Explosive volcanoes are one of the largest hazards on Earth. Many are flooded by lakes or seawater, such as Taal volcano in the Philippines, and Santorini volcano in Greece. Large numbers of people live around some of these volcanoes, and improved understanding of what happens is needed in order to increase their resilience. The eruptions can be particularly catastrophic because the erupting jet from the volcano is transformed by the rapid passage through shallow standing water. Water is entrained into margins of the vertical jet, flashes to steam, and expands explosively, transforming the dynamics of the eruption and its effects on the surrounding environment1-3. Large ‘hydrovolcanic’ eruptions of this type are thought to be particularly violent and hazardous. They generate vast quantities of fine volcanic ash that chokes the atmosphere and surrounding landscape, and they likely generate destructive tsunami, but the processes have not yet been modelled. Small hydrovolcanic explosions have been investigated (e.g. ‘fuel-coolant interactions’) but the physical processes of larger, more sustained eruptions (e.g.1-3) remain poorly understood.




Explosive jet through standing water, Tonga
(from volcanoes4.wikispaces.com/Volcanoes)


This project will develop a mathematical model of a steady-state explosive volcanic eruption from a shallow, underwater source vent. Initially, modelling will be one-dimensional, with variables along the vertical coordinate, from the seafloor vent up through the water column into the atmosphere. A simplified model of water entrainment and explosive boiling along the boundary of the gas jet will be used to determine the shape of the underwater plume. This will allow you to estimate how much water gets drawn into the gas jet, and it will also allow you to estimate how long it takes to exhaust an entire water reservoir (for example a lake) so that the eruption reverts to dry (‘magmatic’) conditions. Subsonic and supersonic gas jets will be considered separately. Later, a numerical three-dimensional model of the plume will be developed, assuming axial symmetry. The bulk part of the plume and the boundary layer, separating the gas stream and surrounding water will be treated separately. The student will publish different stages of the research as the modelling progresses.

The results of this project will spearhead future research on large hydrovolcanic eruptions, including the fragmentation mechanisms, the controlling parameters, ash dispersal in the atmosphere, and hazards, towards improving our understanding of these unusually hazardous events.

Training and Skills

CENTA students benefit from 45 days training throughout their PhD including a 10 day placement. In the first year, students will be trained as a single cohort on environmental science, research methods and core skills. Throughout the PhD, training will progress from core skills sets to master classes specific to the student's projects and themes.

This project will suit a student with a strong numerical background who wishes to apply these skills to the exciting field of volcanic eruptions. Depending on your background there will be opportunities to sit in on geophysics and volcanology lectures and practical classes. You will also receive hands-on training in numerical modelling and in physical volcanology, and will participate in residential field workshops on the Canary Islands to learn about the physical volcanology of explosive eruptions. There may be an opportunity to visit Taal volcano in the Philippines, where the volcanic lake is 25 km in size and millions of people are threatened.

You will join a thriving research community within the Volcanoes, Tectonics and Mineral Resources Research Group at the University of Leicester, and gain a set of skills that will be ideal for a career in applied mathematics and/or modelling of hazardous processes in Earth Sciences. You will attend seminars and lab groups in the departments of Mathematics and Geology, and will attend national and international conferences.

By the end of the project you will have developed leading expertise in physical volcanology and in the numerical modelling of volcanic eruptions.


Year 1: The project will start in October 2018 with preliminary reading about underwater gas jets5 and eruption models. One-dimensional modelling will begin. You will participate in a field training workshop, and a national conference.

Year 2 Complete one dimensional modelling and write-up results for publication. Begin 3-dimensional modelling. Present work-in-progress at national applied maths and volcanology meetings. Field visit to a flooded caldera volcano. Mentoring in finite element modelling techniques will be provided. You will present a poster at a national conference,

Year 3 Continue 3-dimensional modelling, and refine in collaboration with volcanologists. Write-up results for publication, and present at an international conference.

Partners and collaboration (including CASE)

Professor Michael Branney is a physical volcanologist who has published extensively on large explosive eruptions around the world, with expertise on hydrovolcanism and eruption processes.

Prof Nikolai Brilliantov is a leading mathematician, with expertise on numerical models, including jets on planets and satellites

Dr Emmanuil Georgoulis is a mathematician with expertise on finite element modelling.

Further Details

Please contact Professor Michael Branney, University of Leicester (mjb26@le.ac.uk).