Helicity Transport Research Articles

Lagrangian investigation of the correlation of helicity with coherent flow characteristics for turbulent transport

The correlation between helicity and turbulent transport in turbulent flows is probed with the use of direct numerical simulation and Lagrangian scalar tracking. Channel flow and plane Couette flow at friction Reynolds number 300 and Lagrangian data along the trajectories of fluid particles and passive particles with Schmidt numbers 0.7 and 6 are used. The goal is to identify characteristics of the flow that enhance turbulent transport from the wall, and how flow regions that exhibit these characteristics are related to helicity. The relationship between vorticity and relative helicity along particle trajectories is probed, and the relationship between the distribution of helicity conditioned on Reynolds stress quadrants is also evaluated. More importantly, the correlation between relative helicity density and the alignment of vorticity with velocity vectors and eigenvectors of the rate of strain tensor is presented. Separate computations for particles that disperse the farthest into the flow field and those that disperse the least are conducted to determine the flow structures that contribute to turbulent dispersion. The joint distribution of helicity and vertical velocity, and helicity and vertical vorticity depends on the location of particle release and the Schmidt number. The trajectories of particles that disperse the least are characterized by a correlation between the absolute value of the relative helicity density and the absolute value of the cosine between the vorticity vector and the eigenvectors of the rate of strain tensor, while the value of this correlation approaches zero for the particles that disperse the most.

Recent progress on understanding coronal mass ejection/flare onset by a NASA living with a star focused science team

We present a report of recent progress on the topic of understanding solar coronal mass ejection (CME) onset from both modeling and observational viewpoints, as carried out from 2019 to the present by the NASA Living with a Star Focused Science Topic team on “Understanding the Onset of Major Solar Eruptions.” Following the typical Focused Science Topic paradigm, a number of research groups were selected and joined together to tackle this problem. The work being carried out by this team explores the role of topology and of helicity transport in creating an environment favorable to CME eruption and in then providing the energy required for CME onset. The team investigated CME energization and initiation via photospheric shearing, via flux rope formation, and via magnetic flux emergence. This article will highlight recent progress made by six American research groups working in these areas. We do not intend to present an exhaustive review of these topics, but rather summarize the ideas from these research groups regarding ongoing and upcoming challenges to the questions of how, when, and why coronal mass ejections erupt from the sun.

Identifying precursor of Sumatra squall line

Sumatra Squall Line (SSL) is a detectable mesoscale meteorological phenomenon at least prior to 3 hour using Doppler radar imagery interpretation. By identifying precursors, SSL can be detected 6-12 hours earlier before the occurences. Infrared data from MTSAT satellite were used to identify clusters of SSL clouds which then produce two types of SSL with different orientations, namely Northwest SSL (oriented northwest - southeast) and Northeast SSL (oriented northeast - southwest). Wind, helicity, and moisture transport were selected as precursor variables due to their importance information of squall line. The results of the precursor variable pattern comparison in the case of SSL with non-SSL showed clear differences. Bottom layer convergence and the westerlies wind patterns were proven to be formed in SSL cases. Helicity concentration was related to orientation of SSL cloud cluster. The convergence of moisture transport was detected 6 hours before the SSL occurences.

Runaway dynamics in tokamak disruptions with current relaxation

The safe operation of tokamak reactors requires a reliable modelling capability of disruptions, and in particular the spatio-temporal dynamics of associated runaway electron currents. In a disruption, instabilities can break up magnetic surfaces into chaotic field line regions, causing current profile relaxation, as well as a rapid radial transport of heat and particles. Using a mean-field helicity transport model implemented in the disruption runaway modelling framework Dream, we calculate the dynamics of runaway electrons in the presence of current relaxation events. In scenarios where flux surfaces remain intact in parts of the plasma, a skin current is induced at the boundary of the intact magnetic field region. This skin current region becomes an important centre concerning the subsequent dynamics: it may turn into a hot ohmic current channel, or a sizeable radially localized runaway beam, depending on the heat transport. If the intact region is in the plasma edge, runaway generation in the countercurrent direction can occur, which may develop into a sizeable reverse runaway beam. Even when the current relaxation extends to the entire plasma, the final runaway current density profile can be significantly affected, as the induced electric field is reduced in the core and increased in the edge, thereby shifting the centre of runaway generation towards the edge.

