Inertial Scale Research Articles

Compaction Evolution and Mechanisms of Granular Materials Due to Gyratory Shearing

Granular systems, no matter whether they are dry or saturated, are commonly encountered in both natural scenarios and engineering applications. In this work, we tackle the compaction problem of both dry and saturated granular systems under gyratory shearing compaction, where particles are subjected to constant pressure and continuous shear rate, which is quite different from the traditional cyclic shearing compaction. Such phenomena are crucial to the compaction of asphalt mixtures or soils in civil engineering and can be extended to other areas, such as powder processing and pharmaceutical engineering. In this study, we investigated the behavior of both dry and fully saturated mono-dispersed granular materials under gyratory shearing compaction using the discrete element method (DEM) and found that the gyratory speed or interstitial fluid viscosity has almost no impact on the compaction behavior, while the pressure and the particle size play more important roles. Additionally, it is the inertial time scale which dictates the compaction behavior under gyratory shearing in most cases; meanwhile, the viscous time scale can also have influence in some conditions. This work determines the similarity and unity between the granular gyratory compaction and the rheology of granular systems, which has direct relevance to various natural and engineering systems.

Electron-only Reconnection and Ion Heating in 3D3V Hybrid-Vlasov Plasma Turbulence

We perform 3D3V hybrid-Vlasov simulations of turbulence with quasi-isotropic, compressible injection near ion scales to mimic the Earth’s magnetosheath plasma, and investigate the novel electron-only reconnection, recently observed by NASA’s Magnetospheric Multiscale mission, and its impact on ion heating. Retaining electron inertia in the generalized Ohm's law enables collisionless magnetic reconnection. Spectral analysis shows a shift from kinetic Alfvén waves to inertial kinetic Alfvén and inertial whistler waves near electron scales. To distinguish the roles of inertial scale and gyroradius (d i and ρ i), three ion beta (β i = 0.25, 1, 4) values are studied. Ion-electron decoupling increases with β i, as ions become less mobile when the injection scale is closer to ρ i than d i, highlighting the role of ρ i in achieving an electron magnetohydrodynamic regime at sub-ion scales. This regime promotes electron-only reconnection in turbulence with small-scale injection at β i ≳ 1. We observe significant ion heating even at large β i, with Q i/ϵ ≈ 69%, 91%, and 96% at β i = 0.25, 1, and 4, respectively. While ion heating is anisotropic at β i ≤ 1 (T i,⊥ > T i,∥), it is marginally anisotropic at β i > 1 (T i,⊥ ≳ T i,∥). Our results show ion turbulent heating in collisionless plasmas is sensitive to the separation between injection scales (λ inj) and ρ i, β i, and finite-k ∥ effects, necessitating further investigation for accurate modeling. These findings have implications for other collisionless astrophysical environments, like high-β plasmas in intracluster medium, where processes such as microinstabilities or shocks may inject energy near ion-kinetic scales.

Decay of magnetohydrodynamic turbulence in the expanding solar wind: WIND observations

We have studied the decay of turbulence in the solar wind. Fluctuations carried by the expanding wind are naturally damped because of flux conservation, slowing down the development of a turbulent cascade. The latter also damps fluctuations but results in plasma heating. We analyzed time series of the velocity and magnetic field ($ v $ and $ B $, respectively) obtained by the WIND spacecraft at 1 au. Fluctuations were recast in terms of the Elsasser variables, $ z v B rho $, with rho being the average density, and their second- and third-order structure functions were used to evaluate the Politano-Pouquet relation, modified to account for the effect of expansion. We find that expansion plays a major role in the Alfv\'enic stream, those for which $z_+ z_-$. In such a stream, expansion damping and turbulence damping act, respectively, on large and small scales for $z_+$, and also balance each other. Instead, $z_-$ is only subject to a weak turbulent damping because expansion is a negligible loss at large scales and a weak source at inertial range scales. These properties are in qualitative agreement with the observed evolution of energy spectra that is described by a double power law separated by a break that sweeps toward lower frequencies for increasing heliocentric distances. However, the data at 1 au indicate that injection by sweeping is not enough to sustain the turbulent cascade. We derived approximate decay laws of energy with distance that suggest possible solutions for the inconsistency: in our analysis, we either overestimated the cascade of $z_ or missed an additional injection mechanism; for example, velocity shear among streams.

