Job offers

(2026) Post-doctoral position: Quantum-inspired approaches for the simulation of turbulent flows

Tensor networks are widely used in quantum mechanics to effectively and dramatically reduce the number of degrees of freedom required to represent complex quantum states. More recently, they have also emerged as a promising approach to represent and simulate various classical systems including turbulent flows.

The aim of this post-doctoral project is to explore the simulation of turbulent flows using tensor networks. The goal will be to determine whether such approach can enable the investigation of high Reynolds number flows which are out of reach for traditional methods, or whether a low-order model based on this representation can capture the main statistical features of turbulent flows. The methods will then be applied to investigate fundamental aspects of turbulent flows and the emergence of extreme events in turbulence.

Expected start date: September or October 2026

Project duration: 18 to 24 months

See PDF file for more details.

(2026) PhD position: Waves and turbulence in rotating superfluid helium-4

Near absolute zero, liquid helium-4 enters a superfluid phase known as He II where it displays unique hydrodynamical properties. At finite temperatures between about 1 and 2 K, He II can be seen as a mixture of a viscous normal fluid and a superfluid without viscosity, whose rotational degrees of freedom are concentrated on so-called quantum vortices with atomic-scale thickness and quantised intensity. Remarkably, when He II is set in rotation, quantum vortices tend to align with the rotation axis and form a highly regular vortex lattice. When perturbed by external mechanisms, rotating He II can host a variety of wavelike motions, such as inertial waves propagating through the fluid as in classical rotating flows, but also waves which are specific to the singular nature of vortices in He II. As the perturbation is intensified, a disordered state known as rotating quantum turbulence (QT) can be triggered, which is still today very poorly understood.

In this PhD project, we will study the mechanisms leading to the destabilisation of the rotating quantum vortex lattice by external perturbations and the fully turbulent states beyond that. We will characterise the spatial structure of quantum vortices in rotating QT and aim at unveiling possible similarities with classical rotating turbulence, where inertial waves play a major role and where scale-by-scale energy transfer mechanisms are strongly altered by rotation. To study these fundamental mechanisms, we will perform the first numerical simulations of rotating QT in spatially-homogeneous settings, which is enabled by a novel numerical method recently developed at LEGI. Our numerical results will be quantitatively compared to experimental measurements in a rotating platform at Institut Néel, where quantum vortices can be directly visualised. This project will substantially advance our understanding of rotating He II flows, in particular in transitional and fully turbulent regimes where experimental measurements become very challenging. It will also reinforce the analogy between classical and quantum turbulence, potentially leading to novel approaches for modelling turbulent flows in classical fluids.

Expected start date: 1 October 2026

Project duration: 36 months

See PDF file for more details.

(2023) PhD position: Quantum turbulence simulations using a vortex filament model

A PhD position is open at LEGI to work on simulations of quantum turbulent flows (observed for instance in superfluid helium) at the absolute zero, where they are described as a collection of interacting vortex filaments. The main objective is to investigate the possible similarities between quantum and classical turbulence, in order to strengthen the link between both systems.

Summary

   Superfluids, such as liquid helium at very low temperatures, are characterised by an absence of viscosity at the absolute zero. In this limit, they are effectively composed of very thin vortex filaments about which the velocity circulation takes discrete values. The complex interaction between these quantum vortices can lead to a state known as quantum turbulence, characterised by an extremely wide range of scales going from the vortex thickness (~1 Å) to the size of existent experimental facilities (up to ~1 metre). This state has been shown to present quantitative similarities with classical turbulent flows, and thus provides an interesting avenue for a better understanding of classical turbulence. With this in mind, simulations of the vortex filament model (VFM) will be performed in this thesis to study quantum turbulent flows. In the VFM, vortices are described as three-dimensional curves which interact according to Biot–Savart’s law. In particular, a reformulation of the VFM will be used for the first time to speed-up the simulation of strongly turbulent regimes in fully periodic domains. The proposed method will be first validated by comparing simple cases (e.g. the collision between two vortices leading to their reconnection) against results known from a compressible atomic-scale model. Then, a statistical analysis of the quantum turbulent state will be performed. The main objective is to compare high-order statistics associated to extreme events to results known from classical turbulence, as an attempt to further advance the analogy between both systems. In particular, statistics associated to Eulerian and Lagrangian velocities will be considered. The motion of vortex filaments will be tracked in time to characterise the emergence and decay of extreme events. This study will serve as a first step towards an accurate description of superfluid helium flows, which will require coupling the VFM to the Navier–Stokes equations.

Application deadline

   12 May 2023

Start date

   1 October 2023

PhD duration

   3 years

See PDF file for more information on the project and on how to apply.