The role of field correlations on turbulent dissipation

Nonlinear phenomena and turbulence are central to our understanding and modeling the dynamics of fluids and plasmas, and yet they still resist analytical resolutions in many instances. However, progress has been made recently, displaying a richness of phenomena which was somewhat unexpected a few years back, such as the double constant-flux cascades of a same invariant to both the large and to the small scales, or the presence of non-Gaussian wings in the large-scale fields, for fluids and plasmas. Here, I will concentrate on the direct measurement of the magnitude of dissipation and an evaluation of intermittency in a turbulent plasma using exact laws stemming from invariance principles and involving cross-correlation tensors with both the velocity and the magnetic fields. I will illustrate these points through scaling laws, together with data analysis from existing experiments, observations and numerical simulations. Finally, I will also briefly explore the possible implications for validity and use of several modeling strategies. To appear, Plasma Physics and Controlled Fusion, 2023

Long-time properties of MHD turbulence and the role of symmetries

We investigate long-time properties of three-dimensional MHD turbulence in the absence of forcing and examine in particular the role played by the quadratic invariants of the system and by the symmetries of the initial configurations. We observe that, when sufficient accuracy is used, initial conditions with a high degree of symmetries, as in the absence of helicity, do not travel through parameter space over time whereas by perturbing these solutions either explicitly or implicitly using for example single precision for long times, the flows depart from their original behavior and can become either strongly helical, or have a strong alignment between the velocity and the magnetic field. When the symmetries are broken, the flows evolve towards different end states, as predicted by statistical arguments for non-dissipative systems with the addition of an energy minimization principle, as already analyzed in \cite{stribling_90} for random initial conditions using a moderate number of Fourier modes. Furthermore, the alignment properties of these flows, between velocity, vorticity, magnetic potential, induction and current, correspond to the dominance of two main regimes, one helically dominated and one in quasi-equipartition of kinetic and magnetic energy. We also contrast the scaling of the ratio of magnetic energy to kinetic energy as a function of wavenumber to the ratio of eddy turn-over time to Alfv\'en time as a function of wavenumber. We find that the former ratio is constant with an approximate equipartition for scales smaller than the largest scale of the flow whereas the ratio of time scales increases with increasing wavenumber.Comment: 14 pages, 6 figure

Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation

We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behavior of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number Re=1000, with the ratio between the Brunt-V\"ais\"al\"a frequency N and the inertial frequency f varying from 1/4 to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range 0.02 < Fr < 0.32. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio N/f increases, also in the stratified case, although less and less so. However, when N/f increases, the inverse cascade of the slow modes becomes weaker and weaker, and it vanishes in the purely stratified case. We discuss how the disappearance of the inverse cascade of energy with increasing N/f can be interpreted in terms of the waves and vortices, and identify three major effects that can explain this transition based on inviscid invariants arguments

On the emergence of helicity in rotating stratified turbulence

We perform numerical simulations of decaying rotating stratified turbulence and show, in the Boussinesq framework, that helicity (velocity-vorticity correlation), as observed in super-cell storms and hurricanes, is spontaneously created due to an interplay between buoyancy and rotation common to large-scale atmospheric and oceanic flows. Helicity emerges from the joint action of eddies and of inertia-gravity waves (with inertia and gravity with respective associated frequencies $f$ and $N$), and it occurs when the waves are sufficiently strong. For $N/f < 3$ the amount of helicity produced is correctly predicted by a quasi-linear balance equation. Outside this regime, and up to the highest Reynolds number obtained in this study, namely $Re\approx 10000$, helicity production is found to be persistent for $N/f$ as large as $\approx 17$, and for $ReFr^2$ and $ReRo^2$ respectively as large as $\approx 100$ and $\approx 24000$.Comment: 10 pages, 5 figure

A hybrid MPI-OpenMP scheme for scalable parallel pseudospectral computations for fluid turbulence

A hybrid scheme that utilizes MPI for distributed memory parallelism and OpenMP for shared memory parallelism is presented. The work is motivated by the desire to achieve exceptionally high Reynolds numbers in pseudospectral computations of fluid turbulence on emerging petascale, high core-count, massively parallel processing systems. The hybrid implementation derives from and augments a well-tested scalable MPI-parallelized pseudospectral code. The hybrid paradigm leads to a new picture for the domain decomposition of the pseudospectral grids, which is helpful in understanding, among other things, the 3D transpose of the global data that is necessary for the parallel fast Fourier transforms that are the central component of the numerical discretizations. Details of the hybrid implementation are provided, and performance tests illustrate the utility of the method. It is shown that the hybrid scheme achieves near ideal scalability up to ~20000 compute cores with a maximum mean efficiency of 83%. Data are presented that demonstrate how to choose the optimal number of MPI processes and OpenMP threads in order to optimize code performance on two different platforms.Comment: Submitted to Parallel Computin

Rotating turbulence under "precession-like" perturbation

The effects of changing the orientation of the rotation axis on homogeneous turbulence is considered. We perform direct numerical simulations on a periodic box of $1024^3$ grid points, where the orientation of the rotation axis is changed (a) at a fixed time instant (b) regularly at time intervals commensurate with the rotation time scale. The former is characterized by a dominant inverse energy cascade whereas in the latter, the inverse cascade is stymied due to the recurrent changes in the rotation axis resulting in a strong forward energy transfer and large scale structures that resemble those of isotropic turbulence.Comment: 7 pages, 8 figures, The European Physical Journal E (EPJ E