Near Subsonic Solar Wind Outflow from an Active Region

During Parker Solar Probe (Parker) Encounter 15 (E15), we observe an 18 hr period of near-subsonic (M S ∼ 1) and sub-Alfvénic (SA), M A ⋘ 1, slow-speed solar wind from 22 to 15.6 R ⊙. As the most extreme SA interval measured to date and skirting the solar wind sonic point, it is the deepest Parker has probed into the formation and acceleration region of the solar wind in the corona. The stream is also measured by Wind and the Magnetosonic Multiscale mission near 1 au at times consistent with ballistic propagation of this slow stream. We investigate the stream source, properties, and potential coronal heating consequences via combining these observations with coronal modeling and turbulence analysis. Through source mapping, in situ evidence, and multipoint arrival time considerations of a candidate coronal mass ejection, we determine the stream is a steady (nontransient), long-lived, and approximately Parker spiral aligned and arises from overexpanded field lines mapping back to an active region. Turbulence analysis of the Elsässer variables shows the inertial range scaling of the z + mode (f ∼ −3/2) to be dominated by the slab component. We discuss the spectral flattening and difficulties associated with measuring the z − spectra, cautioning against making definitive conclusions from the z − mode. Despite being more extreme than prior SA intervals, its turbulent nature does not appear to be qualitatively different from previously observed streams. We conclude that this extreme low-dynamic-pressure solar wind interval (which has the potential for extreme space-weather conditions) is a large, steady structure spanning at least to 1 au.

Cold ion effects in density-asymmetric collisionless magnetic reconnection

The coexistence of low-energy (cold) ions and thermal (warm) ions is commonly observed in space and laboratory plasmas, such as those in magnetopause and fusion fueling processes. In certain events, the cold ion proportion may play a crucial role in plasma processes, especially magnetic reconnection. In this paper, magnetic reconnection with density-asymmetric cold ions is investigated in implicit particle-in-cell (iPIC) simulations. It is found that in such events the reconnection rate decreases as the cold ion distribution depth into the current sheet increases, mainly due to the mass-loading effect. Particularly, a density-peak structure of cold ions is developed in the reconnection region owing to the bounce motion of cold ions entering from the opposite inflow region. In the y–vy phase space where the y-direction is normal to the current sheet, a cold ion ring structure related to the bounce motion is formed and amplified by the Hall electric field. Furthermore, the cold ions become a notable current carrier due to its shorter inertial scale than the warm ions. Consequently, the asymmetry of the cold ion distribution significantly breaks the symmetry in the Hall magnetic field, eventually leading to asymmetric cold ion density peak structure. Such structures can be taken as significant signals of cold ion existence in in situ spacecraft observations.

Extreme statistics and extreme events in dynamical models of turbulence.

We present a study of the intermittent properties of a shell model of turbulence with statistics of ∼10^{7} eddy turn over time, achieved thanks to an implementation on a large-scale parallel GPU factory. This allows us to quantify the inertial range anomalous scaling properties of the velocity fluctuations up to the 24th-order moment. Through a careful assessment of the statistical and systematic uncertainties, we show that none of the phenomenological and theoretical models previously proposed in the literature to predict the anomalous power-law exponents in the inertial range are in agreement with our high-precision numerical measurements. We find that at asymptotically high-order moments, the anomalous exponents tend toward a linear scaling, suggesting that extreme turbulent events are dominated by one leading singularity. We found that systematic corrections to scaling induced by the infrared and ultraviolet (viscous) cutoffs are the main limitations to precision for low-order moments, while high orders are mainly affected by the finite statistical samples.. The high-fidelity numerical results reported in this work offer an ideal benchmark for the development of future theoretical models of intermittency in dynamical systems for either extreme events (high-order moments) or typical fluctuations (low-order moments). For the latter, we show that we achieve a precision in the determination of the inertial range scaling exponents of the order of one part over ten thousand (fifth significant digit), which may be considered a record for out-of-equilibrium fluid-mechanics systems and models.

