Particle energization inside plasmoids: numerical and analytical investigations

<div> <div> <div> <p>In an idealized system where four magnetic islands interact in a two-dimensional periodic setting, we follow the detailed evolution of current sheets forming in between the islands, as a result of an enforced large-scale merging by magnetohydrodynamic (MHD) simulation. The large-scale island merging is triggered by a perturbation to the velocity field, which drives one pair of islands move towards each other while the other pair of islands are pushed away from one another. The "X"-point located in the midst of the four islands is locally unstable to the perturbation and collapses, producing a current sheet in between with enhanced current and mass density. Using grid-adaptive resistive magnetohydrodynamic (MHD) simulations, we establish that slow near-steady Sweet-Parker reconnection transits to a chaotic, multi-plasmoid fragmented state, when the Lundquist number exceeds about 3×10<sup>4</sup>, well in the range of previous studies on plasmoid instability. The extreme resolution employed in the MHD study shows significant magnetic island substructures. Turbulent and chaotic flow patters are also observed inside the islands. We set forth to explore how charged particles can be accelerated in embedded mini-islands within larger (monster)-islands on the sheet. We study the motion of the particles in a MHD snapshot at a fixed instant of time by the Test-Particle Module incorporated in AMRVAC (). The planar MHD setting artificially causes the largest acceleration in the ignored third direction, but does allow for full analytic study of all aspects leading to the acceleration and the in-plane, projected trapping of particles within embedded mini-islands. The analytic result uses a decomposition of the test particle velocity in slow and fast changing components, akin to the Reynolds decomposition in turbulence studies. The analytic results allow a complete fit to representative proton test particle simulations, which after initial non-relativistic motion throughout the monster island, show the potential of acceleration within a mini-island beyond (√2/2)c≈0.7c, at which speed the acceleration is at its highest efficiency. Acceleration to several hundreds of GeVs can happen within several tens of seconds, for upward traveling protons in counterclockwise mini-islands of sizes smaller than the proton gyroradius.</p> </div> </div> </div><div></div><div></div>

Flow around an oscillating grid in water and shear-thinning polymer solution at low Reynolds number

The study of turbulence in complex fluids is of great interest in many environmental and industrial applications, in which the interactions between liquid phase rheology, turbulence, and other phenomena such as mixing or heat and mass transfer have to be understood. Oscillating grid stirred tanks have been used for many purposes in research involving turbulence. However, the mechanisms of turbulence production by the oscillating grid itself have never been studied, and oscillating grid turbulence (OGT) remained undescribed in non-Newtonian, shear-thinning, dilute polymer solutions until recently (Lacassagne et al., in Phys Fluids 31(8):083,102, 2019). The aim of this paper is to study the influence of the shear-thinning property of dilute polymer solutions (DPS), such as xanthan gum (XG), on mean flow, oscillatory flows, and turbulence around an oscillating grid. Liquid phase velocity is measured by particle image velocimetry (PIV) in a vertical plane above the central grid bar. Mean, oscillatory and turbulent components of the velocity fields are deduced by triple Hussain–Reynolds decomposition based on grid phase-resolved measurements. Outside of the grid swept region, the amplitude of oscillatory fluctuations quickly become negligible compared to that of turbulent fluctuations, and the triple and classical Reynolds decomposition become equivalent. Oscillatory jets and wakes behind the grid and their interactions are visualized. Turbulent (Reynolds) and oscillatory stresses are used to evidence a modification of oscillatory flow and turbulence intensity repartition in and around the grid swept region. Energy transfer terms between mean, oscillatory and turbulent flows are estimated and used to describe turbulence production in the grid swept region. Energy is injected by the grid into the oscillatory component. In water, it is transferred to turbulence mostly inside the grid swept region. In DPS, oscillatory flow persists outside of the grid swept zone. Energy is transferred not only to turbulence , in the grid swept region, and far from the tank’s walls, but also to the mean flow, leading to an enhancement of the latter. Mean flow production and enhancement mechanisms are explainable by oscillatory jet variable symmetry and intensity, and by time- and space-variable viscosity. Backward transfer from turbulence to oscillatory flow is also evidenced in DPS. Finally, using phased root mean square (rms) values of turbulent velocity fluctuations, it is shown that in water, the decay of turbulence intensity behind an oscillating grid can be related to the decay of fixed grid turbulence for specific grid positions, a result no longer valid in DPS. Graphic abstract

A critical assessment of turbulence models for 1D core-collapse supernova simulations

It has recently been proposed that global or local turbulence models can be used to simulate core-collapse supernova explosions in spherical symmetry (1D) more consistently than with traditional approaches for parametrized 1D models. However, a closer analysis of the proposed schemes reveals important consistency problems. Most notably, they systematically violate energy conservation as they do not balance buoyant energy generation with terms that reduce potential energy, thus failing to account for the physical source of energy that buoyant convection feeds on. We also point out other non-trivial consistency requirements for viable turbulence models. The Kuhfuss model from the 1980s proves more consistent than the newly proposed approaches for supernovae, but still cannot account naturally for all the relevant physics for predicting explosion properties. We perform numerical simulations for a $20 \, \mathrm{M}_\odot$ progenitor to further illustrate problems of 1D turbulence models. If the buoyant driving term is formulated in a conservative manner, the explosion energy of ${\sim }2\times 10^{51}\, \mathrm{erg}$ for the corresponding non-conservative turbulence model is reduced to $\lt 10^{48} \, \mathrm{erg}$ even though the shock expands continuously. This demonstrates that the conservation problem cannot be ignored. Although plausible energies can be reached using an energy-conserving model when turbulent viscosity is included, it is doubtful whether the energy budget of the explosion is regulated by the same mechanism as in multidimensional models. We conclude that 1D turbulence models based on a spherical Reynolds decomposition cannot provide a more consistent approach to supernova explosion and remnant properties than other phenomenological approaches before some fundamental problems are addressed.

