Mathematical and Experimental Modelling of Gravity Currents Over Variable Cross-Section in Oscillating Environments - Mathematics - EPSRC DTP funded PhD Studentship Ref: 2922

About the award

This project is one of a number funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership to commence in September 2018. This project is in direct competition with others for funding; the projects which receive the best applicants will be awarded the funding.

The studentships will provide funding for a stipend which is currently £14,553 per annum for 2017-2018. It will provide research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

Please note that of the total number of projects within the competition, up to 15 studentships will be filled.

Dr Hamid Alemi Ardakani

Professor Stuart Townley

Professor Lars Johanning

Professor Tom Bridges

Penryn Campus,Cornwall

Project Description
This PhD studentship research project is concerned with the modelling, simulation, and experimental study of non-Boussinesq gravity currents in an oscillating container with variable rectangular cross-section. A key motivating application of this model is for two-fluid flows in floating ocean wave energy converters such as the wave energy converter (WEC) proposed by Offshore Wave Energy Ltd (OWEL). The aim is to optimise the energy harvesting capability and to contribute to the next generation patent application and the design of WECs in general. The OWEL WEC is a floating rectangular device, developed for offshore high-energy, deep water oceanic locations, open at one end to capture the incoming wave field. Once the waves are trapped, they undergo interior fluid sloshing, and are then induced within the duct to grow, as the sides and floor of the vessel are angled inward. The waves hit the upper rigid lid and create a seal resulting in a moving trapped pocket of air ahead of the wave front which drives the power take off (PTO) by passing the air through a turbine. Understanding the dynamics of the two-phase wet-dry wave fronts created by the wave input is the key to the optimisation of the energy extraction in the PTO system. 

The project partners, University of Surrey and ITPenergised [1], will advise on a regular basis. Industry experts from ITPenergised will provide the required information about the PTO design and how it would be operated (please see the attached letter of support from Dr Ned Minns). The current patent on the OWEL WEC expires in 2021 and, rather than renew the current patent, the intention is that the proposed research will lead to University of Exeter involvement in a new patent. Towards this end, the project will tackle key open problems that will enhance the commercialisation and patentability of the OWEL WEC. The three key themes are:

Gravity currents and the PTO: development of experimental, theoretical and numerical methods to study the trapping and movement of the air bubble that drives the PTO. Principle tools: extension of the analytical theory of gravity currents in a vessel with OWEL-type geometry (variable rectangular cross-section), the use of two-layer shallow-water equation models, new directions in numerical modelling using f-wave finite volume solvers developed by the primary supervisor [2,3,4,5], and experiments on the air-cavity (gravity-current) propagation inside a model of the OWEL WEC. A literature review and feasibility study on the adaptation of the theory and experiments on gravity currents to the OWEL configuration has been developed by the project supervisor [6]. The experiments will be performed in the Laboratory of Ocean Technology at the University of Exeter, Penryn Campus, directed by Professor Lars Johanning.  

Stabilisation using control theory: experiments by the OWEL show that the efficiency of the PTO decreases when the vessel undergoes large motion. Hence, a key strategy is to stabilise the motion of the OWEL WEC. The starting point is free-flooding motion stabilisers for pitch stabilisation using control theory, which can be modelled as a coupled sloshing problem using the adaptation of methods developed in [7,8]. 

Direct numerical simulation (DNS): DNS of gravity-current propagation inside a vessel with OWEL-type geometry. This part of the project contains numerical simulation of the Navier-Stokes equations with high-order finite-difference methods, accompanied by volume-of-fluid surface representation which can capture wetting-drying wave fronts, as well as complicated air-cavity and free surface motion. The DNS will provide a numerical wave tank for exploratory calculations which can extend the parameter range of the experiments in a cost effective and timely manner.

The proposed research based on the theory of gravity-currents will result in a new method for analysing wave energy converters that has not been tried in the industry to date. It will be applicable to OWEL wave energy converter and also more widely to generic devices such as Oscillating Water Columns (OWC). Moreover, the proposed research will lead to new analytical and numerical methods for the analysis of the theory of gravity currents over variable cross-section in oscillating environments which may have some applications in geophysical fluid dynamics. 

Applicants should hold, or expect to be awarded, a good degree in Mathematics, Engineering, or Physics.

Entry Requirements

You should have or expect to achieve at least a 2:1 Honours degree, or equivalent, in [Mathematics, Engineering, or Physics]. Experience in [Fluid Mechanics, CFD, and programming in MATLAB, Fortran or Python] is desirable.

If English is not your first language you will need to meet the English language requirements and provide proof of proficiency. Click here for more information and a list of acceptable alternative tests.

The majority of the studentships are available for applicants who are ordinarily resident in the UK and are classed as UK/EU for tuition fee purposes.  If you have not resided in the UK for at least 3 years prior to the start of the studentship, you are not eligible for a maintenance allowance so you would need an alternative source of funding for living costs. To be eligible for fees-only funding you must be ordinarily resident in a member state of the EU.  For information on EPSRC residency criteria click here.

Applicants who are classed as International for tuition fee purposes are NOT eligible for funding. International students interested in studying at the University of Exeter should search our funding database for alternative options.


Application deadline:10th January 2018
Value:3.5 year studentship: UK/EU tuition fees and an annual maintenance allowance at current Research Council rate. Current rate of £14,553 per year.
Duration of award:per year
Contact: Doctoral

How to apply

You will be required to upload the following documents:
•       CV
•       Letter of application outlining your academic interests, prior research experience and reasons for wishing to
        undertake the project.
•       Transcript(s) giving full details of subjects studied and grades/marks obtained.  This should be an interim
        transcript if you are still studying.
•       If you are not a national of a majority English-speaking country you will need to submit evidence of your current
        proficiency in English.  For further details of the University’s English language requirements please see

The closing date for applications is midnight (GMT) on Wednesday 10 January 2018.  Interviews will be held at the University of Exeter in late February 2018.

If you have any general enquiries about the application process please email:
Project-specific queries should be directed to the supervisor.

During the application process, the University may need to make certain disclosures of your personal data to third parties to be able to administer your application, carry out interviews and select candidates.  These are not limited to, but may include disclosures to:

• the selection panel and/or management board or equivalent of the relevant programme, which is likely to include staff from one or more other HEIs;
• administrative staff at one or more other HEIs participating in the relevant programme.

Such disclosures will always be kept to the minimum amount of personal data required for the specific purpose. Your sensitive personal data (relating to disability and race/ethnicity) will not be disclosed without your explicit consent.