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The existence of a total energy cascade and the scale-locality of the total energy flux are rigorously established working directly from the 3D MHD equations and under assumptions consistent with physical properties of turbulent plasmas.…

A novel concept of quantum turbulence in finite size superfluids, such as trapped bosonic atoms, is discussed. We have used an atomic $^{87}\mathrm{Rb}$ BEC to study the emergence of this phenomenon. In our experiment, the transition to the…

The turbulence of superfluid helium is investigated numerically at finite temperature. Direct numerical simulations are performed with a "truncated HVBK" model, which combines the continuous description of the…

The velocity circulation, a measure of the rotation of a fluid within a closed path, is a fundamental observable in classical and quantum flows. It is indeed a Lagrangian invariant in inviscid classical fluids. In quantum flows, circulation…

The ocean and the atmosphere, and hence the climate, are governed at large scale by interactions between pressure gradient, Coriolis and buoyancy forces. This leads to a quasi-geostrophic balance in which, in a two-dimensional-like fashion,…

This article reviews recent developments in quantum fluid dynamics and quantum turbulence (QT) for superfluid helium and atomic Bose-Einstein condensates. Quantum turbulence was discovered in superfluid $^4$He in the 1950s, but the field…

The statistical properties of turbulent flows are fundamentally different from those of systems at equilibrium due to the presence of an energy flux from the scales of injection to those where energy is dissipated by the viscous forces: a…

We derive the exact relation for the energy transfer in three-dimensional compressible two-fluid plasma turbulence. In the long-time limit, we obtain an exact law which expresses the scale-to-scale average energy flux rate in terms of two…

To answer the question whether a cascade of energy exists or not in turbulence, we propose a set of correlation functions able to test if there is an irreversible transfert of energy, step by step, from large to small structures. These…

The energy cascade, i.e. the transfer of kinetic energy from large-scale to small-scale flow motions, has been the cornerstone of turbulence theories and models since the 1940s. However, understanding the spatial organization of the energy…

We report evidence for an enstrophy cascade in large-scale point-vortex simulations of decaying two-dimensional quantum turbulence. Devising a method to generate quantum vortex configurations with kinetic energy narrowly localized near a…

In fluid turbulence, energy is transferred from a scale to another by an energy cascade that depends only on the energy dissipation rate. It leads by dimensional arguments to the Kolmogorov 1941 (K41) spectrum. Remarkably the normal modes…

We investigate the kinetic energy cascade in zero-temperature quantum turbulence. Using simple theoretical arguments and unprecedented numerical simulations, we unveil an universal mechanism transferring energy directly from large to very…

We present results from an ensemble of 50 runs of two-dimensional hydrodynamic turbulence with spatial resolution of 2048^2 grid points, and from an ensemble of 10 runs with 4096^2 grid points. All runs in each ensemble have random initial…

Turbulence is ubiquitous in plasmas, leading to rich dynamics characterized by irregularity, irreversibility, energy fluctuations across many scales, and energy transfer across many scales. Another fundamental and generic feature of…

Turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across a broad spectrum of length and time scales. While turbulence is ubiquitous, from teacups to planetary atmospheres,…

In fully developed three dimensional fluid turbulence the fluctuating energy is supplied at large scales, cascades through intermediate scales, and dissipates at small scales. It is the hallmark of turbulence that for intermediate scales,…

Turbulence in stratified and rotating turbulent flows is characterized by an interplay between waves and eddies, resulting in continuous exchanges between potential and kinetic energy. Here, we study how these processes affect the turbulent…

Turbulent flows in three dimensions are characterized by the transport of energy from large to small scales through the energy cascade. Since the small scales are the result of the nonlinear dynamics across the scales, they are often…

We calculate the net energy per unit time exchanged between two sets of modes in a generic system governed by a three-wave kinetic equation. Our calculation is based on the property of detailed energy conservation of the triadic resonant…