Vortex polarization and circulation statistics in isotropic turbulence.

We carry out an in-depth analysis of a recently introduced vortex gas model of homogeneous and isotropic turbulence. Direct numerical simulations are used to provide a concrete physical interpretation of one of the model's constituent fields: the degree of vortex polarization. Our investigations shed light on the complexity underlying vortex interactions and reveal, furthermore, that despite some striking similarities, classical and quantum turbulence exhibit distinct structural characteristics, even at inertial range scales. Crucially, these differences arise due to correlations between the polarization and circulation intensity within vortex clusters.

Unsteady Flows and Component Interaction in Turbomachinery

Unsteady component interaction represents a crucial topic in turbomachinery design and analysis. Combustor/turbine interaction is one of the most widely studied topics both using experimental and numerical methods due to the risk of failure of high-pressure turbine blades by unexpected deviation of hot flow trajectory and local heat transfer characteristics. Compressor/combustor interaction is also of interest since it has been demonstrated that, under certain conditions, a non-uniform flow field feeds the primary zone of the combustor where the high-pressure compressor blade passing frequency can be clearly individuated. At the integral scale, the relative motion between vanes and blades in compressor and turbine stages governs the aerothermal performance of the gas turbine, especially in the presence of shocks. At the inertial scale, high turbulence levels generated in the combustion chamber govern wall heat transfer in the high-pressure turbine stage, and wakes generated by low-pressure turbine vanes interact with separation bubbles at low-Reynolds conditions by suppressing them. The necessity to correctly analyze these phenomena obliges the scientific community, the industry, and public funding bodies to cooperate and continuously build new test rigs equipped with highly accurate instrumentation to account for real machine effects. In computational fluid dynamics, researchers developed fast and reliable methods to analyze unsteady blade-row interaction in the case of uneven blade count conditions as well as component interaction by using different closures for turbulence in each domain using high-performance computing. This research effort results in countless publications that contribute to unveiling the actual behavior of turbomachinery flow. However, the great number of publications also results in fragmented information that risks being useless in a practical situation. Therefore, it is useful to collect the most relevant outcomes and derive general conclusions that may help the design of next-gen turbomachines. In fact, the necessity to meet the emission limits defined by the Paris agreement in 2015 obliges the turbomachinery community to consider revolutionary cycles in which component interaction plays a crucial role. In the present paper, the authors try to summarize almost 40 years of experimental and numerical research in the component interaction field, aiming at both providing a comprehensive overview and defining the most relevant conclusions obtained in this demanding research field.

Kinetic stability of Chapman–Enskog plasmas

In this paper, we investigate the kinetic stability of classical, collisional plasma – that is, plasma in which the mean-free-path $\lambda$ of constituent particles is short compared with the length scale $L$ over which fields and bulk motions in the plasma vary macroscopically, and the collision time is short compared with the evolution time. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman–Enskog (CE) expansion in $\lambda /L \ll 1$ , and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless length scales and/or time scales. We find that at sufficiently high plasma $\beta$ , the CE distribution function can be subject to numerous microinstabilities across a wide range of scales. For a particular form of the CE distribution function arising in strongly magnetised plasma (viz. plasma in which the Larmor periods of particles are much smaller than collision times), we provide a detailed analytic characterisation of all significant microinstabilities, including peak growth rates and their associated wavenumbers. Of specific note is the discovery of several new microinstabilities, including one at sub-electron-Larmor scales (the ‘whisper instability’) whose growth rate in certain parameter regimes is large compared with other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of $\lambda$ , the electron inertial scale $d_e$ and the plasma $\beta$ . This work is of general consequence in emphasising the fact that high- $\beta$ collisional plasmas can be kinetically unstable; for strongly magnetised CE plasmas, the condition for instability is $\beta \gtrsim L/\lambda$ . In this situation, the determination of transport coefficients via the standard CE approach is not valid.

