Cascade Of Helicity Research Articles

Balanced Turbulence and the Helicity Barrier in Black Hole Accretion

Horizon-scale observations from the Event Horizon Telescope (EHT) have enabled precision study of supermassive black hole accretion. Contemporary accretion modeling often treats the inflowing plasma as a single, thermal fluid, but microphysical kinetic effects can lead to significant deviations from this idealized picture. We investigate how the helicity barrier influences EHT-accessible electromagnetic observables by employing a simple model for electron heating based on kinetic physics and the cascade of energy and helicity in unbalanced turbulence. Although the helicity barrier plays only a minor role in regions with high plasma β, like in standard and normal evolution (SANE) disks, it may substantially impact regions with more ordered magnetic fields, such as the jet and its surrounding wind in SANE flows as well as throughout the entire domain in magnetically arrested disk (MAD) flows. In SANE flows, emission shifts from the funnel wall toward the lower-magnetization disk region; in MAD flows the emission morphology remains largely unchanged. Including the helicity barrier leads to characteristically lower electron temperatures, and neglecting it can lead to underestimated accretion rates and inferred jet powers. The corresponding higher plasma densities result in increased depolarization and Faraday depths thereby decreasing the amplitude of the β 2 coefficient while leaving its angle unchanged. Both the increased jet power and lower β2 may help alleviate outstanding tensions between modeling and EHT observations. We also find that the estimated ring diameter may be underestimated when the helicity barrier is neglected. Our results underscore the significance of the helicity barrier in shaping black hole observables and inferred accretion system parameters.

Point-vortex statistical mechanics applied to turbulence without vortex stretching

In turbulent systems with inverse cascades, energy will pile up at large scales if no large-scale sink is present. We observe that in forced-dissipative three-dimensional turbulence from which vortex-stretching is removed, such condensation is observed, associated with an inverse cascade of helicity. The large-scale structure of this condensate is characterized by a hyperbolic sine relation between vorticity and velocity, analogous to the sinh relation between vorticity and stream function observed in freely decaying 2D turbulence in periodic domains. We generalize a 2D point-vortex statistical mechanics approach to our 3D system. It is shown that the predictions of this approach are in agreement with observations of both the forced-dissipative system, after appropriate averaging, and of the freely decaying system.

Quiet Sun flux rope formation via incomplete Taylor relaxation

Context. Low-altitude nanoflares are among the candidates for atmospheric heating in the quiet Sun’s corona. Low-altitude twisted magnetic fields may be involved in such events, as they are in larger flares. But for nanoflares, the exact role, topology, and formation mechanisms of these twisted fields remain to be studied. Aims. In this paper, we investigate the formation and evolution of a preflare flux rope in a fully stratified, 3D magnetohydrodynamics simulation of the quiet Sun using the Bifrost code. This study focuses on the time period before the rope eventually reconnects with an overlying field, resulting in a nanoflare-scale energy on the order of 1017 J. One puzzle is that this modeled flux rope does not form by any of the mechanisms usually at work in larger flares, such as flux emergence, flux cancellation, or tether-cutting reconnection. Methods. Using Lagrangian markers to trace representative field lines, we follow the spatiotemporal evolution of the flux rope. By focusing on current volumes (which we call current sheets) between these lines, we identify flux bundles and associated reconnecting field line pairs. We also analyze the time-varying distribution function for the force-free parameter as the flux rope relaxes. Lastly, we compare different seeding methods for tracing magnetic field lines, and discuss their relevance to the analysis. Results. We show that the modeled flux rope is gradually built from the coalescence of numerous current-carrying flux tubes. This occurs through a series of component reconnections that are continuously driven by the complex flows in the underlying convection zone. These reconnections lead to an inverse cascade of helicity from small scales to larger scales. We also find that the system attempts to relax toward a linear force-free field, but that the convective drivers and the nanoflare event prevent full Taylor relaxation. Conclusions. Using a self-consistently driven simulation of a nanoflare event, we show for the first time an inverse helicity cascade tending toward a Taylor relaxation in the Sun’s corona, resulting in a well-ordered flux rope that later reconnects with surrounding fields. This provides context clues toward understanding the buildup of nanoflare events in the quiet Sun through incomplete Taylor relaxations, when no relevant flux emergence or cancellation is observed.

Helical model based on artificial neural network for large eddy simulation of compressible wall-bounded turbulent flows

Similar to the kinetic energy cascade, a helicity cascade is also a basic and key process in the generation and evolution of the turbulent flows. Furthermore, the helicity flux (HF) plays a crucial role between two scales in the helicity cascade. In this study, we will supply a new helical model constrained by the helicity flux for the large eddy simulation of the compressible turbulent flows. Then, in order to obtain a more precise HF, the local coefficient of the modeled HF is determined by the artificial neural network (ANN) method. The new model combines merits of the high robustness and the correlation with the real turbulence. In the test case of the compressible turbulent channel flow, the new model can supply a more accurate mean velocity profile, turbulence intensities, Reynolds stress, etc. Then, for the test in the compressible flat-plate boundary layer, the new model can also precisely predict the onset and peak of the transition process, the skin-friction coefficient, the mean velocity in the turbulent region, etc. Moreover, the ANN here is a semi-implicit method, and the new model would be easier to be generalized to simulate other types of the compressible wall-bounded turbulent flows.

