Erosion and riverbank failure driven by extreme water flow: a mathematical, computational and experimental study

About the Project

Extreme weather is an ever more pertinent consequence of climate change. Of particular concern to the UK, whilst also applying globally, is the often-devastating outcome of extreme rainfall events. Flooding, fast-flowing rivers and the accompanying erosion and deposition of granular material are a direct threat to the population but also have severe indirect costs to our much-loved landscape, buildings and livelihoods. To ever have a chance of reliably predicting and mitigating against these extreme events will require accurate physical, mathematical and numerical tools for the underlying processes involved.

This project will focus on the interaction between flowing water and granular material in order to understand and quantify the mechanisms underpinning soil erosion, riverbank failure, and the sudden course changes of waterways, along with related geophysical phenomena. We will bring together expertise on the mathematical and numerical modelling of granular flow with expertise on the geophysical consequences and laboratory methods. This holistic partnership will co-create novel experimental, theoretical and numerical workflows to unlock future large-scale modelling of the natural world, so we can better address current and future environmental hazards and degradation.

Specifically, Dr Barker will oversee the theoretical development of a novel two-phase flow theory for grain-water mixtures, this model will then be implemented in a bespoke numerical solver to study idealised geometries, in parallel Dr Daniels will supervise the fabrication of laboratory flow cells, matching the numerical geometry, which will be used for scale physical experiments. The project will culminate with the synthesis of the numerical and experimental data to validate and challenge the theoretical modelling.

Project partner: Dr Katherine Daniels (School of Earth and Environmental Sciences, Cardiff University)

What we offer:

Cardiff's School of Mathematics provides an excellent postgraduate research environment including:

• research facilities at Abacws (co-designed by our PGR community),
• a vibrant research culture including a wide range of research events,
• access to national course centres in mathematics, statistics and Operational Research,
• comprehensive professional skills training offered by Cardiff’s Doctoral Academy.
• collaborations with other disciplines and with a wide range of external partners (industry and society).

The PGR community is very active in running the SIAM-IMA Student Chapter, a valuable forum for exchange of ideas and public engagement.

This studentship will be undertaken within the Applied and Computational Mathematics Research Group at the School of Mathematics. The group’s members have wide-ranging interests, and offer a dynamic environment for the student to engage with experts in stochastic processes, statistics, data science and many other fields in mathematics and other disciplines. The group hosts a weekly seminar inviting external speakers.

Completing a PhD in mathematics opens up a range of possible next steps, from continuing an academic career to working in mathematically technical roles in industry.

The 3.5 year programme does not have any funding attached but successful applicants will receive a small Research Training Support Grant to cover costs such as research consumables, training, conferences and travel.

The possible start dates for this PhD are October, January, April or July.

What you bring:

You should have a 1st or upper 2nd class UK Honours degree (or equivalent) and/or a Master’s degree in mathematics or a suitable related subject.

Applicants for whom English is not their first language must demonstrate their proficiency by obtaining an IELTS score of at least 6.5 overall, with a minimum of 5.5 in each skills component, or equivalent qualification.

Cardiff University is committed to supporting and promoting equality and diversity and to creating an inclusive research environment. We particularly welcome applications from underrepresented groups.

How to apply:

Applicants should apply through the Cardiff University online PhD application portal, for a Doctor of Philosophy in Mathematics with your desired entry point.

You must include

• Transcript(s) of your degree(s) (with certified translations if appropriate)
• Degree certificates (with certified translations if appropriate)
• References - these should be current and verifiable
• Personal statement (as part of the university application form, or as a separate attachment, if you prefer) this should provide a clear explanation of your research interest, preparation undertaken, and an understanding of the project.

Note that the 'register interest' option will not submit an application. Please follow the instructions above and submit your application via our online portal. Incomplete applications will not be considered.

Funding Notes

We welcome applications from potential students who have their own sponsorship in place or are in a position to self-fund.

In the Research Proposal section of your application, please specify the project title and supervisors of this project.

In the funding section, please select that you will be self-funding and enter your source of funding.