University of Bristol, with G.K. Batchelor Laboratory, University of Cambridge

The project:  Project duration: 3.5 years.

Internal gravity waves are found in density-stratified systems such as the deep ocean. They can arise both from direct excitation (e.g. movement of the fluid relative to a boundary), or indirectly due to flow structures such as a collapsing patch of turbulence. Unlike surface waves, which are mostly wind-driven and propagate on the two-dimensional surface of the ocean, internal waves in a continuous stratification are three-dimensional, and have the peculiar property that their phase (the wave crests and troughs) travels perpendicular to the direction in which the disturbance as a whole is moving. There are many sources of such waves, ranging from tidal flow around topography and underwater avalanches to storm events and whales. Characterising the signature of the waves generated, and understanding how these interact with other features of the ocean is important in determining how the waves propagate, transmitting energy and potentially triggering mixing events and other alterations to the flow far from their source. Of particular interest here is the interaction between the internal waves and a sheared pycnocline (statically stable density interface). Such interactions may lead to significant amplification of the waves and the growth of instabilities. A key question to be addressed in this project is what information can be determined about the source of the waves from observations of the density interface.

Implementation: This project provides the opportunity to work in two internationally leading universities. The successful candidate will be based at the University of Bristol, supervised by Dr. Andrew Lawrie, but will spend around 25% of their time at the University of Cambridge with Dr. Stuart Dalziel, who is co-supervising this project. The project involves elements of theoretical, experimental and numerical modelling, making it an ideal launch pad for a successful career in academic or industrial research.

Theoretical developments in this project will include linear and weakly non-linear stability analysis of internal waves with given incident spectra impacting on a statically stable density interface. When sheared, such interfaces can become unstable to Holmboe and/or Kelvin-Helmholtz instabilities. Theoretical predictions will be confirmed by comparison with laboratory experiments of the same configuration using advanced image processing techniques for measuring the density and velocity fields, and also through numerical simulation. The ultimate goal is to tackle the inverse problem, using measurements of motion on the interface to provide bounds on the characteristics of the source of the waves.

Candidate requirements: Due to funding restrictions, this studentship is only open to UK nationals.

A first-class honours degree in Mathematics, or a physical science with strong mathematical content. A good understanding of fluid mechanics and inverse problem theory will be considered highly desirable; applicants with equivalent industrial experience are strongly encouraged.

Funding: Studentship covers full UK PhD tuition fees and a tax-free stipend starting at £13,590 per year.

Funding from Defence Science and Technology Laboratory.

Support from Frazer-Nash Consultancy Ltd.

How to apply: Please make an online application for this project at the apply button below. Please select Mechanical Engineering (PhD) on the Programme Choice page and enter details of the studentship when prompted in the Funding and Research Details sections of the form.

Contacts: Dr. Andrew Lawrie (Bristol) or Dr. Stuart Dalziel (Cambridge) by contacting queens-internalwaves-phd@bristol.ac.uk before making a formal application to the University of Bristol

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