Extending a Physics-informed Machine-learning Network for Superresolution Studies of Rayleigh–Bénard Convection

Advancing our understanding of astrophysical turbulence is bottlenecked by the limited resolution of numerical simulations that may not fully sample scales in the inertial range. Machine-learning (ML) techniques have demonstrated promise in upscaling resolution in both image analysis and numerical simulations (i.e., superresolution). Here we employ and further develop a physics-constrained convolutional neural network ML model called “MeshFreeFlowNet” (MFFN) for superresolution studies of turbulent systems. The model is trained on both the simulation images and the evaluated partial differential equations (PDEs), making it sensitive to the underlying physics of a particular fluid system. We develop a framework for 2D turbulent Rayleigh–Bénard convection generated with the Dedalus code by modifying the MFFN architecture to include the full set of simulation PDEs and the boundary conditions. Our training set includes fully developed turbulence sampling Rayleigh numbers (Ra) of Ra = 106–1010. We evaluate the success of the learned simulations by comparing the power spectra of the direct Dedalus simulation to the predicted model output and compare both ground-truth and predicted power spectral inertial range scalings to theoretical predictions. We find that the updated network performs well at all Ra studied here in recovering large-scale information, including the inertial range slopes. The superresolution prediction is overly dissipative at smaller scales than that of the inertial range in all cases, but the smaller scales are better recovered in more turbulent than laminar regimes. This is likely because more turbulent systems have a rich variety of structures at many length scales compared to laminar flows.

Inertial range scaling of inhomogeneous turbulence

We investigate how inhomogeneity influences the $k^{-5/3}$ inertial range scaling of turbulent kinetic energy spectra (with $k$ the wavenumber). For weak statistical inhomogeneity, the energy spectrum can be described as an equilibrium spectrum plus a perturbation. Theoretical arguments suggest that this latter contribution scales as $k^{-7/3}$ . This prediction is assessed using direct numerical simulations of three-dimensional Kolmogorov flow.

Turbulence via intermolecular potential: Uncovering the origin

In recent works, we proposed a hypothesis, according to which turbulence in gases is created by the mean field effect of an intermolecular potential. We discovered that, in a numerically simulated inertial flow, turbulent solutions indeed spontaneously emerge from a laminar initial condition, as observed in nature and experiments. To study the origin of turbulent dynamics, in the current work we examine the equations of a two-dimensional inertial flow, linearized around a large scale constant vorticity state. Remarkably, even in this simplified setting, we find that turbulent dynamics emerge as linearly unstable fluctuations of the velocity divergence.In particular, for the linearized dynamics at a high Reynolds number, we find that, at short time scales, the coupling of the mean field potential with the large scale background vorticity creates linearly unstable and rapidly oscillating fluctuations of the divergence of velocity at inertial scales. In the asymptotic time limit, we find a persistent eigenvector, also aligned largely with the divergence of velocity, which allows these fluctuations to propagate in the form of traveling waves in the Fourier domain. Remarkably, these traveling waves decay at a constant, scale-independent exponential rate. Furthermore, it appears that the Kolmogorov scaling of the kinetic energy is produced by this persistent velocity divergence, due to a cubic relation between the physical time variable, and a pseudo-time variable, in which the dynamics become autonomous. These effects vanish when the mean field potential is removed.

