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Chaos and fractals in fluid motion


Project 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 and 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.

Candidates should have (or expect to achieve) a UK honours degree at 2.1 or above (or equivalent) in Physics, mathematics, computer science, or similar degree along with knowledge of calculus and basic differential equations and some experience with programming.

APPLICATION PROCEDURE:

• Apply for Degree of Doctor of Philosophy in Physics
• State name of the lead supervisor as the Name of Proposed Supervisor
• State ‘Self-funded’ as Intended Source of Funding
• State the exact project title on the application form

When applying please ensure all required documents are attached:

• All degree certificates and transcripts (Undergraduate AND Postgraduate MSc-officially translated into English where necessary)
• Detailed CV
• Details of 2 academic referees

Informal inquiries can be made to Dr Alessandro Moura () with a copy of your curriculum vitae and cover letter. All general enquiries should be directed to the Postgraduate Research School ()

Funding Notes

This project is advertised in relation to the research areas of the discipline of Physics. The successful applicant will be expected to provide the funding for Tuition fees, living expenses and maintenance. Details of the cost of study can be found by visiting View Website. THERE IS NO FUNDING ATTACHED TO THESE PROJECTS.

References

De Moura, A. (2011). Reacting Particles in Open Chaotic Flows. Physical Review Letters, 107(27), 274501. doi:10.1103/PhysRevLett.107.274501
De Moura, A. P. S. (2014). Strange eigenmodes and chaotic advection in open fluid flows. EPL (Europhysics Letters), 106(3), 34002. doi:10.1209/0295-5075/106/34002
Aref, H., Blake, J. R., Budišić, M., Cartwright, J. H. E., Clercx, H. J. H., Feudel, U., … Tuval, I. (2017). Frontiers of chaotic advection. Reviews of Modern Physics, 89, 025007.

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