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The interaction of collisionless shocks with fully developed plasma turbulence is numerically investigated. Hybrid kinetic simulations, where a turbulent jet is slammed against an oblique shock, are employed to address the role of upstream turbulence on plasma transport. A technique, using coarse graining of the Vlasov equation, is proposed, showing that the particle transport strongly depends on upstream turbulence properties, such as strength and coherency. These results might be relevant for the understanding of acceleration and heating processes in space plasmas.

Characterization of turbulence in natural bed streams is one of the most fascinating problems of fluid dynamics. In this study, a statistical description of turbulence in a natural pebble bed flow is presented applying the laws of turbulence. A laboratory experiment was conducted to measure the three-dimensional instantaneous velocity components in a flow over heterogeneous coarse sediments that simulated a natural bed. The analysis reveals that the spectra (in Fourier space) show a power-law scaling, $E(k)\\sim k^{{\\it\\alpha}}$ , suggesting the presence of inertial range turbulence. The exponent ${\\it\\alpha}$ is slightly shallower than the Kolmogorov $5/3$ scaling law, with this deviation possibly due to the bed roughness heterogeneity and to fluctuation anisotropy. The Taylor frozen-in approximation is broken at smaller scales towards the roughness crest level; therefore, a new statistical tool for the validation of this approximation is proposed. The Kolmogorov $4/5$ -law for the longitudinal increments and simultaneously the Monin–Yaglom $4/3$ -law for the nonlinear normal fluxes (both in physical space) are preserved, providing an accurate estimation of the turbulent kinetic energy dissipation rate. The heterogeneity of the bed acts to induce the transport of finite kinetic helicity to the outer layer through persistently prolonged vortices. An associated $2/15$ -law for the cascade of helicity has been locally found. These findings open a new direction in turbulence research for flows over highly rough beds.

We introduce a novel logarithmic approach within the Baumgarte–Shapiro–Shibata–Nakamura (BSSN) formalism for self-consistently solving the equations of general relativistic hydrodynamics (GRHD) in evolving curved spacetimes. This method employs a “3 + 1” decomposition of spacetime, complemented by the “1 + log” slicing condition and Gamma-driver shift conditions, which have been shown to improve numerical stability in spacetime evolution. A key innovation of our work is the logarithmic transformation applied to critical variables such as rest-mass density, energy density, and pressure, thus preserving physical positivity and mitigating numerical issues associated with extreme variations. Our formulation is fully compatible with advanced numerical techniques, including spectral methods and Fourier-based algorithms, and it is particularly suited for simulating highly nonlinear regimes in which gravitational fields play a significant role. This approach aims to provide a solid foundation for future numerical implementations and investigations of relativistic hydrodynamics, offering promising new perspectives for modeling complex astrophysical phenomena in strong gravitational fields, including matter evolution around compact objects like neutron stars and black holes, turbulent flows in the early universe, and the nonlinear evolution of cosmic structures.

We argue that the hypothesis of preservation of shape of dimensionless second- and third-order correlations during decay of incompressible homogeneous magnetohydrodynamic (MHD) turbulence requires, in general, at least two independent similarity length scales. These are associated with the two Elsässer energies. The existence of similarity solutions for the decay of turbulence with varying cross-helicity implies that these length scales cannot remain in proportion, opening the possibility for a wide variety of decay behaviour, in contrast to the simpler classic hydrodynamics case. Although the evolution equations for the second-order correlations lack explicit dependence on either the mean magnetic field or the magnetic helicity, there is inherent implicit dependence on these (and other) quantities through the third-order correlations. The self-similar inertial range, a subclass of the general similarity case, inherits this complexity so that a single universal energy spectral law cannot be anticipated, even though the same pair of third-order laws holds for arbitrary cross-helicity and magnetic helicity. The straightforward notion of universality associated with Kolmogorov theory in hydrodynamics therefore requires careful generalization and reformulation in MHD.

