Patterns and instabilities in doubly diffusive convection

Doubly diffusive convection is frequently encountered in natural sciences. <br /> For example, solar radiations heat the oceans making their surface warmer. <br /> In addition, due to evaporation, the density of salt in the oceans <br /> (salinity) increases towards the surface. This doubly diffusive <br /> configuration where salinity and temperature diffuse in the ocean is <br /> called thermohaline convection and gives rise to interesting phenomena. <br /> Indeed, the oceans are structured into thermohaline staircases in which <br /> the salinity remains mostly constant but jumps at specific depth levels. <br /> Thermohaline convection in these staircases is responsible for an <br /> instability called salt finger instability whereby the interface between <br /> two layers of different salinities becomes unstable and produces <br /> vertically elongated structures (fingers) of salty fluid sinking within <br /> the purer layer. This instability has been widely studied and was found to <br /> play a major role in the mixing of the oceans at low latitude and to <br /> strongly interact with large scale oceanic currents.<br /> <br /> Doubly diffusive convection, whether in the above setup or another, <br /> supports a large number of instabilities giving rise to exotic patterns <br /> and chaotic flows. In this project, we will try to understand more about <br /> these instabilities and pattern forming mechanisms. Among the several <br /> poorly understood phenomena stand (i) spatial localisation and (ii) direct <br /> transition to chaos. Spatially localised states take the form of a few <br /> convection rolls surrounded by quiescent fluid. They are called convectons <br /> in the stationary regime but can also be found in the time-dependent <br /> regime. These states are especially counter-intuitive that they present <br /> spatial heterogeneities despite the fact that the fluid is homogeneously <br /> forced. Outstanding questions related to localised states include finding <br /> stable convectons and exploring their various time-dependent counterparts. <br /> Another avenue for research is related to how abruptly doubly diffusive <br /> convection can transition to chaos in the presence of secondary <br /> subcritical instabilities. This route to chaos can be explored by means of <br /> simulating the full fluid flow or by taking on a reduced model.<br />

<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>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Applied Mathematics FT</strong></em> and in the research information section&nbsp;that the research degree you wish to be considered for is <em><strong>Patterns and instabilities in doubly diffusive convection</strong></em>&nbsp;as well as <a href="https://physicalsciences.leeds.ac.uk/staff/7/dr-c-dric-beaume">Dr&nbsp;Cedric Beaume</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>&nbsp;</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><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK&nbsp;</strong>&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a>, <a href="https://phd.leeds.ac.uk/funding/198-akroyd-and-brown-scholarship-2022">Akroyd &amp; Brown</a>, <a href="https://phd.leeds.ac.uk/funding/199-frank-parkinson-scholarship-2022">Frank Parkinson</a> and <a href="https://phd.leeds.ac.uk/funding/204-boothman-reynolds-and-smithells-scholarship-2022">Boothman, Reynolds &amp; Smithells</a> Scholarships 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 </strong>&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>

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