Kármán–Howarth solutions of homogeneous isotropic turbulence

The Kármán–Howarth equation (KHEq) is solved using a closure model to obtain solutions of the second-order moment of the velocity increment, $S_2$ , in homogeneous isotropic turbulence (HIT). The results are in good agreement with experimental data for decaying turbulence and are also consistent with calculations based on the three-dimensional energy spectrum for decaying HIT. They differ, however, from those for forced HIT, the difference occurring mainly at large scales. This difference is attributed to the fact that the forcing generates large-scale motions which are not compatible with the KHEq. As the Reynolds number increases, the impact of forcing on the small scales decreases, thus allowing the KHEq and spectrally based solutions to agree well in the range of scales unaffected by forcing. Finally, the results show that the two-thirds law is compatible with the KHEq solutions as the Reynolds number increases to very large, if not infinite, values.

Dynamic Alignment and Plasmoid Formation in Relativistic Magnetohydrodynamic Turbulence

We present high-resolution 2D and 3D simulations of magnetized decaying turbulence in relativistic, resistive magnetohydrodynamics. The simulations show dynamic formation of large-scale intermittent long-lived current sheets being disrupted into plasmoid chains by the tearing instability. These current sheets are locations of enhanced magnetic-field dissipation and heating of the plasma. We find magnetic energy spectra ∝k −3/2, together with strongly pronounced dynamic alignment of Elsässer fields and of velocity and magnetic fields, for strong guide-field turbulence, whereas we retrieve spectra ∝k −5/3 for the case of a weak guide-field.

Role of Parallel Solenoidal Electric Field on Energy Conversion in 2.5D Decaying Turbulence with a Guide Magnetic Field

We perform 2.5D particle-in-cell simulations of decaying turbulence in the presence of a guide (out-of-plane) background magnetic field. The fluctuating magnetic field initially consists of Fourier modes at low wavenumbers (long wavelengths). With time, the electromagnetic energy is converted to plasma kinetic energy (bulk flow+thermal energy) at the rate per unit volume of J · E for current density J and electric field E . Such decaying turbulence is well known to evolve toward a state with strongly intermittent plasma current. Here we decompose the electric field into components that are irrotational, E ir, and solenoidal (divergence-free), E so. E ir is associated with charge separation, and J · E ir is a rate of energy transfer between ions and electrons with little net change in plasma kinetic energy. Therefore, the net rate of conversion of electromagnetic energy to plasma kinetic energy is strongly dominated by J · E so, and for a strong guide magnetic field, this mainly involves the component E so,∥ parallel to the total magnetic field B . We examine various indicators of the spatial distribution of the energy transfer rate J ∥ · E so,∥, which relates to magnetic reconnection, the best of which are (1) the ratio of the out-of-plane electric field to the in-plane magnetic field, (2) the out-of-plane component of the nonideal electric field, and (3) the magnitude of the estimate of current helicity

Universality in Decaying Turbulence at High Reynolds Numbers

In the limit of very large Reynolds numbers for homogeneous isotropic turbulence of an incompressible fluid, the statistics of the velocity differences between two points in space are expected to approach universal power laws at scales smaller than those at which energy is injected. Even at the highest Reynolds numbers available in laboratory and natural flows such universal power laws have remained elusive. On the other hand, power laws have been observed empirically in derived quantities, namely in the relative scaling in statistics of different orders according to the Extended Self Similarity hypothesis. Here we present experimental results from the Max Planck Variable Density Turbulence Tunnel over an unprecedented range of Reynolds numbers. We find that the velocity difference statistics take a universal functional form that is distinct from a power law. By applying a self-similar model derived for decaying turbulence to our data, an effective scaling exponent for the second moment can be derived that agrees well with that obtained from Extended Self Similarity.

