Mathematical modelling of sea wave impact (COOKERU17SF) at University of East Anglia on FindAPhD.com

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Dr M Cooker No more applications being accepted Self-Funded PhD Students Only

About the Project

When a water wave approaches the seashore it steepens and overturns. If such a wave hits a sea wall then the fluid velocity everywhere changes quickly, and the pressure field is briefly. The mechanics of the flow can be described mathematically through the idea of an impulsive pressure in the fluid, and on the seawall, along with a change in momentum. To solve such a problem mathematically requires solving Laplace’s equation in the fluid domain at the start of impact, subject to mixed boundary conditions. The boundary conditions describe a free surface of the water, and a boundary condition of an impermeable rigid seawall. The references show that much work has been published in two space dimensions (2D), but little in 3D. This PhD project extends the existing published modelling, to treat the more realistic situation of a structure with cracks, gaps or holes. The use of shaped concrete blocks to lessen wave energy is now worldwide, and yet the fluid mechanics of flows inside these structures is not well understood. To understand the process we will need to model the impulsive pressures due to impact on one side of a saturated porous structure. A breaking wave impact against this type leads to a violent flow that can penetrate the gaps between the constituent blocks. This flow needs to be modelled better to understand the internal fluid forces that can potentially separate the blocks. A better understanding of the fluid mechanics in this PhD research will help coastal engineers to quantify the energy budget of waves encountering porous structures, to interpret wave damage, and to design better seawalls in future.

The project may be available at an earlier start date of 1 April or 1 July 2017 but should be discussed with the primary supervisor in the first instance.

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 http://www.uea.ac.uk/pgresearch/pgrfees.

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.

References

i) Cooker, M.J. and D.H. Peregrine (1995) Pressure impulse theory for liquid impact problems. Journal of Fluid Mechanics, 297, 193–214.
ii) Cooker, M.J. (2013) A theory for the impact of a wave breaking onto a permeable barrier with jet generation. J. Eng. Math. 79, 1–12.
iii) Cooker, M.J. (2016) Some mathematics for splashes: sea-wave impact on coastal structures. In P. As- ton, A.J. Mulholland, K.M.M. Tant (eds) UK Success Stories in Industrial Mathematics, Springer, p83–90
iv) Chatjigeorgiou, I., M.J. Cooker and A.A. Korobkin, (2016) Steep wave impact onto a vertical plate of finite width. To appear: Proceedings of the Royal Society of London A, 26pp.

Where will I study?

University of East Anglia

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Mathematical modelling of sea wave impact (COOKERU17SF)

University of East Anglia School of Mathematics