Tracking of magnetic helicity evolution in the inner heliosphere

Context. Magnetic helicity is one of the invariants in ideal magnetohydrodynamics, and its spectral evolution has a substantial amount of information to reveal the mechanism that are behind turbulence in space and astrophysical plasmas. Aims. The goal of our study is to observationally characterize the magnetic helicity evolution in the inner heliosphere by resolving the helicity transport in a scale-wise fashion in the spectral domain. Methods. The evolution of the magnetic helicity spectrum in the inner heliosphere was tracked using a radial alignment event achieved by Parker Solar Probe at a distance of 0.17 astronomical units (AU) from the Sun and BepiColombo at 0.58 AU with a delay of about 3.5 days. Results. The reduced magnetic helicity resolved in the frequency domain shows three main features: (1) a coherent major peak of a highly helical component at the lowest frequency at about 5 × 10−4 Hz, (2) a damping of helicity oscillation at the intermediate frequencies from 10−3 to 10−2 Hz when observed at 0.58 AU, and (3) a coherent nonhelical component in the ion-kinetic range at frequencies of about 0.1 − 1 Hz. Conclusions. Though limited in the frequency range, the main message from this work is that the solar wind develops into turbulence by convecting large-scale helicity components on the one hand and creating and annihilating helical wave components on the other hand. Excitation of waves can overwrite the helicity profile in the inner heliosphere. By comparing this with the typical helicity spectra at a distance of 1 AU (that is, a randomly oscillating helicity sign in the intermediate frequency range up to about 1 Hz), the helicity evolution reaches a nearly asymptotic state at the Venus orbit (about 0.7 AU) and beyond.

Measurement of helicity flux density using the eddy-current diagnostic system in Keda Torus eXperiment device

The flux of magnetic helicity characterizes how the topology of a magnetic field changes and helicity and its transport play essential roles in plasma equilibrium and instabilities in the reversed-field pinch (RFP) device configuration. Used to suppress magnetohydrodynamic instabilities effectively, the stabilizing conducting shell located at the boundary of an RFP device is always characterized by an eddy-current distribution that evolves rapidly with time. After measuring and analyzing the eddy currents on this stabilizing shell during tokamak discharges in the Keda Torus eXperiment device, the distributions of multiple physical quantities on the shell are obtained, including the magnetic fields, eddy currents, and electric fields. An experimental technique for measuring helicity flux density is demonstrated, combined with eddy-current diagnosis and these physical vectors on the boundary. How the magnetic and current helicity flux densities evolve is given by a feasible mathematical analysis, and data suggest that the plasma mediates both the generation and transport of magnetic helicity during the discharge. The experimental results of the distribution of the magnetic helicity flux densities (MHFDs) due to the instability on the boundary are given, and the average of these MHFDs over the whole boundary surface is far less than the maximum value of the MHFDs. In addition, the results of current helicity flux densities on the boundary are also presented.

Responsive Polymers with Contraction-arisen Helicity and Biomimetic Membrane-spanning Transport Functions

Responsive Polymers with Contraction-arisen Helicity and Biomimetic Membrane-spanning Transport Functions

Production, transport and dissipation of turbulent helicity in rotating channel flow

Production, transport and dissipation of turbulent helicity in rotating channel flow

Production and transport of turbulent helicity in turbulent channel flow with wall-normal system rotation

Production and transport of turbulent helicity in turbulent channel flow with wall-normal system rotation

Analysis of the Helical Kink Stability of Differently Twisted Magnetic Flux Ropes

