Research Interests

My research interests lie in the modelling of the complex interactions between coherent nonlinear structures and turbulent fluctuations in turbulent fluid flows. This involves understanding vortex dynamics, nonlinear wave interactions, and stochastic fluctuations. I predominantly deal with turbulent flows in two-dimensional and geophysical fluid dynamics (atmospheres and oceans), quantum fluids such as those appearing as Bose-Einstein Condensates (BECs) or superfluid helium, and fluid analogies in nonlinear optics and cosmology.

Below is a selection of funding opportunities and current research projects that any potential PhD student or postdoctoral researcher who is interested in working under my supervision can apply for or freely discuss with me.

Funding Opportunities

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:

Current Research Projects

Two-Dimensional and Geophysical Turbulence

Many geophysical flows are quasi-two-dimensional in nature, with motion restricted in one dimension by rotation, stratification, or physical confinement. At the most basic level, these geophysical flows can 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 buildup 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.

two-dimensional turbulence

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  • A. Frishman, J. Laurie and G. Falkovich, Jets or Vortices--What Flows are Generated by an Inverse Turbulence Cascade?, Phys. Rev. Fluids, 2, 032602(R), (2017)  DOI 10.1103/PhysRevFluids.2.032602  arXiv:1608.04628
  • J. Laurie, G. Boffetta, G. Falkovich, I. Kolokolov and V. Lebedev, Universal Profile of the Vortex Condensate in Two-Dimensional Turbulence, Phys. Rev. Lett. 113, 254503, (2014)  DOI 10.1103/PhysRevLett.113.254503  arXiv:1406.1349
Quantum Turbulence

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, 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.

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Optical Turbulence

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.

Optical Turbulence

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  • J. Laurie, U. Bortolozzo, S. Nazarenko and S. Residori, One-Dimensional Optical Wave Turbulence: Experiment and Theory, Phys. Rep. 514, No. 4, 121-175, (2012)  DOI 10.1016/j.physrep.2012.01.004  arXiv:1110.4644
  • U. Bortolozzo, J. Laurie, S. Nazarenko and S. Residori, Optical Wave Turbulence and the Condensation of Light, J. Opt. Soc. Am. B, 26, No.12, 2280-2284, (2009)  DOI 10.1364/JOSAB.26.002280  arXiv:0904.2552
Gravitational Waves

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.

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  • S. Galtier, J. Laurie and S. Nazarenko, A Plausible Model of Inflation Driven by Strong Gravitational Wave Turbulence, Universe, 6, 98, (2020)  DOI 10.3390/universe6070098  arXiv:1910.07634