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Mathematical modelling of impacts by breaking ocean waves (COOKERMU20SF)

School of Mathematics

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Dr M Cooker , Prof A Korobkin No more applications being accepted Self-Funded PhD Students Only

About the Project

When an ocean wave travels from deep water into shallower coastal water, it steepens and overturns as a breaking wave. While a wave is breaking, it can exert damaging forces on a structure in its path. The force of impact is impulsive -- both very large and short lived. Cooker and Peregrine (1995) model the impulsive pressure distribution in impacting wave water, and the total impulse on a structure. Such violent flows can be modelled mathematically by solving mixed boundary-value problems. One challenge of this project is to extend the theory to describe influences from the third dimension of the fluid domain on the distribution of impulsive pressure. This is important to do when a breaking wave hits a realistic solid structure: one with roughness, permeability and crevices. For example, re-entrant corners in a seawall are known to cause increased impulsive loads, and hence more damage. The influence of the third dimension was examined by Cox and Cooker (2001), who modelled violent flows in the confined space of a crevice in a seawall. Wave-impact pressure forces crevices to widen and deepen.

In this PhD project you will learn to model time-dependent impacting flows, by using inviscid fluid mechanics and setting up mixed boundary-value problems. You will learn techniques for solving the equations, with exact analysis, asymptotic methods and efficient computation.

The physical interpretation of results has important consequences for abrupt changes in the velocity field within the wave water, and the distribution of maximum pressure. This is especially important when a structure moves while the wave-force is being exerted. See Cooker (2013) and Chatjigeorgiou et al. (2016). You can also explore new areas of violent wave flows near structures.


Project supervisor:
Mode of study: Full time
Start date: October 2020
Entry requirements: First degree (2:1 or above) in Mathematics.

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

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.


M.J. Cooker and D.H. Peregrine (1995) Pressure impulse theory for liquid impact problems. Journal of Fluid Mechanics, 297, 193—214.

S.J. Cox and M.J. Cooker (2001) The pressure impulse in a fluid saturated crack in a sea wall. Coastal Engineering, 42, 241--256.

M.J. Cooker (2013) A theory for the impact of a wave breaking onto a permeable barrier with jet generation. Journal of Engineering Mathematics, 79, 1—12.

I. Chatjigeorgiou, M.J. Cooker, A.A. Korobkin, (2016) Three-dimensional water impact at normal inci-dence to a blunt structure. Proc. R. Soc. Lond. A20150849,
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