# PhD Studentship: Can you move a Thousand-ton Boulder with Water? (COOKER_UMTH18EE)

### University of East Anglia - School of Mathematics

Start Date: October 2018

No. of positions available: 1

Supervisor: Dr Mark J. Cooker

Project description: Background: 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.

Training: 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.

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 on 12/13 February 2018.

For further information, please visit www.enveast.ac.uk/apply

Person specification: Degree in Mathematics, or other numerate degree, including knowledge of applied mathematical modelling, especially in fluid dynamics. EnvEast welcomes applicants from quantitative disciplines who may have limited background in environmental sciences. Excellent candidates will be considered for an award of an additional 3-month stipend to take appropriate advanced-level courses in the subject area.

Funding notes: Successful candidates who meet RCUK’s eligibility criteria will be awarded a NERC studentship - in 2017/18, the stipend is £14,553. 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 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.