From incoherent field to coherent reconnection

Context. Magnetic reconnection in the quiet Sun is a phenomenon that is consistently observed, however, its conditions of occurrence are not as well known as for more energetic events. It has recently become feasible to address this issue with 3D numerical simulations of realistically stratified and convection-driven reconnection. Aims. We aim to illustrate ways by which quiet Sun fields may contribute to solar atmospheric heating via magnetic reconnection that is driven by convective motion. We also aim to compare our complex stratified model to earlier idealized coronal models in terms of reconnection drivers and topological conditions. Methods. We analyzed a simulation of the quiet Sun in which a complex coronal magnetic field is self-consistently driven by the underlying convection. We employed a selection of Lagrangian markers to trace the spatiotemporal behavior of specific magnetic features that are relevant to magnetic reconnection and atmospheric heating. Results. A relatively large-scale reconnection-driven heating event occurs in the simulated corona, in a flattened X-shaped feature characterized by a weak field and high current. It is reminiscent of a hyperbolic flux tube (HFT), which is located at the interface between multiple flux systems. One of these is a smooth overlying horizontal field and the two most relevant others are located below the HFT. They consist of an arcade and a horizontal flux rope which eventually reconnect with the overlying field, raising coronal plasma temperatures up to 1.47 MK. Conclusions. We have identified a reconnection-driven coronal heating event in a quiet Sun simulation. We find that our results are in good phenomenological agreement with idealized coronal flare models, which demonstrates that the same general physical concepts are valid. However, we also find that the reconnecting flux rope and arcade are neither formed by any obvious coherent flux emergence, nor by any ordered photospheric motion or flux cancellation. Instead, they seem to develop merely from the self-consistent convective driving of pre-existing tangled field lines. This gradual and smooth ordering suggests an inverse cascade of magnetic helicity via smaller reconnection events, located at or above slowly-moving photospheric flux concentrations. We suggest that this case is representative of many heating events that may be ubiquitous in the real quiet Sun.

STITCH: A Subgrid-scale Model for Energy Buildup in the Solar Corona

The solar corona routinely exhibits explosive activity, in particular coronal mass ejections and their accompanying eruptive flares, which have global-scale consequences. These events and their smaller counterparts, coronal jets, originate in narrow, sinuous filament channels. The key processes that form and evolve the channels operate on still smaller spatial scales and much longer timescales, culminating in a vast separation of characteristic lengths and times that govern these explosive phenomena. In this article, we describe implementation and tests of an efficient subgrid-scale model for generating eruptive structures in magnetohydrodynamics (MHD) coronal simulations. STITCH—STatistical InjecTion of Condensed Helicity—is a physics-based, reduced representation of helicity condensation: a process wherein small-scale vortical surface convection forms ubiquitous current sheets and pervasive reconnection across the sheets mediates an inverse cascade of magnetic helicity and free energy, thereby forming the filament channels. We have developed a formalism, STITCH, that abstracts these complex processes into a single term in Ohm’s law and the induction equation that directly injects tangential magnetic flux into the low corona. We show that our approach is in very good agreement with a full helicity condensation calculation that treats all of the dynamics explicitly, while enabling substantial reductions in temporal duration and spatial resolution. In addition, we illustrate the flexibility of STITCH at forming localized filament channels and at energizing complex surface flux distributions that have sinuous boundaries. STITCH is simple to implement and computationally efficient, making it a powerful technique for physics-based modeling of solar eruptive events.

On the simultaneous cascades of energy, helicity, and enstrophy in incompressible homogeneous turbulence

We characterise the incompressible turbulence cascade in terms of the concurrent inter-scale and inter-space exchanges of the scale-by-scale energy, helicity and enstrophy. The governing equations for the scale-by-scale helicity and enstrophy are derived in a similar fashion to that of the second order structure function following Hill (J. Fluid Mech., vol. 468, 2002, pp. 317–326). We examine the instantaneous dynamics, applying these equations to forced periodic turbulence and a von Kármán flow focusing on scales in the dissipative range$r=2.5\eta$, the near-dissipative range$r=0.5\lambda$and the onset inertial range$r=\lambda$(where$\eta$and$\lambda$are the Kolmogorov and Taylor length scales, respectively). The signature of the random sweeping effect is observed in all three individual budgets and between the energy and enstrophy transfers. As in the energy cascade, the anti correlation of the pressure transport and non-linear transfer is identified also in the helicity cascade. Owing to its lack of positive definiteness, the helicity transfers are found to be decorrelated from the others. However a connection between the energy cascade and helicity is identified kinematically. This connection reveals the large-scale sweeping motions are a key element in the overall energy cascade and underpins previous observations of large-scale intermittency. Taken together, this work extends a classic framework to gain novel insight on turbulence dynamics that underlay the statistically steady state, and demonstrates how transfers are interconnected.

