Turbulent flows are characterized by the non-linear cascades of energy and other inviscid
invariants across a huge range of scales, from where they are injected to where they are …

We briefly review helicity dynamics, inverse and bidirectional cascades in fluid and
magnetohydrodynamic (MHD) turbulence, with an emphasis on the latter. The energy of a …

Quantum turbulence—the stochastic motion of quantum fluids such as 4He and 3He-B,
which display pure superfluidity at zero temperature and two-fluid behavior at finite but low …

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 …

We collect and describe the observed geometrical and dynamical properties of turbulence in
quantum fluids, particularly superfluid helium and atomic condensates for which more …

Since the idea of quantum turbulence was first proposed by Feynman and later realized in
experiments of superfluid helium and Bose-Einstein condensates, much emphasis has been …

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 …

We study freely decaying quantum turbulence by performing high-resolution numerical
simulations of the Gross-Pitaevskii equation (GPE) in the Taylor-Green geometry. We use …

Numerical methods for solving the Navier-Stokes equations for classical (or normal) viscous
fluids are well established. This is also the case for the Gross-Pitaevskii equation, governing …

We present numerical evidence of a critical-like transition in an out-of-equilibrium mean-field
description of a quantum system. By numerically solving the Gross-Pitaevskii equation we …