Magnetic flux ropes (MFRs) are usually considered to be the magnetic structure that dominates the transport of helicity from the Sun into the heliosphere. They entrain a confined plasma within a helically organized magnetic structure and are able to cause geomagnetic activity. The formation, evolution and twist distribution of MFRs are issues subject to strong debate. Although different twist profiles have been suggested so far, none of them has been thoroughly explored yet. The aim of this work is to present a theoretical study of the conditions under which MFRs with different twist profiles are kink stable and thereby shed some light on the aforementioned aspects. The magnetic field is modeled according to the circular-cylindrical analytical flux rope model in Nieves-Chinchilla et al. (Astrophys. J. 823, 27, 2016) as well as the Lundquist and Gold-Hoyle models, and the kink stability is analyzed with a numerical method that has been developed based on Linton, Longcope, and Fisher (Astrophys. J. 469, 954, 1996). The results are discussed in relation to MFR rotations, magnetic forces, the reversed chirality scenario, and the expansion throughout the heliosphere, among others, providing a theoretical background to improve the current understanding of the internal magnetic configuration of coronal mass ejections (CMEs). The data obtained by new missions like Parker Solar Probe or Solar Orbiter will give the opportunity to explore these results and ideas by observing MFRs closer than ever to the Sun.

On magnetic helicity generation and transport in a nonlinear dynamo driven by a helical flow

The relationship between nonlinear large-scale dynamo action and the generation and transport of magnetic helicity is investigated at moderate values of the magnetic Reynolds number ( $Rm$ ). The model consists of a helically forced, sheared flow in a Cartesian domain. The boundary conditions are periodic in the horizontal and impenetrable for the vertical. The magnetic field is required to be vertical at the upper and lower boundaries. There are two consequences of this choice; one is that the magnetic helicity is not gauge invariant, the second is that fluxes of magnetic helicity are allowed in and out of the domain. We select the winding gauge, define all the contributions to the evolution of the helicity in this gauge and measure these contributions for various solutions of the dynamo equations. We vary $Rm$ and the shear strength, and find a rich landscape of dynamo solutions including travelling waves, pulsating waves and non-wave-like solutions. We find that, at the $Rm$ considered, the main contribution to the growth of magnetic helicity comes from processes throughout the volume of the fluid and that boundary terms respond by limiting the growth. We find that, in this magnetic Reynolds number regime, helicity conservation is not a strong constraint on large-scale dynamo action. We speculate on what may happen at higher $Rm$ .

Spatial scales and locality of magnetic helicity

Context. Magnetic helicity is approximately conserved in resistive magnetohydrodynamic models. It quantifies the entanglement of the magnetic field within the plasma. The transport and removal of helicity is crucial in both dynamo development in the solar interior and active region evolution in the solar corona. This transport typically leads to highly inhomogeneous distributions of entanglement. Aims. There exists no consistent systematic means of decomposing helicity over varying spatial scales and in localised regions. Spectral helicity decompositions can be used in periodic domains and is fruitful for the analysis of homogeneous phenomena. This paper aims to develop methods for analysing the evolution of magnetic field topology in non-homogeneous systems. Methods. The method of multi-resolution wavelet decomposition is applied to the magnetic field. It is demonstrated how this decomposition can further be applied to various quantities associated with magnetic helicity, including the field line helicity. We use a geometrical definition of helicity, which allows these quantities to be calculated for fields with arbitrary boundary conditions. Results. It is shown that the multi-resolution decomposition of helicity has the crucial property of local additivity. We demonstrate a general linear energy-topology conservation law, which significantly generalises the two-point correlation decomposition used in the analysis of homogeneous turbulence and periodic fields. The localisation property of the wavelet representation is shown to characterise inhomogeneous distributions, which a Fourier representation cannot. Using an analytic representation of a resistive braided field relaxation, we demonstrate a clear correlation between the variations in energy at various length scales and the variations in helicity at the same spatial scales. Its application to helicity flows in a surface flux transport model show how various contributions to the global helicity input from active region field evolution and polar field development are naturally separated by this representation. Conclusions. The multi-resolution wavelet decomposition can be used to analyse the evolution of helicity in magnetic fields in a manner which is consistently additive. This method has the advantage over more established spectral methods in that it clearly characterises the inhomogeneous nature of helicity flows where spectral methods cannot. Further, its applicability in aperiodic models significantly increases the range of potential applications.

