Inertial Scale Research Articles

Hall Cascade with Fractional Magnetic Helicity in Neutron Star Crusts

Abstract The ohmic decay of magnetic fields in the crusts of neutron stars is generally believed to be governed by Hall drift, which leads to what is known as a Hall cascade. Here we show that helical and fractionally helical magnetic fields undergo strong inverse cascading like in magnetohydrodynamics (MHD), but the magnetic energy decays more slowly with time t: instead of ∝t −2/3 in MHD. Even for a nonhelical magnetic field there is a certain degree of inverse cascading for sufficiently strong magnetic fields. The inertial range scaling with wavenumber k is compatible with earlier findings for the forced Hall cascade, i.e., proportional to k −7/3, but in the decaying cases, the subinertial range spectrum steepens to a novel k 5 slope instead of the k 4 slope in MHD. The energy of the large-scale magnetic field can increase quadratically in time through inverse cascading. For helical fields, the energy dissipation is found to be inversely proportional to the large-scale magnetic field and proportional to the fifth power of the rms magnetic field. For neutron star conditions with an rms magnetic field of a few times , the large-scale magnetic field might only be , while still producing magnetic dissipation of for thousands of years, which could manifest itself through X-ray emission. Finally, it is shown that the conclusions from local unstratified models agree rather well with those from stratified models with boundaries.

Turbulent Energy Spectrum via an Interaction Potential

For a large system of identical particles interacting by means of a potential, we find that a strong large scale flow velocity can induce motions in the inertial range via the potential coupling. This forcing lies in special bundles in the Fourier space, which are formed by pairs of particles. These bundles are not present in the Boltzmann, Euler and Navier-Stokes equations, because they are destroyed by the Bogoliubov-Born-Green-Kirkwood-Yvon formalism. However, measurements of the flow can detect certain bulk effects shared across these bundles, such as the power scaling of the kinetic energy. We estimate the scaling effects produced by two types of potentials: the Thomas-Fermi interatomic potential (as well as its variations, such as the Ziegler-Biersack-Littmark potential), and the electrostatic potential. In the near-viscous inertial range, our estimates yield the inverse five-thirds power decay of the kinetic energy for both the Thomas-Fermi and electrostatic potentials. The electrostatic potential is also predicted to produce the inverse cubic power scaling of the kinetic energy at large inertial scales. Standard laboratory experiments confirm the scaling estimates for both the Thomas-Fermi and electrostatic potentials at near-viscous scales. Surprisingly, the observed kinetic energy spectrum in the Earth atmosphere at large scales behaves as if induced by the electrostatic potential. Given that the Earth atmosphere is not electrostatically neutral, we cautiously suggest a hypothesis that the atmospheric kinetic energy spectra in the inertial range are indeed driven by the large scale flow via the electrostatic potential coupling.

Constraining Ion-Scale Heating and Spectral Energy Transfer in Observations of Plasma Turbulence.

We perform a statistical study of the turbulent power spectrum at inertial and kinetic scales observed during the first perihelion encounter of the Parker Solar Probe. We find that often there is an extremely steep scaling range of the power spectrum just above the ion-kinetic scales, similar to prior observations at 1A.U., with a power-law index of around -4. Based on our measurements, we demonstrate that either a significant (>50%) fraction of the total turbulent energy flux is dissipated in this range of scales, or the characteristic nonlinear interaction time of the turbulence decreases dramatically from the expectation based solely on the dispersive nature of nonlinearly interacting kinetic Alfvén waves.

Comparison of the Atmospheric and Oceanic Boundary Layers During Convection and their Latitudinal Dependence

AbstractThe boundary layers of the atmosphere and the ocean are compared during convection, and their latitudinal dependence is investigated. The results are applied to examine the parameterization of the boundary layer depth in the K‐profile parameterization (KPP) model. The bulk Richardson number Rib varies excessively with time in the high‐latitude (HL) oceanic boundary layer (OBL) without unresolved shear , as a result of inertial oscillation. Inclusion of is also necessary in the atmospheric boundary layer (ABL) to mitigate the large variation of Rib with wind stress. Stratification and velocity shear near the boundary layer height/depth are stronger and thicker at low latitudes (LLs), where the Ekman length scale is larger and the inertial time scale is longer. This enhanced shear makes the entrainment buoyancy flux larger at LL. Analysis of the turbulent kinetic energy (TKE) budget in the entrainment zone is carried out to explain the variation of Rib depending on the boundary layer and the latitude. This analysis shows that the TKE production in the entrainment zone is dominated by shear production at LL, but by the TKE flux at HL, and that represents the contribution from the TKE flux to the entrainment zone. The enhancement of vertical TKE by Langmuir circulation (LC) does not depend on the latitude, but it decreases with depth faster at LL. The result suggests that the parameterization of the boundary layer depth in the KPP model should be different depending on whether it is the ABL or the OBL and depending on the latitude.

