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Nonlinear internal waves in the presence of bathymetry (PARAUE_U21SF)

School of Mathematics

About the Project

We propose to investigate waves which propagate at the interface of two fluids of different densities. These types of waves occur in many places in oceans or fjords [1], and at smaller scales [4]. The upper fluid is assumed to be bounded above by a rigid lid or a free surface and the lower fluid is flowing over non-uniform bottom topography. A current can also be present in the fluid and can interact with the waves. Two-dimensional and three-dimensional waves will be computed using a variety of numerical methods, such as boundary integral techniques [2,3]. The effect of surface tension [5] or of an elastic plate on the interface on the waves will be considered and solitary waves will also be sought. The evolution in time of the solutions will be investigated. Weakly-nonlinear equations will also be derived and their solutions will be compared with the numerical findings. Experimental data will be analysed using the theoretical results. 

For more information on the supervisor for this project, please go here

Type of programme is a PHD

The start date of the project is 1st October 2021

The mode of study is Full time

Funding Notes

This PhD project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources. Details of tuition fees can be found at View Website
A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. Applicants should contact the primary supervisor for further information about the fee associated with the project.
Entry Requirements are 2:1 in Mathematics, Natural Sciences, Fluid Mechanics


[1] P. Baines, Topographic Effects in Stratified Flows, Cambridge Univeristy Press, 1997.
[2] E.I. Parau, J.-M. Vanden-Broeck, M. J. Cooker, Nonlinear three-dimensional interfacial flows with a free surface, J. Fluid Mechanics,591(2007), 481-494.
[3] O. Trichtchenko, E. I. Parau, J.-M. Vanden-Broeck, P. Milewski, Solitary flexural–gravity waves in three dimensions, Phil. Trans. Royal Soc. A 376, 2129 (2018), 20170345
[4] Z. Wang, E.I. Parau, P. Milewski, J.-M. Vanden-Broeck, Numerical study of interfacial solitary waves propagating under an elastic sheet, Proc. Roy. Soc.A 470 (2014), 20140111
[5] H. Woolfenden, E.I. Parau,  Numerical computation of solitary waves in a two-layer fluids, J. Fluid Mech. 688(2011), 528-550. 

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