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Name of scholarship/program

Chaos and fractals in fluid flows

Important description
The advection of particles and fields by fluid flows is a problem of great interest for both fundamental physics and engineering applications. This area of research encompasses phenomena such as the dispersion of pollutants in the atmosphere and oceans, the mixing of chemicals in chemical and pharmaceutical industry, and many others. The dynamics of these flows is characterised by chaotic advection, which means that particles carried by the flow have complex and unpredictable trajectories; this is an example of the phenomenon of chaos. One consequence of chaotic advection is that any given portion of the fluid is deformed by the flow into a complicated scale-invariant shape with fractal geometry. The exotic geometric properties of this fractal set leads to anomalous behaviour in important dynamical properties of the flow, such as its mixing rates and the rates of chemical reactions and other processes taking place on the flow.

The goal of this project is to investigate the mixing and transport properties of open chaotic flows and develop a general theory capable of predicting and explaining the transport properties of these systems. The theory will be based on the advection-diffusion partial differential equation. The main idea is that the main eigenvalues and eigenmodes of the advection-diffusion operator describe the long-time transport properties of the system. The scaling and behaviour of the eigenmodes will be estimated by developing approximations based on the fractal geometrical properties of the chaotic advection, and will also be calculated numerically for some simple flows. Mixing an reaction dynamics will then be expressed in terms of the eigenmodes and eigenvalues. To test the theory, we will apply it to the flow configuration describing an experiment performed to study geophysical transport mechanisms, and we will compare the theoretical predictions to the experimental findings.

The successful applicant will have a first or upper second class degree (or equivalent) in Physics, Applied Mathematics, Engineering (fluid mechanics) a knowledge of fluid mechanics is desirable but not required.

Eligibility and other criteria
If you have the correct qualifications and access to your own funding, either from your home country or your own finances, your application to work with this supervisor will be considered.

Application deadline
*Applications accepted all year round

Additional information, and important URL
Applications can be accepted from students worldwide. Applicants should note that there is no funding attached to this project therefore the successful candidate will entirely responsible for the payment of tuition fees, living expenses and other such costs associated with living and studying in Aberdeen.

The project will be awarded to the first suitable applicant. The start date will be agreed between the successful applicant and their supervisors.

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