Those interested in pursuing a research project in one of the following areas may freely contact me and also consider applying for one of the following highly prestigious postdoctoral research fellowships:
Two-Dimensional and Geophysical Turbulence
Many geophysical flows are quasi two-dimensional in nature, where the flow is restricted in one dimension by either rotation, stratification, or due to physical confinement. At the most basic level they geophysical flows be modelled by two-dimensional fluid equations such as the two-dimensional Navier-Stokes or quasi-geostrophic equations. In regimes of small-scale pumping and weak dissipation, these systems display a flow of energy towards the largest scales, leading to a phenomenon called energy condensation at the scale of the system. This pile up of energy can induce the self-organization of the fluid flow into large-scale coherent structures that exist on top of a random turbulent background. For geophysical flows, these coherent structures usually take the form of system-sized vortices or zonal jets (think of hurricanes or large-scale ocean jets such as the Gulf Stream). Questions of universality of these structures are the most natural questions to ask for mathematicians. My interests relate to developing a statistical theory for modelling the complex interactions between the large-scale coherent structures and the underlying turbulent fluctuations.
Quantum turbulence is the study of chaotic fluid motion within quantum fluids and gases such as superfluid liquid helium-4 or Bose-Einstein condensates. In these systems, due to quantum mechanical effects, vortices are defined through topological defects in the fluid density and are all identical in size (of the order of 1Å) and strength. It is the fact that all vortices are the same that leads scientists to think that through understanding quantum turbulence dynamics could help progress in understanding classical turbulence - a billion dollar problem in industry. My interests are numerous, but include the investigation of the quasi-classical nature of coarse-grained quantum turbulence and the role of helical Kelvin waves on quantum vortex lines.
Optical turbulence is the study of the nonlinear interaction of light propagating through a nonlinear medium. This can include light propagating through single- and multi-mode optical fibres or through nonlinear liquid crystals. Principally, optical turbulence can be broken down into the study of weakly nonlinear wave interactions optical wave turbulence and the interaction of strongly nonlinear coherent structures in fully developed optical turbulence. My current research activity is focussed on the cross-over from optical wave turbulence to fully developed optical turbulence where the formation of coherent structures such as optical vortices (in defocussing media) and solitons (in focussing media) arise through nonlinear wave interactions.
Gravitational Wave Turbulence
Albert Einstein's theory of general relativity predicts the propagation of gravitational waves through the universe. Recent cosmological observations of gravitational waves have verified Einstein's hypothesis and has led to an immense interest in the dynamics of gravitational waves. My recent research has been on developing a theory for weak and strong nonlinear interactions of many gravitational waves and how this may lead to a new perspective of cosmological inflation.