Abstract
The main aim of this project has been to investigate how turbulence and a patchy environment can affect the dynamics of plankton. In the first chapter, a brief introduction to the subject, both the methods and models we use and some of their behaviour in relation to observed phenomena, is given. In the second chapter, a reduced model for Langmuir circulations is used as a paradigm for chaotic advection of planktonic species. The patchiness of plankton due to such advection is discussed along with the effects of swimming/turbulent diffusion and how we can sometimes gain an analytical hold on the transport of organisms, using Melnikov analysis, in certain flows and we extend the results of previous work in this area. In Chapter 3, the possibility of pattern formation of swimming, spheroidal organisms in a simple, steady shear flow is investigated. In Chapter 4, the effects of turbulence and any inertial effects (buoyancy or density differences) is considered with regard to the initiation and subsequent propagation of phytoplankton blooms. The effect of a patchy environment is studied first, in Chapter 5, for the situation where we know explicitly the dynamics of the plankton. We take a spatially discrete, coupled oscillator approach to the patchy dynamics of plankton. The case where the dynamics of the patches is not known and, consequently all we might have is time series data is studied in Chapter 6. Given only measurements of the dynamics of some patchy population, we present a way of trying to deal with the patchy data in a more rigorous framework as mention of the inherently heterogeneous environments being measured is made but is mostly ignored. A method of first distinguishing independent patch dynamics from deterministically related dynamics is presented based on the algorithm first seen in Pecora et al. Given this deterministic bond between the patches we then set about creating a meta-population time series representing the collective dynamics of the population. This new time series is constructed so as to try and preserve as much of the individual dynamics as possible. Using a non-linear prediction algorithm ideally suited to possibly short data sets, we suggest this new time series can be used to improve short term predictions of general trends in the dynamics and also for the purposes of model fitting. Particular attention is given to using algorithms that can be applied to relatively short data sets, often a problem in studying time series data of ecosystems. (Abstract shortened by ProQuest.).