Research Interests

My main research interests lie in understanding the complex interactions between coherent structures and turbulent fluctuations in fluid flows, whether it is vortex dynamics or nonlinear wave interactions. I mainly deal with flows in geophysical fluid dynamics (atmospheres and oceans) or those found in quantum fluids, such as Bose-Einstein Condensates (BECs) and superfluid helium-4, or their optical anlaogies. I also have a keen interest in studying rare events within such turbulent systems.

Below is a list of possible funding opportunities for PhD and postdoctoral positions, followed by summaries of research projects I offer.

Funding Opportunities

Those interested in pursuing a research project in one of these areas may contact me and may also consider applying for one of the following postdoctoral research fellowships:

Universality of Coherent Structures in Geophysical Fluid Dynamics

Many geophysical flows are quasi two-dimensional in nature. At the most basic level they can be modelled by two-dimensional fluid equations such as the quasi-geostrophic model or the two-dimensional Navier-Stokes equations. In regimes of small-scale pumping and weak dissipation, these systems permit energy to flow towards the largest scales leading to energy condensation at the system size. This pile up of energy can induce the self-organization of the fluid flow into large-scale coherent structures on top of a random turbulent background. For these geophysical fluid models, the coherent structures usually take the form of system-sized vortices or zonal jets. These coherent structures are formed through a balance of energy injection and energy dissipation meaning that the problem is a non-equilibrium one. At a fundamental level, questions of universality are the most natural questions to ask. Using simple arguments based on energy and momentum balance between the dominant mean flow and the weak random turbulent fluctuations, we have successfully determined the universal profile, including numerical prefactors, of the vortex condensate in the two-dimensional Navier-Stokes equations (right). These theoretical predictions agree remarkably well with numerical data. The generality of our theory leads to the application to more physically relevant models and to other physical systems.

Energy Transfer Mechanisms in Quantum Turbulence

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, quantum turbulence arises through the irroational fluid flow created by a complex tangle of quantized vortex lines (see figure for such an example). My interests lie predominately in superfluid helium-4 in the zero temperature limit. Unlike classical fluids where viscosity dissipates energy from the fluid at small-scales, in zero temperature superfluids there is no such mechanism. It is hypothesized that the excitation of Kelvin waves, oscillatory perturbations that propagate along individual quantized vortex lines transfer energy to such small scales that energy is dissipation by phonon emissions. It has been one of my goals to understand the dynamics of these Kelvin waves and other energy transfer mechanisms in superfluid helium-4.

Rare Transitions in Geophysical Fluid Dynamics

Several geophysical fluid flows may have large-scale coherent structures as dynamical attractors. Moreover, in certain regimes there is evidence of more than one possible dynamical attractor. If one includes weak stochastic fluctuations in these bistable regimes the system may undergo spontaneous non-equilibrium phase transitions from one attractor to another. If these transitions are rare, then there has been numerical and experimental evidence that indicates that the way the system switches between two states my concentrate close to a unique path. With the aid of large deviation and instanton theory (a path integral approach) we have developed a non-equilibrium statistical mechanics theory to determine the most probable transition paths between two attractors in turbulent bistable flows.

Wave Turbulence and Photon Condensation in Nonlinear Optics

Optical wave turbulence is the process of weakly nonlinear wave mixing induced by the Kerr effect in nonlinear optics. I have been involved in the development of the theory, experiments and numerical simulations to show the phenomena of wave turbulence and photon condensation in a one-dimensional optical system. Our implementation involves the experimental construction of a nematic liquid crystal cell that provides a nonlinear medium for optical wave turbulence of laser light to occur. We propagate laser light through the liquid crystal cell, where it undergoes nonlinear wave interactions leading to the condensation of photon at the largest scales. This condensation process becomes modulationally unstable leading to filamentation and subsequently the formation of solitons (see figure to the right).