Patterns and instabilities in doubly diffusive convection

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

<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 research information section&nbsp;that the research degree you wish to be considered for is &lsquo;Patterns and instabilities in doubly diffusive convection&rsquo; 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><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>

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.

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<p><strong>Self-Funding Students</strong></p> <p><strong>Funding Eligibility</strong></p> <p><strong>UK/EU</strong> &ndash;&nbsp;Leeds Doctoral Scholarship Award paying Academic Fees and Maintenance matching EPSRC rate of &pound;15,009 per year for 3 years, School of Mathematics Scholarship award paying Academic Fees and Maintenance matching EPSRC rate of &pound;15,009 per year for 3 years.&nbsp; Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p> <p><strong>International Students</strong> &ndash;&nbsp;China Scholarship Council-University of Leeds Scholarship Award paying Academic Fees for 3 years,&nbsp;School of Mathematics Scholarship award paying Academic Fees for 3 years, Commonwealth Scholarship and Commonwealth Split Site Scholarships.&nbsp; Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</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>