Can you move a one-thousand tonne boulder with water?


Can you move a one-thousand tonne boulder with water?


Project Description


Dr Mark Cooker (UEA Mathematics)

Prof Jan Alexander (UEA Environmental Sciences)


We will explore how violent natural flows, such as flash-floods, can move large boulders. A large boulder may measure several metres across, weighing thousands of tonnes, and it spends most of its time at rest. However, when an exceptionally violent flow arrives, such as a flash-flood in mountain landscape, the agitated water is capable of moving boulders hundreds of metres. The motion and impact of colliding boulders damages valuable infrastructure, and is a hazard to life.

Student Role

You will work with a renowned sedimentologist and an experienced applied mathematician, on producing a theory of boulder motion.

You will start by considering the fundamentals of fluid-solid interactions. Informed by existing laboratory and field observations, the preliminary work will produce a means of predicting when a boulder will start to slide or roll in water. The work will lead on to considering a field of boulders on the bed, and their nearby interactions, in a realistic setting. This will produce another model of boulder-boulder-flow force interactions. Throughout the project the verification of assumptions and predictions will be made by comparing with existing measurements, and there will be opportunities to test predictions in realistic settings. Encapsulating the theory within a computer code will be one primary objective.


You will learn the theory of pressure-impulses. This leads to setting up appropriate boundary-value problems for analysing 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 differential equations for the boulder’s motion. You will also gain an appreciation of how mathematical modelling can contribute to geophysical environmental sciences.

Apart from the PhD research, you will learn mathematics through the MAGIC graduate-lecture scheme. There will be opportunities to take part in laboratory flume measurements at UEA, and fieldwork at a site subject to flash floods.

Person specification

You must have a degree in Mathematics, Physics or other numerate degree, including knowledge of applied mathematical modelling, especially in fluid dynamics.


  • 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.
  • 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
  • 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
  • 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

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