Exploring the Equivalence between Two-Dimensional Classical and Quantum Turbulence through Velocity Circulation Statistics.

We study the statistics of velocity circulation in two-dimensional classical and quantum turbulence. We perform numerical simulations of the incompressible Navier-Stokes and the Gross-Pitaevskii (GP) equations for the direct and inverse cascades. Our GP simulations display clear energy spectra compatible with the double cascade theory of two-dimensional classical turbulence.

Self-similar evolution of wave turbulence in Gross-Pitaevskii system.

We study the universal nonstationary evolution of wave turbulence (WT) in Bose-Einstein condensates (BECs). Their temporal evolution can exhibit different kinds of self-similar behavior corresponding to a large-time asymptotic of the system or to a finite-time blowup. We identify self-similar regimes in BECs by numerically simulating the forced and unforced Gross-Pitaevskii equation (GPE) and the associated wave kinetic equation (WKE) for the direct and inverse cascades, respectively.

Direct and Inverse Cascades in Turbulent Bose-Einstein Condensates.

When a Bose-Einstein condensate (BEC) is driven out of equilibrium, density waves interact nonlinearly and trigger turbulent cascades. In a turbulent BEC, energy is transferred toward small scales by a direct cascade, whereas the number of particles displays an inverse cascade toward large scales. In this work, we study analytically and numerically the direct and inverse cascades in wave-turbulent BECs.

Energy Spectrum of Two-Dimensional Acoustic Turbulence.

We report an exact unique constant-flux power-law analytical solution of the wave kinetic equation for the turbulent energy spectrum, E(k)=C_{1}sqrt[ϵac_{s}]/k, of acoustic waves in 2D with almost linear dispersion law, ω_{k}=c_{s}k[1+(ak)^{2}], ak≪1. Here, ϵ is the energy flux over scales, and C_{1} is the universal constant which was found analytically. Our theory describes, for example, acoustic turbulence in 2D Bose-Einstein condensates.

Editorial: Scaling the Turbulence Edifice (part 2).

This is the second part of a two-part special issue of the Philosophical Transactions of the Royal Society A, which recognizes, and hopefully encourages, the growing convergence of interests amongst mathematicians and physicists to scale the turbulence edifice. This convergence is explained in more detail in the editorial which accompanies the first part (Bec . 2022 , 20210101.

Editorial: Scaling the Turbulence Edifice.

Turbulence is unique in its appeal across physics, mathematics and engineering. And yet a microscopic theory, starting from the basic equations of hydrodynamics, still eludes us. In the last decade or so, new directions at the interface of physics and mathematics have emerged, which strengthens the hope of 'solving' one of the oldest problems in the natural sciences.

Vortex clustering, polarisation and circulation intermittency in classical and quantum turbulence.

The understanding of turbulent flows is one of the biggest current challenges in physics, as no first-principles theory exists to explain their observed spatio-temporal intermittency. Turbulent flows may be regarded as an intricate collection of mutually-interacting vortices. This picture becomes accurate in quantum turbulence, which is built on tangles of discrete vortex filaments.

Counterflow-Induced Inverse Energy Cascade in Three-Dimensional Superfluid Turbulence.

Finite-temperature quantum turbulence is often described in terms of two immiscible fluids that can flow with a nonzero-mean relative velocity. Such out-of-equilibrium state is known as counterflow superfluid turbulence. We report here the emergence of a counterflow-induced inverse energy cascade in three-dimensional superfluid flows by performing extensive numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model.

Irreversible Dynamics of Vortex Reconnections in Quantum Fluids.

We statistically study vortex reconnections in quantum fluids by evolving different realizations of vortex Hopf links using the Gross-Pitaevskii model. Despite the time reversibility of the model, we report clear evidence that the dynamics of the reconnection process is time irreversible, as reconnecting vortices tend to separate faster than they approach. Thanks to a matching theory devised concurrently by Proment and Krstulovic [Phys.

Publisher's Note: Self-truncation and scaling in Euler-Voigt-α and related fluid models [Phys. Rev. E 92, 013020 (2015)].

This corrects the article DOI: 10.1103/PhysRevE.92.

Phase transition in time-reversible Navier-Stokes equations.

We present a comprehensive study of the statistical features of a three-dimensional (3D) time-reversible truncated Navier-Stokes (RNS) system, wherein the standard viscosity ν is replaced by a fluctuating thermostat that dynamically compensates for fluctuations in the total energy. We analyze the statistical features of the RNS steady states in terms of a non-negative dimensionless control parameter R_{r}, which quantifies the balance between the fluctuations of kinetic energy at the forcing length scale ℓ_{f} and the total energy E_{0}. For small R_{r}, the RNS equations are found to produce "warm" stationary statistics, e.

