Pattern formation by swimming micro-organisms in chaotic flows, turbulence and bioconvection.

The following explores the behaviour of self propelled micro organisms throughout various flows, setting and geometries. To retain biological relevance and ensure these studies are comparable to natural situations all studies are carried out in three dimensions. Cells which are bottom heavy and primarily swim vertically are idealised throughout which all together result in cells exhibiting a process called gyrotaxis. Despite limiting to these specific cell types a range of models will be implemented to resolve both motion of individual cells as well as how the background flow field in which they are immersed evolves. Chapter 4 explores the behaviour of the these cells in a pair of imposed test flows. Moreover as one of these is known to exhibit chaos the role of swimming speed, re-orientation rate and eccentricity in suppressing this is explored. Chapter 5 focuses on more real world applications as the role of increasing self propulsion is examined for cells located within a turbulent environment. Chapter 6 explores a phenomenon known as bioconvection in a horizontally oriented, rotating cylindrical pipe. Since both motion and orientation of cells are inherently three dimensional all models assume this form to ensure a correspondence to real life applications