velocity. This result can then be incorporated into a population-level equation which then describes the time-evolution of the spatial distribution of a patch of phytoplankton. This advection diffusion model extends previous work which has concentrated on developing models for population dispersal in linear homogeneous flows using the macroscopic generalised Taylor dispersion method.

This talk will begin with a description of the advection-diffusion model, by showing how it is built up from the simple flow model, and show comparisons of this population-level model with simulations of individuals in turbulent flows. Finally, an application to the modelling of the effects of turbulence on the recruitment of gyrotactic cells into a pre-existing stratified fluid.

Date received: May 15, 2008