MMS Observations of Intense Whistler Waves Within Earth's Supercritical Bow Shock: Source Mechanism and Impact on Shock Structure and Plasma Transport

AbstractThe properties of whistler waves near lower‐hybrid frequencies within Earth's quasi‐perpendicular bow shock are examined using data from the Magnetospheric Multiscale (MMS) mission. These waves appear as right‐hand polarized wave packets propagating upstream obliquely to the magnetic field and shock normal with phase speeds from a few hundred up to 1,600 km/s. The wavelengths are near the ion inertial length scale (λ∼ 0.3–1.3 λi). Detailed analysis finds characteristics consistent with the modified two‐stream instability mechanism driven by the reflected ion and electron drift. Correlations between wave and electron anisotropy variations reveal that the whistlers are affecting electron dynamics and thus their perpendicular and parallel temperatures. The electron signatures are explainable via the interaction of magnetized electrons in the whistler induced nonmonotonic magnetic fields. These waves have intense magnetic fields (δB/B∘∼ 0.1–1) and carry sizable currents that are a significant fraction of the thermal current (|J/Jvte|∼ 0.1–0.5). The whistler‐induced currents and the electron anisotropies are sufficiently large to respectively excite high‐frequency (HF) electrostatic (>100 Hz) and HF whistler waves (f∼ 0.1–0.5 fce). Energy dissipation J·E from whistlers at 30 Hz and below range from a few thousandths to few hundredths of μW/m3. Comparisons reveal that plasma energy is converted to wave energy in the foot, whereas wave energy gets dissipated into the plasma in the ramp, where irreversible heating occurs. These observed features are indicative of an intricate coupling between small‐scale interaction processes and larger‐scale structure transpiring within the layer. Such a characterization is only made possible now with the MMS high‐time‐resolution measurements.

In Situ Observation of Hall Magnetohydrodynamic Cascade in Space Plasma.

We present estimates of the turbulent energy-cascade rate derived from a Hall-magnetohydrodynamic (MHD) third-order law. We compute the contribution from the Hall term and the MHD term to the energy flux. Magnetospheric Multiscale (MMS) data accumulated in the magnetosheath and the solar wind are compared with previously established simulation results. Consistent with the simulations, we find that at large (MHD) scales, the MMS observations exhibit a clear inertial range dominated by the MHD flux. In the subion range, the cascade continues at a diminished level via the Hall term, and the change becomes more pronounced as the plasma beta increases. Additionally, the MHD contribution to interscale energy transfer remains important at smaller scales than previously thought. Possible reasons are offered for this unanticipated result.

Nanoflare Theory and Stochastic Reconnection

Abstract Local magnetic reversals are an inseparable part of magnetohydrodynamic turbulence whose collective outcome may lead to a global reconnection with a rate independent of the small scale physics—stochastic reconnection. We show that this picture is related to the nanoflare theory, which is one of the most plausible models to solve the coronal heating problem. The magnetic field follows the turbulent flow in a statistical sense by means of stochastic flux freezing. Hence the turbulence, which bends and stretches the initially smooth field, will tend to increase the field’s spatial complexity. Strong magnetic shears associated with such a highly tangled field can trigger local reversals and field annihilations on a wide range of inertial scales, which convert magnetic energy into kinetic and thermal energy respectively. The former enhances the turbulence while the latter enhances heat generation on any inertial scale. These theoretical predictions are supported by scaling laws and simulations.

Electron-only Reconnection in Kinetic-Alfvén Turbulence

Abstract We study numerically small-scale reconnection events in kinetic, low-frequency, quasi-2D turbulence (termed kinetic-Alfvén turbulence). Using 2D particle-in-cell simulations, we demonstrate that such turbulence generates reconnection structures where the electron dynamics do not couple to the ions, similarly to the electron-only reconnection events recently detected in the Earth’s magnetosheath by Phan et al. Electron-only reconnection is thus an inherent property of kinetic-Alfvén turbulence, where the electron current sheets have limited anisotropy and, as a result, their sizes are smaller than the ion inertial scale. The reconnection rate of such electron-only events is found to be close to 0.1.