Conditions for validity of mean flow stability analysis

This article provides theoretical conditions for the use and meaning of a stability analysis around a mean flow. As such, it may be considered as an extension of the works by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to non-parallel flows and by Turton et al. (Phys. Rev. E, vol. 91 (4), 2015, 043009) to broadband flows. Considering a Reynolds decomposition of the flow field, the spectral (or temporal Fourier) mode of the fluctuation field is found to be equal to the action on a turbulent forcing term by the resolvent operator arising from linearisation about the mean flow. The main result of the article states that if, at a particular frequency, the dominant singular value of the resolvent is much larger than all others and if the turbulent forcing at this frequency does not display any preferential direction toward one of the suboptimal forcings, then the spectral mode is directly proportional to the dominant optimal response mode of the resolvent at this frequency. Such conditions are generally met in the case of weakly non-parallel open flows exhibiting a convectively unstable mean flow. The spatial structure of the singular mode may in these cases be approximated by a local spatial stability analysis based on parabolised stability equations (PSE). We have also shown that the frequency spectrum of the flow field at any arbitrary location of the domain may be predicted from the frequency evolution of the dominant optimal response mode and the knowledge of the frequency spectrum at one or more points. Results are illustrated in the case of a high Reynolds number turbulent backward facing step flow.

On the use of the Reynolds decomposition in the intermittent region of turbulent boundary layers

In the analysis of velocity fields in turbulent boundary layers, the traditional Reynolds decomposition is universally employed to calculate the fluctuating component of streamwise velocity. Here, we demonstrate the perils of such a determination of the fluctuating velocity in the context of structural analysis of turbulence when applied in the outer region where the flow is intermittently turbulent at a given wall distance. A new decomposition is postulated that ensures non-turbulent regions in the flow do not contaminate the fluctuating velocity components in the turbulent regions. Through this new decomposition, some of the typical statistics concerning the scale and structure of turbulent boundary layers are revisited.

PIV Measurements of Turbulent Flows Over Single and Dual Rectangular Cavities

Particle Image Velocimetry (PIV) was used to measure the turbulent flow fields over single and dual rectangular cavities. Four sets of PIV measurements were acquired, corresponding to two Reynolds numbers per each cavity configuration. The cavity depth based Reynolds number was varied between 21,000 and 42,000, while the cavity length-to-depth ratio was fixed at four. Galilean decomposition is used to present instantaneous velocity fields. Turbulent velocity fields are presented using Reynolds decomposition into mean and fluctuating components. Characteristics of the instantaneous and time-averaged velocity fields corresponding to a single cavity configuration are in agreement with the observations from previous studies. All mean flow field results display a large vortical structure spanning the entire length and height of each cavity. In the case of a dual cavity configuration, the free shear layer and trailing edge regions of the second cavity were found to always display higher streamwise and crosswise flow fluctuations in comparison with the first cavity. Furthermore, a wider free shear layer region is observed in the second cavity, in comparison with the first cavity.

Eulerian Three-Phase Flow Model Applied to Trickle-Bed Reactors

The majority of publications and monographs present investigations which concern exclusively twophase flows and particulary dispersed flows. However, in the chemical and petrochemical industries as well as in refineries or bioengineering, besides the apparatuses of two-phase flows there is an extremely broad region of three-phase systems, where the third phase constitutes the catalyst in form of solid particles (Duduković et al., 2002; Martinez et al., 1999) in either fixed bed or slurry reactors. Therefore, the goal of this study is to develop macroscopic, averaged balances of mass, momentum and energy for systems with three-phase flow. Local instantaneous conservation equations are derived, which constitute the basis of the method applied, and are averaged by means of Euler’s volumetric averaging procedure. In order to obtain the final balance equations which define the averaged variables of the system, the weighted averaging connected with Reynolds decomposition is used. The derived conservation equations of the trickle-bed reactor (mass, momentum and energy balance) and especially the interphase effects appearing in these equations are discussed in detail.

Effect of Reynolds Number on the Turbulent Flow Structure in the Near-Wall Region of an Impinging Round Jet

Time-Resolved Particle Image Velocimetry was used to study the effect of the Reynolds number on the turbulent flow structure of a submerged water jet impinging normally on a smooth and flat surface. A fully developed turbulent jet and a semi-confined flow configuration ensured properly characterized boundary conditions allowing for straightforward assessment of turbulence models and numerical schemes. The Reynolds number based on jet mean exit velocity was 5,000, 10,030 and 15,050 while the pipe-to-plate separation distance was fixed at two diameters. Turbulent velocity fields are presented using Reynolds decomposition into mean and fluctuating components while Proper Orthogonal Decomposition (POD) analysis identified the most energetic coherent structures in the stagnation and wall-jet regions.