Nonlinear dynamics of large-amplitude, small-scale Alfvén waves

We study large-amplitude, very oblique Alfvén waves at low β, with small gradient length scales, comparable to the ion inertial scale di. Such waves have large density fluctuations and slight dispersion from finite-frequency and finite-ion sound radius effects. We derive a weakly nonlinear evolution equation governing the behavior of the waves in one dimension and categorize the different solitons appearing in different regimes: the regular solitons involve full rotations of the transverse magnetic field similar to modified Korteweg–de Vries (mKdV) solitons (our nonlinear equation reduces to the mKdV equation in the long-wavelength limit). However, for sufficiently small soliton widths, some become singular, small-amplitude solitons with density discontinuities and, are, thus expected to become strongly dissipative in a real plasma. These solutions may be useful in explaining some aspects of the sharp, ion-scale magnetic field rotations (switchbacks) observed in the near-Sun solar wind by Parker Solar Probe.

Simultaneous measurements of kinetic and scalar energy spectrum time evolution in the Richtmyer–Meshkov instability upon reshock

The Richtmyer–Meshkov instability (Richtmyer, Commun. Pure Appl. Maths, vol. 13, issue 2, 1960, pp. 297–319; Meshkov, Fluid Dyn., vol. 4, issue 5, 1972, pp. 101–104) of a twice-shocked gas interface is studied using both high spatial resolution single-shot (SS) and lower spatial resolution, time-resolved, high-speed (HS) simultaneous planar laser-induced fluorescence and particle image velocimetry in the Wisconsin Shock Tube Laboratory's vertical shock tube. The initial condition (IC) is a shear layer with broadband diffuse perturbations at the interface between a helium–acetone mixture and argon. This IC is accelerated by a shock of nominal strength Mach number $M = 1.75$ , and then accelerated again by the transmitted shock that reflects off the end wall of the tube. An ensemble of experiments is analysed after reshock while the interface mixing width grows linearly with time. The kinetic and scalar energy spectra and the terms of their evolution equation are calculated and compared between SS and HS experiments. The inertial range scaling of the scalar power spectrum is found to follow Gibson's relation (Gibson, Phys. Fluids, vol. 11, issue 11, 1968, pp. 2316–2327) as a function of Schmidt number when the effective turbulent Schmidt number is used in place of the material Schmidt number that controls equilibrium scaling. Further, the spatially integrated scalar flux follows similar behaviour observed for the kinetic energy in large eddy simulation studies by Zeng et al. (Phys. Fluids, vol. 30, issue 6, 2018, 064106) while the spatially varying scalar flux exhibits back scatter along the centre of the mixing layer and forward energy transfer in the spike and bubble regions.

Stochastic modeling of turbulent mixing based on a hierarchical swapping of fluid parcels

AbstractTurbulent mixing is an omnipresent phenomenon that constantly affects our everyday life and plays an important role in a variety of industrial applications. The simulation of turbulent mixing poses great challenges, since the full resolution of all relevant length and time scales is associated with an immense computational effort. This limitation can be overcome by only resolving the large‐scale effects and completely model the sub‐grid scales. The development of an accurate sub‐grid mixing model is therefore a key challenge to capture all interactions in the sub‐grid scales. At this place, the hierarchical parcel‐swapping (HiPS) model formulated by A.R. Kerstein [J. Stat. Phys. 153, 142–161 (2013)] represents a computationally efficient and scale‐resolving turbulent mixing model. HiPS mimics the effects of turbulence on time‐evolving, diffusive scalar fields. In HiPS, the diffusive scalar fields or a state space is interpreted as a binary tree structure, which is an alternative approach compared to the most common mixing models. Every level of the tree represents a specific length and time scale, which is based on turbulence inertial range scaling. The state variables are only located at the base of the tree and are treated as fluid parcels. The effects of turbulent advection are represented by stochastic swaps of sub‐trees at rates determined by turbulent time scales associated with the sub‐trees. The mixing only takes places between adjacent fluid parcels and at rates consistent with the prevailing diffusion time scales. In this work, the HiPS model formulation for the simulation of passive scalar mixing is detailed first. Preliminary results for the mean square displacement, passive scalar probability density function (PDF) and scalar dissipation rate are given and reveal the strengths of the HiPS model considering the reduced order and computational efficiency. These model investigations are an important step of further HiPS advancements. The integrated auxiliary binary tree structure allows HiPS to satisfy a large number of criteria for a good mixing model. From this point of view, HiPS is an attractive candidate for modeling the mixing in transported PDF methods.

