Read about my four main areas of research below
My research centres on wave propagation and interactions with turbulent flow in the atmosphere and ocean.
I apply tools of differential geometry to gain new insight into the dynamics of fluids.
I am CoI of the EPSRC programme grant Probing multiscale complex multiphase flows with positrons.
Waves & flows
The dynamics of the atmosphere and ocean is characterised by the interactions of two types of motion with well separated time scales: slow, balanced flow– associated with eddies and currents – and fast internal waves. I study interactions between these two motions, mainly the scattering of the waves that results from their avection and refraction by turbulence, and the feedback that the waves extert on the flow through wave–mean-flow processes.
My current projects include an NSF-NERC-funded collaboration with W R Young (Scripps) and H Kafiabad (Edinburgh) on stimulated loss of balanced, and work on phase-space (position-wavevector) modelling of the scattering induced by balanced turbulence (with H Kafiabad and Miles Savva).
Geometric fluid dynamics
In collaboration with A D Gilbert (Exeter), we use tools of differential geometry such as exterior forms to study fundamental aspects of fluid dynamics and magnetohydrodynamics. This enables us to obtain geometrically intrinsic results, which hold on arbitrary manifolds and are independent of coordinates; this has benefits even for fluid dynamics in standard Euclidean space.
I work on the geometry of theories of wave–mean-flow interactions (Generalised Lagrangian mean and thickness-weighted averaging) and on the geometry of stress tensors. I have also been studying vorticity dynamics on a Mobius strip; the twisted topology introduces a few twists in the fluid dynamics.
Positron Emission Particle Tracking is an innovative imaging technique for opaque fluids: the trajectories of particles tagged with a radioactive label are reconstructed from the detection of emitted gamma rays. The technique is particularly useful for multiphase (fluid-particle) flows at high particle density which cannot be imaged by optical methods. As part of an EPSRC programme grant with Birmingham and KCL led by M Barigou, I am developing techniques to infer flow and fluid properties from Lagrangian trajectories derived from PEPT data (with A Renaud).
Transport & mixing
I am developing and analysing models of transport of constituents by fluid flows. The main aim is to derive simplified models which describe the evolution of the constituent concentration after long times, once the spatial scale of the concentration fields is much larger than that of the flow. This can be done systematically by applying the method of homogenisation or, when the concentration tails matter, large-deviation theory.
My current projects in this area consider complex geometries and obstacles (with A Tzella (Biringham) and random flows (with P H Haynes, Cambridge, and A Renaud, Edinburgh). Together with Y K Ying and J R Maddison (Edinburgh), we are developing Bayesian techniques for the inference of ocean eddy diffusivity fields from trajectory data.