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Applications are now open for PhD studentships starting in October 2018. 

Please read the recruitment introduction for more information about eligibility, how to apply, and possibilities for further funding.

The deadline for applications is 8 January 2018.

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COOKER_UMTH18EE - Can you move a thousand-ton boulder with water?

Project description

Selected other project supervisors:
Professor Jan Alexander (UEA Environmental Sciences)

This project will explore how violent natural flows, such as flash-floods, can move boulders.  The motion and impact of boulders cause damage to valuable infrastructure, and is a hazard to human  life.  A large boulder can be several metres in width and height, and it spends much of its life at rest. However,  in a mountain landscape  a  flash-flood can suddenly arrive, and such a  flow is capable of moving boulders distances of hundreds of metres.

Student Role
You will work closely with a sedimentologist and an applied mathematician, on producing a mathematical model of this phenomenon. You will start by considering the fundamentals of fluid-solid interaction mechanics. Informed by existing laboratory and field observations, the preliminary work will produce a theory for predicting when a single boulder will start to slide or roll in the water flow. The work will lead on to considering a whole field of boulders on the bed, and their nearby interactions, in a realistic flow setting. This will produce a model of the flow-force interactions between neighbouring boulders. Throughout the project the verification of the model and any assumptions will be made by comparing with laboratory experiments.. There will also be opportunities to test theoretical predictions in the field. Developing the theory into a computer simulation will also be an objective.
You will learn the mathematical theory of pressure-impulses. This path leads to setting up appropriate boundary-value problems from understanding the sudden motion of a boulder in an accelerating flow. The partial differential equation for the flow is coupled (in a non-linear way) with boundary conditions on the boulder’s surface, and with ordinary differential equations of motion of the boulder. You will also gain an appreciation of how mathematical modelling can make an important contribution to geophysical environmental science.  There will be opportunities to take part in flume measurements at UEA, and fieldwork at a site subject to flash floods.  Apart from the PhD research, you will learn mathematics through the MAGIC graduate-lecture scheme.

Person specification
Degree in Mathematics, or other numerate degree, including knowledge of applied mathematical modelling, especially in fluid dynamics.

This project has been shortlisted for funding by the EnvEast NERC Doctoral Training Partnership, comprising the Universities of East Anglia, Essex and Kent, with over twenty other research partners. Undertaking a PhD with the EnvEast DTP will involve attendance at mandatory training events throughout the course of the PhD.

Shortlisted applicants will be interviewed by EnvEast on 12/13 February 2018.

Selected candidates who meet RCUK’s eligibility criteria will be awarded a NERC studentship - in 2017/18, the stipend is £14,553. Ordinarily, EnvEast studentships are for 3.5 years, although longer awards may be made to applicants from quantitative disciplines who have limited experience in the environmental sciences, to allow them to take appropriate advanced-level courses in the subject area.

In most cases, UK and EU nationals who have been resident in the UK for 3 years are eligible for a stipend. For non-UK EU-resident applicants NERC funding can be used to cover tuition fees, RTSG and training costs, but not any part of the stipend. Individual institutes may, however, elect to provide a stipend from their own resources.

This PhD studentship is expected to begin in September/October 2018. Both full-time and part-time study are possible (those planning to study part-time may wish to discuss this with the supervisor before applying).


  1. J. Alexander, J. Barclay, J. Sušnik, S.C. Loughlin, R.A. Herd, A. Darnell and S. Crosweller (2010) Sediment-charged flash floods on Montserrat: the influence of synchronous tephra fall and varying extent of vegetation damage. J. Volcanology and Geothermal  Research, 194, 127–138.
  2. J. Alexander and M.J. Cooker (2016) Moving boulders in flash floods and estimating flow conditions using boulders in ancient deposits. Sedimentology, DOI: 10.1111/sed.12274
  3. M.J. Cooker and D.H. Peregrine (1995) Pressure impulse theory for liquid impact problems. Journal of Fluid Mechanics 297, 193–214.  DOI: 10.1017/S0022112095003053
  4. S.J. Cox and M.J. Cooker (1999) The motion of a rigid body impelled by sea-wave impact. Applied Ocean Research 21, 113–125.  DOI: 10.1016/S0141-1187(99)00005-X