Marc Etienne Brachet

Quantum turbulence shares many similarities with classical turbulence in the isotropic and homogeneous case, despite the inviscid and quantized nature of its vortices. However, when quantum fluids are subjected to rotation, their turbulent dynamics depart significantly from the classical expectations. We explore the phenomenology of rotating quantum turbulence, emphasizing how rotation introduces new regimes with no classical analogues. We review recent theoretical, experimental and numerical developments, and present new numerical results that map out distinct dynamical regimes arising from the interplay of rotation, quantization, nonlinearities and condensed matter regimes. In particular, we show the importance of distinguishing the dynamics of rotating quantum fluids in the slowly rotating, rapidly rotating and low Landau level regimes. The findings have implications for the dynamics of liquid helium, atomic Bose–Einstein condensates and neutron stars, and show how rotating quantum fluids can serve as a unique platform bridging turbulence theory and condensed matter physics, revealing novel states of out-of-equilibrium quantum matter. This article is part of the theme issue ‘Frontiers of turbulence and statistical physics’.

In this work, we investigate the Navier–Stokes equation in the presence of thermal noise, both at finite viscosity (revisiting the seminal work by Forster–Nelson–Stephen) and in the inviscid limit,which has not yet been explored. We determine the space-time velocity correlations in this dynamics, using functional renormalization group (RG) and direct numerical simulations. While spectrally truncated three-dimensional (3D) Euler flows reach a stationary equilibrium state, they exhibit non-trivial temporal correlations. We show that these non-trivial correlations persist for small but finite viscosity, yielding an emergent τ∼k-1 dynamical scaling, where τ is the decorrelation time. We characterize the crossover from the scaling τ∼1/(νk2), expected at large viscosity, to the scaling τ∼1/(urmsk) found in the inviscid limit. This article is part of the theme issue ‘Frontiers of turbulence and statistical physics’.

We provide an overview of the Gross–Pitaevskii– Poisson equation (GPPE) that is used to model self-gravitating superfluid systems, which include gravitationally collapsed boson and axion stars and dark-matter haloes (DMHs). We outline how this framework can be used to develop minimal models for neutron stars and for pulsars and their glitches. We account not only for vortices in the neutron superfluid inside these stars but also for the flux tubes in the proton-superconductor subsystem, using a coupled model with the neutron superfluid, proton superconductor, the Maxwell equations for the vector potential A and the Poisson equation for self-gravity. This article is part of the theme issue ‘Frontiers of turbulence and statistical physics’.

We present a review of results concerning the properties of scales larger than the forcing scale in turbulent flows. In three-dimensional turbulence, when the power driving the flow is injected at a well-defined scale, the injection scale separates the small-scale range, where the Kolmogorov cascade takes place, from the large-scale range across which the mean energy flux is zero, suggesting that these modes are in equilibrium. We show that, in the case of spatially periodic forcing involving only a few modes, an equipartition energy spectrum is generated at large scales, and we discuss the deviations from equipartition observed with more complex forcings. In two-dimensional turbulence, the injection scale separates the direct enstrophy cascade towards small scales from the inverse energy cascade towards large scales. Because of the inverse cascade, one would not expect equilibrium statistical physics tools to be suitable for describing the large-scale structures. Yet this is precisely the situation in which such tools have been most widely used. We indeed show that the bifurcations observed between different large-scale regimes of two-dimensional turbulence, both in experiments and in direct numerical simulations (DNS), can be qualitatively described by the truncated Euler equations (TEE), whose solutions satisfy statistical equilibrium. This article is part of the theme issue ‘Frontiers of turbulence and statistical physics’.

Vortex lattices -- highly ordered arrays of vortices -- are known to arise in quantum systems such as type II superconductors and Bose-Einstein condensates. More recently, similar arrangements have been reported in classical rotating fluids. However, the mechanisms governing their formation, stability, and eventual breakdown remain poorly understood. We explore the dynamical stability of vortex lattices in three-dimensional rotating flows. To that end we construct controlled initial conditions consisting of vortex lattices superimposed on turbulent backgrounds. We then characterize their evolution across different Rossby numbers and domain geometries. By introducing an Ekman drag we are able to reach a steady state where vortex lattices persist with near constant amplitude up until spontaneous breakup of the lattice, or an equivalent of ``melting,'' occurs. We examine an ensemble of runs in order to determine the mean lifetime of the lattice as a function of the system parameters. Our results reveal that the stability of the lattices is a memory-less random process whose mean life-time depends sensitively on the system parameters that if finely tuned can lead to very long lived lattice states. These metastable states exhibit statistical properties reminiscent of critical systems and can offer insight into long-lived vortex patterns observed in planetary atmospheres.

We investigate a shift in the critical temperature of rotating Bose-Einstein condensates mediated by the melting of the vortex lattice. Numerical simulations reveal that this temperature exhibits contrasting behavior depending on the system configuration: a negative shift occurs for fixed trap potentials due to the expansion of the condensate, while a positive shift is observed for fixed volumes, where vortex lattice rigidity suppresses thermal fluctuations. We introduce a vortex-energy model that captures the role of vortex interactions, the positional energy of the vortex lattice, as well as the phase transition and how the vortex lattice disappears. The findings provide insights into the thermodynamic properties of rotating condensates and the dynamics of vortex lattice melting, offering potential parallels with other quantum systems such as type-II superconductors.