Evolution of electron current layer during anti-parallel magnetic reconnection

Electron current layer (ECL) in the diffusion region plays an important role on energy dispassion and generation of a magnetic island during collisionless magnetic reconnection. In this study, kinetic simulations with high-resolution grids are performed to investigate the evolution of ECL during anti-parallel magnetic reconnection. It is found that ECL splits into two sublayers at the electron inertial scale, not long after the triggering of reconnection. The sublayers keep moving away from each other until reconnection rate reaches the maximum. We find the formation reason and maintaining mechanism of these sublayer structures of the ECL. When electrons flow toward the midplane, out-of-plane velocity is increased by the reconnection electric field. The deflection of magnetic field makes the out-of-plane component of velocity partly converted to the z direction. Electron flows pass through the mid-plane with super-Alfvenic speed. When they enter the other side, the increasing magnetic field makes velocity in the z direction gradually converted to the out-of-plane. Slowdown of the flows causes the density accumulation at the two sides of the mid-plane. The redistribution of electrons brings an extra pressure gradient to the ECS region, balancing the electric force and Ampere force.

Heating of Heavy Ions in Low-beta Compressible Turbulence

Abstract Enhancement of minor ions such as 3He and heavy ions in flare-associated solar energetic particle (SEP) events remains one of the major puzzles in heliophysics. In this work, we use 3D hybrid simulations (kinetic protons and fluid electrons) to investigate particle energization in a turbulent low-beta environment similar to solar flares. It is shown that in this regime the injected large-amplitude Alfvén waves develop into compressible and anisotropic turbulence, which efficiently heats thermal ions of different species. We find that temperature increase of heavy ions is inversely proportional to the charge-to-mass ratio, which is consistent with observations of impulsive SEP events. Further analysis reveals that ions are energized by interacting with nearly perpendicular magnetosonic waves near a proton inertial scale.

Coupling Large Eddies and Waves in Turbulence: Case Study of Magnetic Helicity at the Ion Inertial Scale

In turbulence, for neutral or conducting fluids, a large ratio of scales is excited because of the possible occurrence of inverse cascades to large, global scales together with direct cascades to small, dissipative scales, as observed in the atmosphere and oceans, or in the solar environment. In this context, using direct numerical simulations with forcing, we analyze scale dynamics in the presence of magnetic fields with a generalized Ohm’s law including a Hall current. The ion inertial length ϵ H serves as the control parameter at fixed Reynolds number. Both the magnetic and generalized helicity—invariants in the ideal case—grow linearly with time, as expected from classical arguments. The cross-correlation between the velocity and magnetic field grows as well, more so in relative terms for a stronger Hall current. We find that the helical growth rates vary exponentially with ϵ H , provided the ion inertial scale resides within the inverse cascade range. These exponential variations are recovered phenomenologically using simple scaling arguments. They are directly linked to the wavenumber power-law dependence of generalized and magnetic helicity, ∼ k − 2 , in their inverse ranges. This illustrates and confirms the important role of the interplay between large and small scales in the dynamics of turbulent flows.

Homogenization for Generalized Langevin Equations with Applications to Anomalous Diffusion

We study homogenization for a class of generalized Langevin equations (GLEs) with state-dependent coefficients and exhibiting multiple time scales. In addition to the small mass limit, we focus on homogenization limits, which involve taking to zero the inertial time scale and, possibly, some of the memory time scales and noise correlation time scales. The latter are meaningful limits for a class of GLEs modeling anomalous diffusion. We find that, in general, the limiting stochastic differential equations for the slow degrees of freedom contain non-trivial drift correction terms and are driven by non-Markov noise processes. These results follow from a general homogenization theorem stated and proven here. We illustrate them using stochastic models of particle diffusion.

Hierarchical Parcel‐Swapping: An efficient mixing model for turbulent reactive flows

AbstractHierarchical Parcel‐Swapping (HiPS) developed by A.R. Kerstein [J. Stat. Phys. 153, 142‐161 (2013)] is a computationally efficient and novel model for the effects of turbulence on time‐evolving, diffusive scalar fields. The characteristic feature of HiPS is the interpretation of the one‐dimensional flow domain or a state space as a binary tree structure. Every tree level corresponds to a specific length and time scale, which is based on a turbulence inertial range scaling. The state variables reside at the base of the tree and are interpreted 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 of adjacent fluid parcels is done at rates consistent with the prevailing diffusion time scales. In this work, we investigate the influence of turbulent time scale variations on an isothermal series‐parallel reaction scheme. The production of a desired chemical species is evaluated by means of a defined selectivity and is strongly affected by the underlying mixing time scales.