Wave statistics and energy dissipation of shallow-water breaking waves in a tank with a level bottom

The present study focuses on two-dimensional direct numerical simulations of shallow-water breaking waves, specifically those generated by a wave plate at constant water depths. The primary objective is to quantitatively analyse the dynamics, kinematics and energy dissipation associated with wave breaking. The numerical results exhibit good agreement with experimental data in terms of free-surface profiles during wave breaking. A parametric study was conducted to examine the influence of various wave properties and initial conditions on breaking characteristics. According to research on the Bond number ( $Bo$ , the ratio of gravitational to surface tension forces), an increased surface tension leads to the formation of more prominent parasitic capillaries at the forwards face of the wave profile and a thicker plunging jet, which causes a delayed breaking time and is tightly correlated with the main cavity size. A close relationship between wave statistics and the initial conditions of the wave plate is discovered, allowing for the classification of breaker types based on the ratio of wave height to water depth, $H/d$ . Moreover, an analysis based on inertial scaling arguments reveals that the energy dissipation rate due to breaking can be linked to the local geometry of the breaking crest $H_b/d$ , and exhibits a threshold behaviour, where the energy dissipation approaches zero at a critical value of $H_b/d$ . An empirical scaling of the breaking parameter is proposed as $b = a(H_b/d - \chi _0)^n$ , where $\chi _0 = 0.65$ represents the breaking threshold and $n = 1.5$ is a power law determined through the best fit to the numerical results.

Three‐Dimensional Particle‐In‐Cell Simulations of Electron‐Only Magnetic Reconnection Between Laser‐Produced Plasma Bubbles

AbstractElectron‐only magnetic reconnection, a novel type of reconnection where only electron dynamics is involved, has recently been observed in turbulent plasmas in the Earth's magnetosphere. In this letter, using particle‐in‐cell simulations, we demonstrate that electron‐only reconnection can be created via laser‐plasma interactions. The reconnection current sheet is carried by electrons, and its width is at the electron inertial scale. Moreover, only electron outflow is observed, while the ion outflow is negligible. The duration of the reconnection is found to be within the electron scale, thus there is no sufficient time for ions to respond. The energy conversion during electron‐only reconnection mainly occurs in the vicinity of the X‐line, and is dominated along the perpendicular direction. By analyzing the Poynting flux patterns, we find that the reconnection electric field dominates the whole energy conversion. This study advances our knowledge of the energy dissipation mechanism in the electron‐only reconnection regime.

Compressible two-dimensional turbulence: cascade reversal and sensitivity to imposed magnetic field