The nature of the cross-scale connections between the inertial-range turbulent energy cascade and the small-scale kinetic processes in collisionless plasmas is explored through the analysis of two-dimensional hybrid Vlasov–Maxwell numerical simulation (HVM), with $\\unicode[STIX]{x1D6FC}$ particles, and through a proxy of the turbulent energy transfer rate, namely the local energy transfer (LET) rate. Correlations between pairs of variables, including those related to kinetic processes and to deviation from Maxwellian distributions, are first evidenced. Then, the general properties and the statistical scaling laws of the LET are described, confirming its reliability for the description of the turbulent cascade and revealing its textured topology. Finally, the connection between such proxy and the diagnostic variables is explored using conditional averaging, showing that several quantities are enhanced in the presence of large positive energy flux, and reduced near sites of negative flux. These observations can help in determining which processes are involved in the dissipation of energy at small scales, as for example the ion-cyclotron or mirror instabilities typically associated with perpendicular anisotropy of temperature.

Using high resolution 2D magnetohydrodynamic (MHD) simulations we analyze the formation of coherent structures induced by nonlinear interactions in turbulent flows. The properties of these coherent structures, which at the smallest scales are identified through a spatial intermittent behavior, turn out to be guided by the conservation of ideal quadratic (rugged) invariants of the 2D incompressible MHD equations. Different spatial regions can be identified, where the correlations predicted using the variational principles associated to the rugged invariants are locally displayed. These local correlated structures are produced rapidly, as soon as the turbulence is fully developed. It is worth speculating that the small scale structures under our investigation could give rise to singular weak solutions when letting the dissipative coefficients go to zero. In this case their properties could furnish a key to understand which mathematical conditions characterize singularity emergency in weak solutions of the MHD ideal case.

The statistical properties of ions in two-dimensional fully developed turbulence have been compared between two different numerical algorithms. In particular, we compare Hybrid Particle In Cell (hybrid PIC with fluid electrons) and full PIC simulations, focusing on particle diffusion and acceleration phenomena. To investigate several heliospheric plasma conditions, a series of numerical simulations has been performed by varying the plasma β  – the ratio between kinetic and magnetic pressure. These numerical studies allow the exploration of different scenarios to be performed, going from the solar corona (low  β ) to the solar wind ( β ∼ 1 ), as well as the Earth’s magnetosheath (high  β ). It has been found that the two approaches compare pretty well, especially for the spectral properties of the magnetic field and the ion diffusion statistics. Small differences among the models have been found regarding the electric field behavior at sub-ion scales and the acceleration statistics, due evidently to the more consistent treatment of the plasma in the full PIC approach.

Solar flares are often associated with changes in the fine magnetic structure of the emitting active region. Such topological modification results in variations of both the scaling properties of the fields’ fluctuations, and the fractal dimension of the associated gradients. The use of cancellation analysis of the current density has been attempted for the identification and quantitative estimation of such changes. The characteristics of the magnetic vector as measured by THEMIS telescope for the active region NOAA10019 have been studied in this paper, suggesting the presence of disrupted current filaments. The variation of the fractal dimension of the current structures, and in particular their smoothing, is discussed in relationship with occurrence of one flare in the active region.

A kinetic entropy diagnostic was systematically developed for fully kinetic collisionless particle-in-cell (PIC) simulations in Liang et al., Phys. Plasmas 26, 082903 (2019). Here, we first show that kinetic entropy can be used to quantitatively evaluate numerical dissipation in the PIC simulation. Assuming numerical effects can be treated using a relaxation time approximation collision operator, the rate of increase of the kinetic entropy is related to the kinetic entropy. The effective collision frequency due to numerical effects is then easy to evaluate in a collisionless PIC simulation. We find an effective collision frequency of approximately a tenth of the ion cyclotron frequency. This could have important implications for collisionless PIC simulation studies of magnetic reconnection, plasma turbulence, and collisionless shocks. Then, we analyze the uncertainty of the local kinetic entropy density at different locations as a function of the chosen velocity space grid. We find that although the numerically obtained kinetic entropy density varies significantly for small or large velocity space grids, there is a range for which the kinetic entropy density is only weakly sensitive to the velocity space grid. Our analysis of the uncertainty suggests a velocity space grid close to the thermal velocity is optimal, and the uncertainty introduced is significantly less than the physical change in kinetic entropy density.

Reconnection outflows have been under intense recent scrutiny, from in situ observations and from simulations. These regions are host to a variety of instabilities and intense energy exchanges, often even superior to the main reconnection site. We report here a number of results drawn from an investigation of simulations. First, the outflows are observed to become unstable to drift instabilities. Second, these instabilities lead to the formation of secondary reconnection sites. Third, the secondary processes are responsible for large energy exchanges and particle energization. Finally, the particle distribution function are modified to become non-Maxwellian and include multiple interpenetrating populations.