Elastic weak turbulence: From the vibrating plate to the drum.

Weak wave turbulence has been observed on a thin elastic plates since the work by Düring et al. [Phys. Rev.

Interaction between active particles and quantum vortices leading to Kelvin wave generation.

One of the main features of superfluids is the presence of topological defects with quantised circulation. These objects are known as quantum vortices and exhibit a hydrodynamic behaviour. Nowadays, particles are the main experimental tool used to visualise quantum vortices and to study their dynamics.

Tumbling dynamics of inertial inextensible chains in extensional flow.

This paper investigates the effect of inertia on the dynamics of elongated chains to go beyond the overdamped case that is often used to study such systems. For that purpose, numerical simulations are performed considering the motion of freely jointed bead-rod chains in an extensional flow in the presence of thermal noise. The coil-stretch transition and the tumbling instability are characterized as a function of three parameters: the Péclet number, the Stokes number, and the chain length.

Exact result in strong wave turbulence of thin elastic plates.

An exact result concerning the energy transfers between nonlinear waves of a thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the 4/5-Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity, and the Airy stress function of a plate, is proven to be equal to -ɛℓ, where ℓ is a length scale in the inertial range at which the increments are evaluated and ɛ the energy dissipation rate.

Grid superfluid turbulence and intermittency at very low temperature.

Low-temperature grid-generated turbulence is investigated by using numerical simulations of the Gross-Pitaevskii equation. The statistics of regularized velocity increments are studied. Increments of the incompressible velocity are found to be skewed for turbulent states.

Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation.

The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using a recently developed accurate and robust tracking algorithm, all quantized vortices are extracted from the fields. The Vinen's decay law for the total vortex length with a coefficient that is in quantitative agreement with the values measured in helium II is observed.

Clustering, fronts, and heat transfer in turbulent suspensions of heavy particles.

Heavy inertial particles transported by a turbulent flow are shown to concentrate in the regions where an advected passive scalar, such as temperature, displays very strong frontlike discontinuities. This novel effect is responsible for extremely high levels of fluctuations for the passive field sampled by the particles that impacts the heat fluxes exchanged between the particles and the surrounding fluid. Instantaneous and averaged heat fluxes are shown to follow strongly intermittent statistics and anomalous scaling laws.

Kelvin-wave cascade and dissipation in low-temperature superfluid vortices.

We study the statistical properties of the Kelvin waves propagating along quantized superfluid vortices driven by the Gross-Pitaevskii equation. No artificial forcing or dissipation is added. Vortex positions are accurately tracked.

Axial dipolar dynamo action in the Taylor-Green vortex.

We present a numerical study of the magnetic field generated by the Taylor-Green vortex. We show that periodic boundary conditions can be used to mimic realistic boundary conditions by prescribing the symmetries of the velocity and magnetic fields. This gives insight into some problems of central interest for dynamos: the possible effect of velocity fluctuations on the dynamo threshold, and the role of boundary conditions on the threshold and on the geometry of the magnetic field generated by dynamo action.

Alfvén waves and ideal two-dimensional Galerkin truncated magnetohydrodynamics.

We investigate numerically the dynamics of two-dimensional Euler and ideal magnetohydrodynamics (MHD) flows in systems with a finite number of modes, up to 4096(2), for which several quadratic invariants are preserved by the truncation and the statistical equilibria are known. Initial conditions are the Orszag-Tang vortex with a neutral X point centered on a stagnation point of the velocity field in the large scales. In MHD, we observe that the total energy spectra at intermediate times and intermediate scales correspond to the interactions of eddies and waves, E(T)(k)~k(-3/2).

Energy cascade with small-scale thermalization, counterflow metastability, and anomalous velocity of vortex rings in Fourier-truncated Gross-Pitaevskii equation.

The statistical equilibria of the (conservative) dynamics of the Gross-Pitaevskii equation (GPE) with a finite range of spatial Fourier modes are characterized using a new algorithm, based on a stochastically forced Ginzburg-Landau equation (SGLE), that directly generates grand-canonical distributions. The SGLE-generated distributions are validated against finite-temperature GPE-thermalized states and exact (low-temperature) results obtained by steepest descent on the (grand-canonical) partition function. A standard finite-temperature second-order λ transition is exhibited.

Dispersive bottleneck delaying thermalization of turbulent bose-einstein condensates.

A new mechanism of thermalization involving a direct energy cascade is obtained in the truncated Gross-Pitaevskii dynamics. A long transient with partial thermalization at small scales is observed before the system reaches equilibrium. Vortices are found to disappear as a prelude to final thermalization.