Nonlinear capillary waves in Plateau borders (PARAUE_U22SCIO) at University of East Anglia on FindAPhD.com

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Prof E Parau, Dr Davide Proment No more applications being accepted Competition Funded PhD Project (Students Worldwide)

About the Project

Solitary-wave solutions have been studied extensively over the years for the problems of gravity water waves, gravity-capillary waves, in two and three dimensions. They have been observed in nature and experiments, and have been analysed asymptotically and numerically. More recently, solitary waves have been also observed experimentally and investigated on liquid ferrofluid cylinders, see for example [1].

In this project nonlinear waves in novel geometries will be studied. We will consider Plateau borders, which are microchannels obtained by merging three films inside liquid foams. Capillary jumps, solitary and periodic waves along Plateau borders in soap films have been observed experimentally [2,3], but there are far fewer theoretical studies available. The PhD project will aim first to perform a stability analysis of linear capillary waves propagating along the Plateau borders. Weakly nonlinear models such as Korteweg-de Vries [4] and nonlinear Schrodinger equations will then be derived formally near the critical speeds of the dispersion relation. Finally, a numerical scheme to compute solitary and periodic waves of the fully-nonlinear problem in this novel geometry will be built and comparisons with experimental and weakly nonlinear results will be performed.

For more information on the supervisor for this project, please visit the UEA website www.uea.ac.uk

The start date is 1 October 2022

Entry requirements: Acceptable first degree 2:1 in Mathematics, Physics, Engineering

Funding Notes

This PhD project is in a competition for a Faculty of Science funded studentship. Funding is available to UK applicants and comprises ‘home’ tuition fees and an annual stipend of £15,609 for 3 years. Applicants who are not eligible for home tuition fees are welcome to apply but they will be required to fund the difference between home and international tuition fees (which for 2021-22 are detailed on the University’s fees pages at https://www.uea.ac.uk/about/university-information/finance-and-procurement/finance-information-for-students/tuition-fees. Please note tuition fees are subject to an annual increase).

References

[1] Blyth, M. G., & Părău, E. I. (2014). Solitary waves on a ferrofluid jet. Journal of fluid mechanics, 750, 401-420.
[2] Argentina, M., Cohen, A., Bouret, Y., Fraysse, N., & Raufaste, C. (2015). One-dimensional capillary jumps. Journal of Fluid Mechanics, 765, 1-16.
[3] Bouret, Y., Cohen, A., Fraysse, N., Argentina, M., & Raufaste, C. (2016). Solitary-like waves in a liquid foam microchannel. Physical Review Fluids, 1(4), 043902.
[4]. Le Doudic, G., Perrard, S., & Pham, C. T. (2021). Surface waves along liquid cylinders. Part 2. Varicose, sinuous, sloshing and nonlinear waves. Journal of Fluid Mechanics, 923.

Where will I study?

University of East Anglia

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Nonlinear capillary waves in Plateau borders (PARAUE_U22SCIO)

University of East Anglia School of Mathematics