Spatio-Temporal Dynamics of Jerky Flow in High-Entropy Alloy at Extremely Low Temperature

Despite a large body of literature, mechanisms contributing to low temperature jerky flow remain controversial. Here, we report a cross over from a smooth at room and liquid nitrogen temperatures to serrated plastic flow at 4.2 K in high-entropy CrMnFeCoNi alloy. We show that the jerky flow results from an interaction between dislocation inertial motion with Lomer-Cottrell locks. The instability is shown to result from a competition between the inertial and viscous time scales characterized by a Deborah number. A dynamical analysis shows that jerky flow is chaotic characterized by a finite correlation dimension and a positive Lyapunov exponent.

Fast Recursive Reconnection and the Hall Effect: Hall-MHD Simulations

Abstract Magnetohydrodynamic (MHD) theory and simulations have shown that reconnection is triggered via a fast “ideal” tearing instability in current sheets whose inverse aspect ratio decreases to , with S as the Lundquist number defined by the half-length L of the current sheet (of a thickness of 2a). Ideal tearing, in 2D sheets, triggers a hierarchical collapse via stretching of X-points and recursive instability. At each step, the local Lundquist number decreases, until the subsequent sheet thickness either approaches kinetic scales or the Lundquist number becomes sufficiently small. Here we carry out a series of Hall-MHD simulations to show how the Hall effect modifies recursive reconnection once the ion inertial scale is approached. We show that as the ion inertial length becomes of the order of the inner, singular layer thickness at some step of the recursive collapse, reconnection transits from the plasmoid-dominant regime to an intermediate plasmoid+Hall regime and then to the Hall-dominant regime. The structure around the X-point, the reconnection rate, the dissipation property, and the power spectra are also modified significantly by the Hall effect.

Dependence of 3D Self-correlation Level Contours on the Scales in the Inertial Range of Solar Wind Turbulence

Abstract The self-correlation level contours at the 1010 cm scale reveal a 3D isotropic feature in the slow solar wind and a quasi-anisotropic feature in the fast solar wind. However, the 1010 cm scale is approximately near the low-frequency break (outer scale of turbulence cascade), especially in the fast wind. How the self-correlation level contours behave with dependence on the scales in the inertial range of solar wind turbulence remains unknown. Here we present the 3D self-correlation function level contours and their dependence on the scales in the inertial range for the first time. We use data at 1 au from instruments on the Wind spacecraft in the period 2005–2018. We show the 3D isotropic self-correlation level contours of the magnetic field in the inertial range of both slow and fast solar wind turbulence. We also find that the self-correlation level contours of the velocity in the inertial range present 2D anisotropy with an elongation in the perpendicular direction and 2D isotropy in the plane perpendicular to the mean magnetic field. These results indicate differences between the magnetic field and the velocity, providing new clues to interpret the solar wind turbulence on the inertial scale.

Scintillation Arc Brightness and Electron Density for an Analytical Noodle Model

Abstract We show that narrow filaments or sheets of over- or under-dense plasma, or “noodles,” with fluctuations of scattering phase of less than a radian, can form the scintillation arcs seen for many pulsars. The required local fluctuations of electron density are indefinitely small. We assume a cosine profile for the electron column and find the scattered field by analytic Kirchhoff integration. For a large electron column, corresponding to large amplitude of phase variation, the stationary-phase approximation is accurate; we call this regime “ray optics”. For smaller-amplitude phase variation, the stationary-phase approximation is inaccurate or inapplicable; we call this regime “wave optics”. We show that scattering is most efficient when the width of the strip equals that of one pair of Fresnel zones, and in the wave-optics regime. We show that the resolution of present observations is about 100 Fresnel zones on the scattering screen. Incoherent superposition of strips within a resolution element tends to increase the scattered field. We find that observations match a single noodle per resolution element with phase of up to 12 radians; or many noodles per resolution element with arbitrarily small phase variation each, for net phase of less than a radian. Observations suggest a minimum radius for noodles of about 650 km, comparable to the ion inertial scale or the ion cyclotron radius in the scattering plasma.

Turbulence Coherence Within Canonical and Realistic Aeolian Dune-Field Roughness Sublayers

