Instabilities in fluid dynamics

PGR-P-1693

Key facts

Type of research degree: PhD
Application deadline: Ongoing deadline
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

<h2 class="heading hide-accessible">Summary</h2>

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.

<h2 class="heading">How to apply</h2>

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 PHD Applied Mathematics FT, in the research information section that the research degree you wish to be considered for is Instabilities in fluid dynamics as well as <a href="https://eps.leeds.ac.uk/maths/staff/4007/dr-cedric-beaume">Dr Cedric Beaume</a> as your proposed supervisor and in the finance section, please state clearly the funding that you are applying for, if you are self-funding or externally sponsored. 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. Applications will be considered on an ongoing basis.  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. Please note that you must provide the following documents in support of your application by the closing date of 3 April 2024 for Leeds Opportunity Research Scholarship or 8 April 2024 for Leeds Doctoral Scholarship: <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>

<h2 class="heading heading--sm">Entry requirements</h2>

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.

<h2 class="heading heading--sm">English language requirements</h2>

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.

<h2 class="heading">Funding on offer</h2>

Self-Funded or externally sponsored students are welcome to apply. UK – The <a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a> and <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> are available to UK applicants (open from October 2023). <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds. Non-UK – The <a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> is available to nationals of China (now closed for 2024/25 entry). The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds. Important:  Any costs associated with your arrival at the University of Leeds to start your PhD including flights, immigration health surcharge/medical insurance and Visa costs are not covered under this studentship. Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.

<h2 class="heading">Contact details</h2>

For further information about this project, please contact Dr Cedric Beaume by email to <a href="mailto:C.M.L.Beaume@leeds.ac.uk">C.M.L.Beaume@leeds.ac.uk</a> For further information about your application, please contact Doctoral College Admissions by email to <a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a>