Instabilities in fluid dynamics

Key facts

We aim to understand and control fluid instabilities like transition to turbulence and the formation of salt polygons in dry lakes.

We always think of a fluid as a substance that flows but how often do we wonder about how it flows? Open your tap a little and you will see a transparent stream of water. The flow is laminar and all the water particles gently travel in the direction of the stream. Now, open the tap to its fullest. The stream has become opaque! Water now flows in a turbulent fashion. It is full of small vortices that trap air bubbles which disturb the trajectory of light and make the stream opaque. What has happened in this experiment is an instability. At first, the flow is laminar but, at some point, a critical tap opening is reached and transition to turbulence takes place.

Fluid transport in pipes is ubiquitous in industry, from the small scale of ink jets to the large scale of pipeline transport. In most cases, we wish to increase the flow rate but this may lead to an undesirable instability. Turbulent flows in pipes are accompanied with increased wall friction and are, thus, less energetically efficient than their laminar counterparts. In addition, turbulent flow features can, in the long run, damage the pipe. We aim to understand how the instability takes place and how to control it.

Dry salt lakes can be found in many arid regions and give rise to spectacular landscapes constituted of salt polygons (google it!). What has this got to do with fluids? Well, the lake may be dry but water sits not far below the visible surface. It is salty and, when it evaporates, deposits salt into the visible surface crust, contributing to its growth and the creation of salt polygons. The surface crust is further eroded by wind and produces dust that is then transported away. At Owens Lake (California, USA), for example, the dust produced contains arsenic and is hazardous to the neighbouring populations. There, understanding the instability that produces salt polygons and controlling it may drastically increase air quality.

These are just two examples of instabilities that we aim to study. We use a combination of numerical (spectral methods, numerical continuation, etc.) and analytical (linear stability and weakly nonlinear stability analyses, etc.) techniques inspired by dynamical systems in our investigations.

To apply for this project you will need to make a formal application for research degree study through the University website. You will need to create a login ID with a username and PIN.

• For Application type please select Research Degrees – Research Postgraduate.

• The admission year for this project is 2027/28 Academic Year.

• You will need to select your Planned Course of Study from a drop-down menu. For this project, scroll down and select PHP Applied Mathematics Full Time.

• The project start date for this project is 1 October 2027, please use this as your Proposed Start Date of Research.

• Please state clearly in the Research Information Section that the research degree you wish to be considered for is Instabilities in fluid dynamics as well as Dr Cedric Beaume as your proposed supervisor.

Please state clearly in the Finance section, the funding that you are applying for, if you are self-funding or externally sponsored.

More information on how to apply is available on our website here. You will be required to provide a personal statement which outlines your interest in the project you are applying for, why you have chosen it and how your skills map onto the requirements of the project.

We will assess applications continuously as we receive them. We welcome and strongly encourage any potential applicants to contact the supervisor(s) for an informal discussion, prior to applying, and recommend submitting your application early.

If you are applying with external sponsorship or you are funding your own study, please ensure you provide your supporting documents at the point you submit your application:

Full Transcripts of all degree study or if in final year of study, full transcripts to date including the grading scheme

Personal Statement outlining your interest in the project

If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).

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.

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.

This is a non funded PhD project. Applicants are expected to be self funded or to secure external funding.

You can find out more about our Funding Opportunities on our Postgraduate Research Opportunities website.

Important: Please note that all costs associated with your arrival at Leeds (visa, Immigration Health Surcharge, flights etc) would have to be met by yourself, or you will need to find an alternative funding source.

For further information about this project, please contact Dr Cedric Beaume by email to C.M.L.Beaume@leeds.ac.uk

For further information about your application, including how to apply, please contact PGR Admissions by email to phd@engineering.leeds.ac.uk

• Type of research degree: PhD
• Application deadline: Monday 31 May 2027
• Project start date: Friday 1 October 2027
• Country eligibility: International (open to all nationalities, including the UK)
• Funding: Non-funded
• Supervisors: Dr Cedric Beaume
• Schools: School of Mathematics
• Research groups/institutes: Applied Mathematics

Research areas