Large-eddy simulation has been used to study the formation and spatial nature of inertia-dominated turbulent flows responding to aeolian sand dunes. The former is recovered from simulations initialized with a Reynolds-averaged flow, without any small-scale features, which highlights the emergence of salient structures within the dune-field roughness sublayer (RSL). The latter is based upon computation of integral lengths. In the interest of generality, these exercises are based upon flow over canonical dune geometries—which serve as a comparative benchmark—and flow over a section of the White Sands National Monument aeolian dune field in southern New Mexico. These cases, thus, capture a vast range of complexity. In both applications, we report the emergence of mixing-layer-like processes—as per results for other canopy flows—although the distinct geometric nature of the dunes shows the prevalence of a persistent interdune roller, which is aligned most closely with the streamwise direction. In order to demonstrate underlying similarities in the processes occuring above idealized and natural dune fields, we normalize the integral lengths by characteristic length scales: vorticity thickness, attached-eddy-hypothesis mixing length, and dissipation length. This exercise reveals a distinct growth and collapse pattern that is robust across all considered dune arrangements. Herein, ‘growth’ refers to the stage of downflow thickening of vortices produced via vortex shedding off the upflow dune; growth is regulated by the lesser of the distance to the wall or distance to the upflow dune, where the latter marks the beginning of the ‘collapse’ stage. Both are compliant with the notion of wall-attached eddies. In the RSL, we demonstrate that the integral lengths exhibit an optimal collapse when normalized by vorticity thickness, while inertial layer scaling is attained as close as one dune height above the top of the dune canopy. These results help to establish dune-field RSL dynamics within the broader context of canopy turbulence, which is important given the relatively greater efforts devoted to flows over vegetative canopies and urban environments.

Droplet–turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions

We perform direct numerical simulations (DNS) of emulsions in homogeneous isotropic turbulence using a pseudopotential lattice-Boltzmann (PP-LB) method. Improving on previous literature by minimizing droplet dissolution and spurious currents, we show that the PP-LB technique is capable of long stable simulations in certain parameter regions. Varying the dispersed-phase volume fraction$\unicode[STIX]{x1D719}$, we demonstrate that droplet breakup extracts kinetic energy from the larger scales while injecting energy into the smaller scales, increasingly with higher$\unicode[STIX]{x1D719}$, with approximately the Hinze scale (Hinze,AIChE J., vol. 1 (3), 1955, pp. 289–295) separating the two effects. A generalization of the Hinze scale is proposed, which applies both to dense and dilute suspensions, including cases where there is a deviation from the$k^{-5/3}$inertial range scaling and where coalescence becomes dominant. This is done using the Weber number spectrum$We(k)$, constructed from the multiphase kinetic energy spectrum$E(k)$, which indicates the critical droplet scale at which$We\approx 1$. This scale roughly separates coalescence and breakup dynamics as it closely corresponds to the transition of the droplet size ($d$) distribution into a$d^{-10/3}$scaling (Garrettet al.,J. Phys. Oceanogr., vol. 30 (9), 2000, pp. 2163–2171; Deane & Stokes,Nature, vol. 418 (6900), 2002, p. 839). We show the need to maintain a separation of the turbulence forcing scale and domain size to prevent the formation of large connected regions of the dispersed phase. For the first time, we show that turbulent emulsions evolve into a quasi-equilibrium cycle of alternating coalescence and breakup dominated processes. Studying the system in its state-space comprising kinetic energy$E_{k}$, enstrophy$\unicode[STIX]{x1D714}^{2}$and the droplet number density$N_{d}$, we find that their dynamics resemble limit cycles with a time delay. Extreme values in the evolution of$E_{k}$are manifested in the evolution of$\unicode[STIX]{x1D714}^{2}$and$N_{d}$with a delay of${\sim}0.3{\mathcal{T}}$and${\sim}0.9{\mathcal{T}}$respectively (with${\mathcal{T}}$the large eddy timescale). Lastly, we also show that flow topology of turbulence in an emulsion is significantly more different from single-phase turbulence than previously thought. In particular, vortex compression and axial straining mechanisms increase in the droplet phase.

Role of reconnection in inertial kinetic-Alfvén turbulence

In a weakly collisional, low-electron-beta plasma, large-scale Alfv\'en turbulence transforms into inertial kinetic-Alfv\'en turbulence at scales smaller than the ion microscale (gyroscale or inertial scale). We propose that at such kinetic scales, the nonlinear dynamics tend to organize turbulent eddies into thin current sheets, consistent with the existence of two conserved integrals of the ideal equations, energy and helicity. The formation of strongly anisotropic structures is arrested by the tearing instability that sets a critical aspect ratio of the eddies at each scale $a$ in the plane perpendicular to the guide field. This aspect ratio is defined by the balance of the eddy turnover rate and the tearing rate, and varies from $(d_e/a)^{1/2}$ to $d_e/a$ depending on the assumed profile of the current sheets. The energy spectrum of the resulting turbulence varies from $k^{-8/3}$ to $k^{-3}$, and the corresponding spectral anisotropy with respect to the strong background magnetic field from $k_z\lesssim k_\perp^{2/3}$ to $k_z\lesssim k_\perp$.