Nonlinear hydroelastic waves in layered fluids (PARAUU16SF)
This PhD project is concerned with free boundary problems where more than one boundary is unknown. Examples of this type of problems are: stratified oceans covered by an ice sheet, or layered ice and oceans of the type supposed to exist on Ganymede (Jupiter’s moon). The ice sheets can be modelled as elastic plates or visco-elastic plates under certain conditions. The project will look for different types of nonlinear waves which may exist in such situations, such as solitary waves, periodic waves, generalised solitary waves. The influence of gravity and elasticity (of visco-elasticity) will be considered. The problem is challenging due to the nonlinear terms in the boundary conditions on unknown boundaries and due to the coupling between different interfaces which appear in these configurations. The two dimensional and three dimensional waves will be found numerically using computational methods such as boundary integral techniques or spectrals algorithms. Weakly-nonlinear equations will also be derived to validate the numerical findings.
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 http://bit.ly/1Jf7KCr
A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. The amount charged annually will vary considerably depending on the nature of the project and applicants should contact the primary supervisor for further information about the fee associated with the project.
I) 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
ii) P. Guyenne, E.I. Parau, Finite depth effects on solitary waves in a floating ice sheet, J. Fluids and Structures 40 (2014), 242-262.
iii) P. Baines, Topographic Effects in Stratified Flows, Cambridge Univeristy Press, 1997.