Determining the Transport of Magnetic Helicity and Free Energy in the Sun’s Atmosphere

Abstract The most important factors determining solar coronal activity are believed to be the availability of magnetic free energy and the constraint of magnetic helicity conservation. Direct measurements of the helicity and magnetic free energy in the coronal volume are difficult, but their values may be estimated from measurements of the helicity and free energy transport rates through the photosphere. We examine these transport rates for a topologically open system such as the corona, in which the magnetic fields have a nonzero normal component at the boundaries, and derive a new formula for the helicity transport rate at the boundaries. In addition, we derive new expressions for helicity transport due to flux emergence/submergence versus photospheric horizontal motions. The key feature of our formulas is that they are manifestly gauge invariant. Our results are somewhat counterintuitive in that only the lamellar electric field produced by the surface potential transports helicity across boundaries, and the solenoidal electric field produced by a surface stream function does not contribute to the helicity transport. We discuss the physical interpretation of this result. Furthermore, we derive an expression for the free energy transport rate and show that a necessary condition for free energy transport across a boundary is the presence of a closed magnetic field at the surface, indicating that there are current systems within the volume. We discuss the implications of these results for using photospheric vector magnetic and velocity field measurements to derive the solar coronal helicity and magnetic free energy, which can then be used to constrain and drive models for coronal activity.

Helicity transport and dynamo sustainment for helical plasma states

Plasma states dominated by single helical modes are often observed in the Reverse Field Pinch (RFP) plasma confinement devices. In this paper the properties of these states are studied on the basis of a relaxation model that assumes the existence of several topological invariants related to the dominant mode. It is hypothesized that the value of the first invariant in this chain, is determined by the existence of a plasma dynamo mechanism that transport helicity. This hypothesis enables us to determine the steady state properties of the plasma equilibrium and some other interesting physical consequences. Further, by considering the properties of the transfer of helicity from the mesoscale (fluctuations) to the macroscale (equilibrium), through the dynamo field, a nonlinear dynamical model can be constructed, that evolves in time to a steady state with a non-vanishing dynamo field, when helicity is injected in the system, as in the case of the ohmic sustained RFP, while the dynamo oscillates initially, but is damped later in time, for vanishing helicity input.

On the spatial segregation of helicity by inertial waves in dynamo simulations and planetary cores

The distribution of kinetic helicity in a dipolar planetary dynamo is central to the success of that dynamo. Motivated by the helicity distributions observed in numerical simulations of the Earth’s dynamo, we consider the relationship between the kinetic helicity, $h=\boldsymbol{u}\boldsymbol{\cdot }\unicode[STIX]{x1D735}\times \boldsymbol{u}$, and the buoyancy field that acts as a source of helicity, where $\boldsymbol{u}$ is velocity. We show that, in the absence of a magnetic field, helicity evolves in accordance with the equation $\unicode[STIX]{x2202}h/\unicode[STIX]{x2202}t=-\unicode[STIX]{x1D735}\boldsymbol{\cdot }\boldsymbol{F}+S_{h}$, where the flux, $\boldsymbol{F}$, represents the transport of helicity by inertial waves, and the helicity source, $S_{h}$, involves the product of the buoyancy and the velocity fields. In the numerical simulations it is observed that the helicity outside the tangent cylinder is predominantly negative in the north and positive in the south, a feature which the authors had previously attributed to the transport of helicity by waves (Davidson & Ranjan, Geophys. J. Intl, vol. 202, 2015, pp. 1646–1662). It is also observed that there is a strong spatial correlation between the distribution of $h$ and of $S_{h}$, with $S_{h}$ also predominantly negative in the north and positive in the south. This correlation tentatively suggests that it is the in situ generation of helicity by buoyancy that establishes the distribution of $h$ outside the tangent cylinder, rather than the dispersal of helicity by waves, as had been previously argued by the authors. However, although $h$ and $S_{h}$ are strongly correlated, there is no such correlation between $\unicode[STIX]{x2202}h/\unicode[STIX]{x2202}t$ and $S_{h}$, as might be expected if the distribution of $h$ were established by an in situ generation mechanism. We explain these various observations by showing that inertial waves interact with the buoyancy field in such a way as to induce a source $S_{h}$ which has the same sign as the helicity in the local wave flux, and that the sign of $h$ is simply determined by the direction of that flux. We conclude that the observed distributions of $h$ and $S_{h}$ outside the tangent cylinder are consistent with the transport of helicity by waves.

