Hydrodynamic and magnetohydrodynamic instabilities in stellar and planetary interiors

Observational advances in helio- and astero-seismology have highlighted our poor understanding of the mechanisms of chemical mixing and angular momentum transport in the stably-stratified radiation zones of the Sun and other stars. This project will study various hydrodynamic or magnetohydrodynamic instabilities in stellar and planetary interiors that could contribute to mixing and angular momentum transport. These processes can modify the internal rotations, structures and evolutionary ages of stars, but they are commonly either neglected or modelled in an ad-hoc manner in current stellar models. This project will involve a combination of linear analysis and numerical simulations to understand the properties of one or more of these instabilities, and to determine their nonlinear behaviour. This may involve simulations on high-performance computing facilities, such as the Advanced Research Computing facility at Leeds. The ultimate goal is to understand the nonlinear outcome of these instabilities and to provide simple parameterisations of their mixing and angular momentum transport properties that can be incorporated in stellar models.

<p>The group in Leeds is one of the leading groups in the field of <a href="https://agfd.leeds.ac.uk">Astrophysical and Geophysical Fluid Dynamics</a>, and is actively engaged in research on a wide range of topics including planetary and extrasolar planetary dynamics (the geodynamo, planetary dynamos, tidal interactions between planets and stars, planet formation), solar and stellar dynamics (solar and stellar dynamos, hydrodynamic and magnetohydrodynamic instabilities, turbulence), as well as galactic and extragalactic dynamics on the largest scales. Although this project does not have dedicated funding, all successful applicants without funding will be considered for both STFC funding, and for a fully-funded scholarship in an open competition across the entire School of Mathematics.</p>

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Applied Mathematics FT,</strong></em> in the research information section that the research degree you wish to be considered for is <em><strong>Hydrodynamic and magnetohydrodynamic instabilities in stellar and planetary interiors</strong></em> as well as <a href="https://eps.leeds.ac.uk/maths/staff/4006/prof-adrian-j-barker">Professor Adrian Barker</a> as your proposed supervisor and in the finance section, please state clearly and that the funding source you wish to be considered for is <em><strong>STFC Doctoral Training Partnership Studentship 2026/27</strong></em>.</p> <p style="text-align:start; margin-bottom:24px">Applications will be considered after the closing date.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p>Please note that you must provide the following documents in support of your application by the closing date of Friday 13 February 2026:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul> <p style="text-align:start; margin-bottom:24px">If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<p class="MsoNoSpacing" style="text-align:start; margin-bottom:24px">A highly competitive STFC Doctoral Training Partnership Studentship providing full academic fees, together with a tax-free maintenance grant at the standard UKRI rate (£20,780 in academic session 2025/26) for 3.5 years. Training and support will also be provided.<br /> <br /> This opportunity is open to all applicants. All candidates will be placed into the STFC Doctoral Training Partnership Studentship Competition and selection is based on academic merit.</p> <p>Please note that there is only 1 funded place available and this project is in competition with 2 other project(s) to secure this funding.  If you are successful in securing an academic offer, this does not constitute an offer of funding.</p> <p>Important: Please note that that the award does not cover the costs associated with moving to the UK.  All such costs (<a href="https://www.leeds.ac.uk/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights etc) would have to be met by yourself, or you will need to find an alternative funding source. </p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For general enquiries about your application, please contact PGR Admissions by email to <a href="mailto:phd@engineering.leeds.ac.uk">phd@engineering.leeds.ac.uk</a></p> <p>For questions about this research project, please contact Prof Adrian Barker by email to <a href="mailto:A.J.Barker@leeds.ac.uk">A.J.Barker@leeds.ac.uk</a></p> <p> </p>