Mixing occurs in many diverse situations, ranging from large-scale systems such as planets and stars (e.g. the dynamo problem) to small-scale systems such as in the food industry (e.g. optimum ways of mixing as applied to bread making). Mixing is not only particularly rich in terms of applications but also benefits from having an active link with mathematics, largely via the theory of dynamical systems as well as some recent work on topology and functional analysis. Set against this background, the research project/area (depending on the applicant's wish for something shorter and concrete or longer and more open-ended) is motivated by a wish to better understand bio-physical interactions and consequences for ecological behaviour in the ocean.

Motivated by the research in the "fast dynamo" problem in astrophysics (e.g. Soward, 1987, J. Fluid Mech.; Gilbert, 1991, Nature; Galloway & Proctor, 1992, Nature) the proposed project wishes to consider the chaotic mixing of "active" tracer(s), in the sense that the "active" tracer(s) follows it's own governing equation (in this case some ecological model) and the advective flow is prescribed. The initial research will start with a numerical investigation, and has the flexibility to go more into modelling and/or analysis of mixing using more technical mathematical tools depending on the student's interest/training. While the problem is ocean ecology inspired, it is fundamentally a fluid dynamics / applied mathematics problem, so would particularly suit someone with training in a numerate subject (e.g. mathematics, physics, engineering). Willingness to do some scientific programming is essential; knowledge or willingness to learn Julia and/or Python would be desirable.