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Mathematical modelling of impact pressures due to breaking sea waves (COOKERMU19SF)

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  • Full or part time
    Dr M Cooker
    Prof A Korobkin
  • Application Deadline
    No more applications being accepted
  • Self-Funded PhD Students Only
    Self-Funded PhD Students Only

Project Description

When a sea wave travels from deeper into shallower coastal, it tends to steepen and overturn as a breaking wave. A breaking wave 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) models the impulsive pressure distribution in impacting wave water, and the total impulse on a structure. Violent flows such as these can be modelled mathematically by solving appropriate mixed boundary-value problems. One challenge of this project is to extend the mathematics to describe influences from the third dimension of the fluid domain, on the distribution of impulsive pressures. This is important to do when a breaking wave hits a realistic structure (not just a plane surface). For example, re-entrant corners in a seawall are known to cause an increase in impulsive loads, and damage starts at such corners. The influence of the third dimension was examined by Cox and Cooker (2001), who modelled violent flows in the confined space of a seawall crack. Wave-impact pressure acts to enlarge existing cracks.

In this PhD project, the student will learn to model time-dependent impacting flows, using inviscid fluid mechanics, by 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 the abrupt change in the velocity field of the wave-water, and for the distribution of maximum pressure during impact especially when a structure can yield to the wave force exerted on it. See reviews of Cooker (2013) and Chatjigeorgiou et al. (2016). The PhD student can also explore new areas of violent wave flows near structures.

Type of Programme: PhD

Start date of project: October 2019

Mode of study : full time

Acceptable first degree: Minimum 2:1 in Mathematics.

Application deadline: 31 May 2019. Applications are processed as soon as they are received and the project may be filled before the closing date, so early application is encouraged.

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. 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.


M.J. Cooker, D.H. Peregrine (1995) Pressure impulse theory for liquid impact problems. Journal of Fluid Mechanics, 297, 193—214.
S.J. Cox, 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 incidence to a blunt structure. Proc. R. Soc. Lond. A20150849,

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