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# Breaking Waves & Dredging Flows: the Mathematics of Erosion

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database and may not be available.

for PhD studentship opportunities
• Prof O Bokhove
• Applications accepted all year round
• Competition Funded PhD Project (European/UK Students Only)

## Project Description

Breaking Waves & Dredging Flows: the Mathematics of Erosion PhD Project by Prof. O. Bokhove, School of Mathematics, University of Leeds, Leeds, UK - Contact email: [email protected]

Full details with project descriptions - and how to apply at: http://www.maths.leeds.ac.uk/postgraduate-research.html

Along our coastlines, beaches are eroded and built up by breaking waves. Whereas navigation channels are maintained by dredging sand and slurries off sea and river beds. Both cases are examples of the mathematics of erosion - how hydrodynamic flows erode and suspend (sand) particles from a bed.

In principle, the mathematical equations that model water flow around particles, as well as the particle interactions are known to us: Navier-Stokes equations govern the water flow around particles and the continuum mechanics of deformable solids govern their interactions. On larger scales of interest which involve billions of particles, the degrees of freedom involved in the equations are too large: they are too complicated to solve, either analytically or even numerically.

How are such equations simplified? A hierarchy of averaging and asymptotic techniques is required to simplify these equations into formulations that can be mathematically analysed, both analytically and numerically.

The first goal of this PhD project is to investigate 'multi-phase' models within this hierarchy of approximations, for the fluid (water and air) phase and the solid (particle) phase, combined. These models will mainly concern partial differential equations.

The second goal of the PhD project will be to define and explore idealized configurations, both mathematically and maybe experimentally, in order to facilitate potential scientific breakthroughs on a fundamental level.

The final aim is to relate our findings back to practical applications in the coastal context: beach erosion and accretion by breaking waves, and sand removal by dredging. Some progress has already been made in this project, both at Leeds and the University of Twente, particularly concerning the second objective. See the linked page for more information on these dynamics in a narrow, water-particle Hele-Shaw cell for beach erosion and dredging. Our mathematical Hele-Shaw configuration reduces the dynamics to almost two dimensions in a vertical plane, while also permitting laboratory analogues that show the fundamental mathematical investigations to have real-world relevance.

This project offers the opportunity to do leading edge mathematics and experimental research that could facilitate breakthroughs on a fundamental level with real-world applications; a unique opportunity at a PhD level.

http://www1.maths.leeds.ac.uk/~obokhove/PhDMathsErosion20132014.pdf
http://www1.maths.leeds.ac.uk/~obokhove/dredgingtrial.m4v

## Funding Notes

School of Mathematics EPSRC Doctoral Training Grants (DTG)

Value of award full UK/EU Fees + maintenance (£13,726 pa) for up to 3.5 years

Academic requirements - applicants should have, or expect to obtain, a minimum of a UK upper second class honours degree. Applicants whose first language is not English must also meet additional English language requirements.