Energy transport during 3D small-scale reconnection driven by anisotropic turbulence using PIC simulations

<p>Heating and energy dissipation in the solar wind remain important open questions. Turbulence and reconnection are two candidate processes to account for the energy transport to subproton scales at which, in collisionless plasmas, the energy ultimately dissipates. Understanding the effects of small-scale reconnection events in the energy cascade requires the identification of these events in observational data as well as in 3D simulations. We use an explicit fully kinetic particle-in-cell code to simulate 3D small scale magnetic reconnection events forming in anisotropic and Alfvénic decaying turbulence. We define a set of indicators to find reconnection sites in our simulation based on intensity thresholds.  According to the application of these indicators, we identify the occurrence of reconnection events in the simulation domain and analyse one of these events in detail. The event is highly dynamic and asymmetric. We study the profiles of plasma and magnetic-field fluctuations recorded along artificial-spacecraft trajectories passing near and through the reconnection region as well as the energy exchange between particles and fields during this event. Our results suggest the presence of particle heating and acceleration related to asymmetric small-scale reconnection of magnetic flux tubes produced by the anisotropic Alfvénic turbulent cascade in the solar wind. These events are related to current structures of order a few ion inertial lengths in size.</p>

Sounding plasma turbulence at sub-ion scales with Fast Iterative Filtering in space and time.

<p>We present the results from a spacetime study of Hall-MHD and Hybrid-kinetic numerical simulations of decaying turbulence. By combining Fourier analysis and Multivariate Iterative Filtering (a new technique developed for the analysis of nonstationary nonlinear signals) we calculate the <em>kω-</em>power spectrum of magnetic, velocity, and density fluctuations at the maximum of turbulent activity. Results show that the magnetic power spectrum at sub-ion scales is formed by localized structures and/or perturbations with temporal frequencies much smaller than the ion-cyclotron frequency Ω<sub>i</sub>. Going toward smaller ion-kinetic scales, the contribution of low-medium frequency perturbations (<em>ω </em>< 3Ω<sub>i</sub>) to the magnetic spectrum becomes important. Our analysis clearly indicates that such low-frequency perturbations have no kinetic-Alfvén neither Ion-cyclotron origin. At higher frequencies, we clearly identify signatures of both whistler and kinetic-Alfvén wave activity. However, their energetic contribution to the turbulent cascade is negligible. We conclude that the dynamics of turbulence at sub-ion scales is mainly shaped by localized intermittent structures, with no contribution of wavelike perturbations.</p>

Multiscale Sample Entropy of Two-Dimensional Decaying Turbulence

Multiscale sample entropy analysis has been developed to quantify the complexity and the predictability of a time series, originally developed for physiological time series. In this study, the analysis was applied to the turbulence data. We measured time series data for the velocity fluctuation, in either the longitudinal or transverse direction, of turbulent soap film flows at various locations. The research was to assess the feasibility of using the entropy analysis to qualitatively characterize turbulence, without using any conventional energetic analysis of turbulence. The study showed that the application of the entropy analysis to the turbulence data is promising. From the analysis, we successfully captured two important features of the turbulent soap films. It is indicated that the turbulence is anisotropic from the directional disparity. In addition, we observed that the most unpredictable time scale increases with the downstream distance, which is an indication of the decaying turbulence.

Multiscale analysis of Hall-MHD and Hybrid-PIC simulations of plasma turbulence: structures or waves?

<p>Turbulence in space and astrophysical plasmas is an intrinsically chaotic and multiscale phenomenon that involves nonlinear coupling across different temporal and spatial scales. There is growing evidence that plasma instabilities, such as magnetic reconnection taking place in localized current sheets, enhance the energy dissipation toward small sub-ion scales. However, it is hotly debated whether the dominant contribution to the scale-to-scale energy transfer at kinetic scales is due to non-linear wave interactions or to coherent structures. Here we present the results from a multiscale study of 2D Hall-MHD and hybrid Particle-in-cell (PIC) numerical simulations of decaying turbulence, performed by means of Multidimensional Iterative Filters (MIF), a new technique developed for the spatio-temporal analysis of non-stationary non-linear multidimensional signals. Results show that, at the maximum of turbulent activity, the power spectrum of magnetic fluctuations at sub-ion scales is formed by localized structures and/or perturbations with temporal frequencies smaller than the ion-cyclotron frequency. Going toward smaller kinetic scales, the contribution of low-medium frequency perturbations to the magnetic spectrum becomes important. However, the dispersion relation and polarization properties of such perturbations are not consistent with those of Kinetic Alfvèn Waves (KAW). We conclude that the dynamics of turbulence at sub-ion scales is mainly shaped by localized intermittent structures, with no apparent contribution of KAW-like interactions at small scales.</p>