Mathematical modelling of gravity currents over variable cross-section in oscillating environments Ref: 3091

About the award


Dr Hamid Alemi Ardakani, University of Exeter

Second Supervisors:

Professor Andrew Gilbert, University of Exeter

Professor Lars Johanning, University of Exeter

Professor Stuart Townley, University of Exeter

Professor Tom Bridges, University of Surrey

This PhD studentship research project concerns the mathematical modelling, simulation and experimental study of gravity currents in an oscillating vessel with variable rectangular cross-section. The classical gravity current involves the flow of one fluid within another caused by a density difference between the fluids. This has been a major area of study in fluid mechanics motivated by saline intrusions and atmospheric fronts. The gravity current model of greatest interest in this project is where the upper fluid is air and a bubble of air is driven into quiescent or moving fluid over variable bottom topography. A key motivating application of this model is for two-phase fluid flows in Oscillating Water Columns (OWC) and in ducted ocean wave energy converters (WEC) such as the OWEL WEC where the moving bubble as gravity current is driven by the fluid. OWEL is a floating moored device with variable rectangular cross-section. It is developed for offshore high-energy deep water oceanic locations which is open at one end to capture the incoming wave field. Once the waves are trapped within the duct, they undergo interior fluid sloshing, and are then induced 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 wet-dry wave front which drives the power take off (PTO) by passing the air through a turbine. The air-cavity gravity current model can be applied to mathematical modelling of two-phase air-liquid sloshing flows in ships, oscillating fuel tanks and satellites.

The four key themes of the research project are:

(1) Experiments on propagation of air-cavity gravity currents: this part of the project consists of development of experimental set-up (a) first for a stationary vessel with variable cross-section and influx-efflux boundary conditions to study the trapping and movement of the pocket of air inside the vessel, and then (b) for a suspended container undergoing pendular oscillations to study the dynamic coupling of air-cavity fronts with a translating or rotating vessel. Experiments will be performed in the Laboratory of Ocean Technology in the Renewable Energy Department at Penryn Campus.

(2) Development of theoretical and numerical methods for propagation of air-cavity gravity currents over variable cross-section (a) in a stationary vessel where the principal tools are: extension  of the analytical theory of gravity currents to include geometry of the vessel, the use of hyperbolic partial differential equations for two-layer shallow water equation models, and new directions in the numerical modelling using high-resolution finite volume solvers, (b) extension of the theory and numerics to incorporate the dynamic coupling of gravity currents with a vessel undergoing pivoted oscillations.

(3) Development of hybrid finite-element and geometric integration methods to study long time dynamical behaviour of the coupled Hamiltonian system for a suspended pendulum with a rectangular variable cross-section bob, with interior fluid sloshing, undergoing pivoted oscillations.

(4) Fluid sloshing and control theory: the interest in this part of the project is to control the rotational motion of a floating WEC which affects the efficiency of the PTO system. The starting point is free-flooding motion stabilisers for pitch stabilisation using control theory.

Entry requirements

Applicants for this studentship must have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK, 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 have achieved at least 6. in IELTS and no less than 6.0 in any section by the start of the project.  Alternative tests may be acceptable (see

How to apply

In the application process you will be asked to upload several 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)
• Two references from referees familiar with your academic work. If your referees prefer, they can email the reference direct to quoting the studentship reference number.
• If you are not a national of a majority English-speaking country you will need to submit evidence of your proficiency in English.

The closing date for applications is midnight on 28 March 2018. Interviews will be held on the second week of April 2018.

If you have any general enquiries about the application process please email  or phone +44 (0)1392 722730/5150.  Project-specific queries should be directed to the main supervisor Dr Hamid Alemi Ardakani:


Application deadline:28th March 2018
Number of awards:1
Duration of award:per year
Contact: EMPS PGR Support +44 (0)1392 722730/5150