We study the impact of compressibility on two-dimensional turbulent flows, such as those modeling astrophysical disks. We demonstrate that the direction of cascade undergoes continuous transition as the Mach number Ma increases, from inverse at Ma = 0, to direct at . Thus, at comparable amounts of energy flow from the pumping scale to large and small scales, in accord with previous data. For supersonic turbulence with the cascade is direct, as in three dimensions, which results in multifractal density field. For that regime () we derive a Kolmogorov-type law for potential forcing and obtain an explicit expression for the third order correlation tensor of the velocity. We further show that all third order structure functions are zero up to first order in the inertial range scales, which is in sharp contrast with incompressible turbulence where the third order structure function, that describes the energy flux associated with the energy cascade is non-zero. The properties of compressible turbulence have significant implications on the amplification of magnetic fields in conducting fluids. We thus demonstrate that imposing external magnetic field on compressible flows of conducting fluids allows to manipulate the flow producing possibly large changes even at small Mach numbers. Thus Zeldovich’s antidynamo theorem, by which at Ma = 0 the magnetic field is zero in the steady state, must be used with caution. Real flows have finite Ma and, however small it is, for large enough values of I, the magnetic flux through the disk, the magnetic field changes the flow appreciably, or rearranges it completely. This renders the limit Ma → 0 singular for non-zero values of I. Of particular interest is the effect of the density multifractality, at which is relevant for astrophysical disks. We demonstrate that in that regime, in the presence of non-zero I the magnetic field energy is enhanced by a large factor as compared to its estimates based on the mean field. Finally, based on the insights described above, we propose a novel two-dimensional Burgers’ turbulence, whose three-dimensional counterpart is used for studies of the large-scale structure of the Universe, as a model for supersonic two-dimensional magnetohydrodynamic flows.

Multi‐Scale Observation of Magnetotail Reconnection Onset: 2. Microscopic Dynamics

AbstractWe analyze the local dynamics of magnetotail reconnection onset using Magnetospheric Multiscale (MMS) data. In conjunction with MMS, the macroscopic dynamics of this event were captured by a number of other ground and space‐based observatories, as is reported in a companion paper. We find that the local dynamics of the onset were characterized by the rapid thinning of the cross‐tail current sheet below the ion inertial scale, accompanied by the growth of flapping waves and the subsequent onset of electron tearing. Multiple kinetic‐scale magnetic islands were detected coincident with the growth of an initially sub‐Alfvénic, demagnetized tailward ion exhaust. The onset and rapid enhancement of parallel electron inflow at the exhaust boundary was a remote signature of the intensification of reconnection Earthward of the spacecraft. Two secondary reconnection sites are found embedded within the exhaust from a primary X‐line. The primary X‐line was designated as such on the basis that (a) while multiple jet reversals were observed in the current sheet, only one reversal of the electron inflow was observed at the high‐latitude exhaust boundary, (b) the reconnection electric field was roughly five times larger at the primary X‐line than the secondary X‐lines, and (c) energetic electron fluxes increased and transitioned from anti‐field‐aligned to isotropic during the primary X‐line crossing, indicating a change in magnetic topology. The results are consistent with the idea that a primary X‐line mediates the reconnection of lobe magnetic field lines and accelerates electrons more efficiently than its secondary X‐line counterparts.

Turbulence Properties of Interplanetary Coronal Mass Ejections in the Inner Heliosphere: Dependence on Proton Beta and Flux Rope Structure

Interplanetary coronal mass ejections (ICMEs) have low proton beta across a broad range of heliocentric distances and a magnetic flux rope structure at large scales, making them a unique environment for studying solar wind fluctuations. Power spectra of magnetic field fluctuations in 28 ICMEs observed between 0.25 and 0.95 au by Solar Orbiter and Parker Solar Probe have been examined. At large scales, the spectra were dominated by power contained in the flux ropes. Subtraction of the background flux rope fields increased the mean spectral index from −5/3 to −3/2 at kd i ≤ 10−3. Rope subtraction also revealed shorter correlation lengths in the magnetic field. The spectral index was typically near −5/3 in the inertial range at all radial distances regardless of rope subtraction and steepened to values consistently below −3 with transition to kinetic scales. The high-frequency break point terminating the inertial range evolved approximately linearly with radial distance and was closer in scale to the proton inertial length than the proton gyroscale, as expected for plasma at low proton beta. Magnetic compressibility at inertial scales did not show any significant correlation with radial distance, in contrast to the solar wind generally. In ICMEs, the distinctive spectral properties at injection scales appear mostly determined by the global flux rope structure while transition-kinetic properties are more influenced by the low proton beta; the intervening inertial range appears independent of both ICME features, indicative of a system-independent scaling of the turbulence.