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Direct Statistical Simulation of Multiscale Fluids

PGR-P-202

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Country eligibility
International (open to all nationalities, including the UK)
Funding
Competition funded
Supervisors
Professor Steven Tobias
Schools
School of Mathematics
Research groups/institutes
Applied Mathematics
<h2 class="heading hide-accessible">Summary</h2>

This project is to implement the new technique of Direct Statistical Simulation for a range of Astrophysical and Geophysical Flows. Complicated fluid dynamical processes are often investigated using Direct Numerical Simulation of the underlying partial differential equations of fluid mechanics. Many techniques are available for solving for the dynamics of such systems efficiently. However, these techniques are often prohibitively expensive for calculating statistics, which are usually the objects of interest in geophysics and astrophysics.<br /> <br /> In this project, we shall develop and utilise the new technique of Direct Statistical Simulation (DSS) where the statistics of the flow are solved for directly using cumulant hierarchies.<br /> <br /> This novel technique has proven to be extremely efficient for problems with non-trivial mean behaviour and non-local interactions. However, there is much to understand about this procedure, which makes it an ideal topic for a PhD. As this technique is extremely general it can be applied to many problems of geophysical and astrophysical interest such as the formation of jets in planets and the oceans, differential rotation in stars, instabilities in stellar and planetary interiors and atmospheres and the dynamics of accretion disks and astrophysical dynamos.<br /> <br /> This research is to be carried out in the Astrophysical and Geophysical Fluid Dynamics research group, which is one of the largest such research groups in the world.

<h2 class="heading hide-accessible">Full description</h2>

<p>This research is to be carried out in the&nbsp;<a href="https://agfd.leeds.ac.uk/">Astrophysical and Geophysical Fluid Dynamics research group</a><a href="physicalsciences.leeds.ac.uk/info/151/astrophysical_and_geophysical_fluid_dynamics">,</a> which is one of the largest such research groups in the world.</p> <p>&nbsp;</p> <p>&nbsp;</p>

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

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/info/130206/applying/91/applying_for_research_degrees">University&#39;s website</a>.&nbsp;Please state clearly in the research information section&nbsp;that the research degree you wish to be considered for is &lsquo;Direct Statistical Simulation of Mulitscale Fluids&rsquo; as well as&nbsp;<a href="https://physicalsciences.leeds.ac.uk/staff/86/professor-steven-tobias">Prof Steven Tobias</a>&nbsp;as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>We welcome applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.</em></p>

<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>

<p><strong>Self-Funding Students are welcome to apply.</strong></p> <p><strong>UK&nbsp;students</strong>&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarships-2021-january-deadline">Leeds Doctoral Scholarship (January deadline)</a>&nbsp;and the&nbsp;<a href="https://phd.leeds.ac.uk/funding/142-william-wright-smith-scholarship-2021">William Wright Smith Scholarship&nbsp;</a>are available to UK applicants. &nbsp;<a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK students</strong>&nbsp;&ndash; The&nbsp;<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>&nbsp;is available to nationals of China. The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;is available to support US citizens.&nbsp; <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p>

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

<p>For further information regarding your application, please contact Doctoral College Admissions by&nbsp;email:&nbsp;<a href="mailto:EMAIL@leeds.ac.uk">m</a><a href="mailto:maps.pgr.admissions@leeds.ac.uk">aps.pgr.admissions@leeds.ac.uk</a>, or by telephone: +44 (0)113 343 5057</p> <p>For further information regarding the project, please contact Professor Steven Tobias by email:&nbsp;&nbsp;<a href="mailto:S.M.Tobias@leeds.ac.uk">S.M.Tobias@leeds.ac.uk</a></p>


<h3 class="heading heading--sm">Linked research areas</h3>