Measurements of the Canonical Helicity of a Gyrating Kink.

Conversions between magnetic and kinetic energy occur over a range of plasma scales in astrophysical and solar dynamos and reconnection in the solar corona and the laboratory. Canonical flux tubes reconcile all plasma regimes with concepts of twists, writhes, and linkages. We present measurements of canonical flux tubes, their helicity, and their helicity transport in a gyrating plasma kink. The helicity gauge is removed with general techniques valid even if only a limited section of the plasma is measured. Temporal asymmetries in the helicities confirm irreducible 3D fields in the kink.

Helicity transformation under the collision and merging of two magnetic flux ropes

Magnetic helicity has become a useful tool in the analysis of astrophysical plasmas. Its conservation in the magnetohydrodynamic limit (and other fluid approaches) constrains the global behavior of large plasma structures. One such astrophysical structure is a magnetic flux rope: a tube-like, current-carrying plasma embedded in an external magnetic field. Bundles of these ropes are commonly observed in the near-earth environment and solar atmosphere. In this well-diagnosed experiment (three-dimensional measurements of ne, Te, Vp, B, J, E, and uflow), two magnetic flux ropes are generated in the Large Plasma Device at UCLA. These ropes are driven kink-unstable to trigger complex motion. As they interact, helicity conservation is examined in regions of reconnection. We examine (1) the transport of helicity and (2) the dissipation of the helicity. As the ropes move and the topology of the field lines diverge, a quasi-separatrix layer (QSL) is formed. As the QSL forms, magnetic helicity is dissipated within this region. At the same time, there is an influx of canonical helicity into the region such that the temporal derivative of magnetic helicity is zero.

The Great Solar Active Region NOAA 12192: Helicity Transport, Filament Formation, and Impact on the Polar Field

Abstract The solar active region (AR), NOAA 12192, appeared in 2014 October as the largest AR in 24 years. Here we examine the counterintuitive nature of two diffusion-driven processes in the region: the role of helicity buildup in the formation of a major filament, and the relationship between the effects of supergranular diffusion and meridional flow on the AR and on the polar field. Quantitatively, calculations of current helicity and magnetic twist from Helioseismic and Magnetic Imager (HMI) vector magnetograms indicate that, though AR 12192 emerged with negative helicity, positive helicity from subsequent flux emergence, consistent with the hemispheric sign-preference of helicity, increased over time within large-scale, weak-field regions such as those near the polarity inversion line (PIL). Morphologically, Atmospheric Imaging Assembly observations of filament barbs, sigmoidal patterns, and bases of Fe xii stalks initially exhibited signatures of negative helicity, and the long filament that subsequently formed had a strong positive helicity consistent with the helicity buildup along the PIL. We find from full-disk HMI magnetograms that AR 12192's leading positive flux was initially closer to the equator but, owing either to the region’s magnetic surroundings or to its asymmetric flux density distribution, was transported poleward more quickly on average than its trailing negative flux, contrary to the canonical pattern of bipole flux transport. This behavior caused the AR to have a smaller effect on the polar fields than expected and enabled the formation of the very long neutral line where the filament formed.

A field theory approach to the evolution of canonical helicity and energy

A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.

Turbulence laws in natural bed flows

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.