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Ocean Mixing Parameterisation via Categorisation of Nonlinear Flow Structures - Project 1: Mathematical Model Development

   School of Science and Engineering

About the Project

One of the key challenges for large-scale climate models is to accurately parameterise the mixing which occurs in the oceans. Such mixing occurs at small-scales, well below the grid-resolution of the climate models, and consists of the turbulent exchange of heat and salt between neighbouring regions of fluid. In order to build a robust parameterisation of this mixing, we must take a data-driven approach in which oceanographic data are algorithmically categorised according to the type of dynamics they represent.

Mixing at small scales in the ocean is mediated by a class of flows called stratified shear flows. Within such flows, there are three potential routes, or instabilities, leading to turbulence, each with a distinct degree and vigorousness of mixing. Recently, Dr Tom Eaves proposed a categorisation scheme for oceanographic data taken at a single instant in time, which aims to distinguish between these three instabilities at linear and nonlinear levels (predicting what type of mixing will happen next, and what type of mixing just occurred, respectively).

This project will investigate the fidelity of the categorisation scheme, taking it beyond the simplified flows considered in Dr Eaves’ initial study. We will investigate to what extent the linear and nonlinear categorisation algorithms agree with one another (a prediction at one time about what is about to happen should agree with a prediction at some later time about what just occurred), in addition to probing the mathematics underlying the categorisation schemes to build and interrogate nonlinear flow structures associated with stratified shear flows.

We will make use of a number of computational techniques, including direct numerical simulation of stratified shear flows, an asymptotic high-Reynolds-number contour dynamics model developed by Dr Anirban Guha, and computation of families of exact coherent structures. Dr Guha’s asymptotic model will be compared against the direct numerical simulation results and a suite of parametric experiments led by Dr Alan Cuthbertson (see Project 2) , and then used as a starting point for computing families of nonlinear exact coherent flow structures which emerge from the equations of stratified shear flow.

Key skills developed through the project include the direct numerical simulation of fluid flows, mathematical high-Reynolds-number fluid dynamics, and advanced numerical models and techniques for studying fluid flows.

For informal enquiries about the project, contact Dr Thomas Eaves ()

For general enquiries about the University of Dundee, contact

Our research community thrives on the diversity of students and staff which helps to make the University of Dundee a UK university of choice for postgraduate research. We welcome applications from all talented individuals and are committed to widening access to those who have the ability and potential to benefit from higher education.


Applicants must have obtained, or expect to obtain, a first or 2.1 UK honours degree, or equivalent for degrees obtained outside the UK in a relevant discipline.

English language requirement: IELTS (Academic) score must be at least 6.5 (with not less than 5.5 in each of the four components). Other, equivalent qualifications will be accepted. Full details of the University’s English language requirements are available online:


Step 1: Email Dr Thomas Eaves () to (1) send a copy of your CV and (2) discuss your potential application and any practicalities (e.g. suitable start date).

Step 2: After discussion with Dr Eaves, formal applications can be made via our direct application system. When applying, please follow the instructions below:

Apply for the Doctor of Philosophy (PhD) degree in Civil Engineering: Civil engineering research degrees | University of Dundee.

Please select the study mode (full-time/part-time) and start date agreed with the lead supervisor.

In the Research Proposal section, please:

-       Enter the lead supervisor’s name in the ‘proposed supervisor’ box

-       Enter the project title listed at the top of this page in the ‘proposed project title’ box

In the ‘personal statement’ section, please outline your suitability for the project selected.

Funding Notes

There is no funding attached to this project. The successful applicant will be expected to provide the funding for tuition fees, project specific bench fees and living expenses via external sponsorship or self-funding.

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