PhD studentship in Mathematical Sciences

University of Nottingham - School of Mathematical Sciences

Experimental and mathematical models for avalanche fronts

Supervised by Dr Paul Matthews and Dr Barbara Turnbull.

This project will be based at the University of Nottingham in the School of Mathematical Sciences and the Department of Civil Engineering.

Powder snow avalanches are suspensions of ice particles in air that can flow down mountainsides at tens to hundreds of metres per second. The higher bulk density of the suspension compared with its surrounding generates the gravitational force that drives the avalanche. As it passes over the snow cover, the avalanche density can increase as loose snow along the path is fed into the head, but mixing between the suspension and the surrounding air dilutes the flow to slow it down. These competing mechanisms of snow erosion and air entrainment are critical to the longevity of an avalanche and potential stresses it can exert on an obstacle. 

This project examines instabilities at the front of an avalanche, where the majority of snow and air is entrained. We propose an experiment to model a powder snow avalanche that will release high density fluid into a lower density fluid from a central reservoir to propagate down a cone. This symmetry, with its periodic boundary condition, will permit relatively straightforward comparison with mathematical models predicting the front behaviour. Computational and analytical work will be carried out to investigate whether simple mathematical models for the shape of the front provide an accurate description of the experiment. We will then explore the links to real avalanches by investigating steeper slopes, increased density ratios and particle-driven currents.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics (or other highly mathematical field such as Physics or Engineering), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Apply: This studentship is available to start from September 2017 and remain open until it is filled. To apply please visit the University Of Nottingham application page:

For any enquiries please email:

This studentship is open until filled. Early application is strongly encouraged.

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Midlands of England