Saturation of Turbulent Helical Dynamos.

The presence of large scale magnetic fields in nature is often attributed to the inverse cascade of magnetic helicity driven by turbulent helical dynamos. In this Letter, we show that in turbulent helical dynamos, the inverse flux of magnetic helicity toward the large scales Π_{H} is bounded by |Π_{H}|≤cεk_{η}^{-1}, where ε is the energy injection rate, k_{η} is the Kolmogorov magnetic dissipation wave number, and c an order one constant. Assuming the classical isotropic turbulence scaling, the inverse flux of magnetic helicity Π_{H} decreases at least as a -3/4 power law with the magnetic Reynolds number Rm: |Π_{H}|≤cεℓ_{f}Rm^{-3/4}max[Pm,1]^{1/4}, where Pm is the magnetic Prandtl number and ℓ_{f} the forcing length scale. We demonstrate this scaling with Rm using direct numerical simulations of turbulent dynamos forced at intermediate scales. The results further indicate that nonlinear saturation is achieved by a balance between the inverse cascade and dissipation at domain size scales L for which the saturation value of the magnetic energy is bounded by E_{m}≤cL(εℓ_{f})^{2/3}Rm^{1/4}max[1,Pm]^{1/4}. Numerical simulations also demonstrate this bound. These results are independent of the dynamo mechanism considered. In our setup, they imply that inviscid mechanisms cannot explain large scale magnetic fields and have critical implications for the modeling of astrophysical dynamos.

Discovery of the zeroth law of helicity spectrum in the pre-inertial range of wall turbulence

We report an unprecedented existence of the zeroth law of helicity spectrum (i.e., the helicity spectrum becomes independent of the wavenumber) in the transition from production range to inertial range, herein termed the pre-inertial range, of wall turbulence. The zeroth law is explained by the superposition effect of the forward joint cascade of energy and helicity caused by twisting and stretching of wall-attached superstructures in an equilibrium layer. The phenomenological model perfectly predicts the zeroth law in the pre-inertial range. Experimental data support the existence of the zeroth law.

Helicity distributions and transfer in turbulent channel flows with streamwise rotation

Helicity is a quadratic inviscid conservative quantity in three-dimensional turbulent flows and is crucial for turbulent system evolution. Helicity effects have mainly been highlighted over the past few decades to explore the intrinsic mechanism of turbulent flows, while the statistical characteristics of helicity itself are nearly absent in general anisotropic turbulent flows. In this paper, we investigate the helicity statistics in turbulent channel flows with streamwise rotation at moderate rotation numbers ($Ro_{\tau }=7.5,15$and 30) and Reynolds numbers ($Re_{\tau }=180$and 395), including their spatial and scale distributions, anisotropy and cross-scale transfer. The appearance of a mean secondary flow in the spanwise direction corresponds to a mean streamwise vorticity, which indicates the presence of a high-helicity distribution. Numerical results reveal a regular helicity profile along the wall-normal direction, and a new peak is found in the near-wall region around$y^+=6$of the streamwise or spanwise helicity profiles. The inter-scale helicity transfer is analysed by the filtering method, and the numerical consequences reveal that the second channel of the helicity cascade we proposed previously is dominant in contrast to the first channel. The rotation effects are explored by comparing the numerical results obtained under different rotation numbers. With increasing rotation number, more helical structures in the near-wall regions are present, with peaks of helicity profiles and fluxes coming closer to the wall. With a higher Reynolds number, their amplitudes are larger and scale-space transfer is strengthened. These systematic numerical analyses uncover the helicity distributions and transfer in wall-bounded turbulent flows.

Scale-similar structures of homogeneous isotropic non-mirror-symmetric turbulence based on the Lagrangian closure theory

We investigate the effect of helicity on the scale-similar structures of homogeneous isotropic and non-mirror-symmetric turbulence based on the Lagrangian renormalised approximation (LRA), which is a self-consistent closure theory proposed by Kaneda (J. Fluid Mech., vol. 107, 1981, pp. 131–145). In this study, we focus on the time scale representing the scale-similar range. For the LRA, the Lagrangian two-time velocity correlation and response function determine the representative time scale. The LRA predicts that both the Lagrangian two-time velocity correlation and response function equation do not explicitly depend on helicity. We assume the extended scale-similar spectra and time scale by considering the helicity dissipation rate. Considering the small-scale structures, the requirements for the energy and helicity fluxes and response function equation to be scale similar, yield the conventional inertial-range power laws and provide the energy and helicity spectra $\propto k^{-5/3}$ and the time scale $\propto \varepsilon ^{-1/3} k^{-2/3}$ , where $\varepsilon$ and $k$ denote the energy dissipation rate and wavenumber, respectively. Notably, energy flux can be scale similar only when $k^H /k \ll 1$ , where $k^H = \varepsilon ^H/\varepsilon$ and $\varepsilon ^H$ denotes the helicity dissipation rate. This condition makes the energy cascade process in the scale-similar range completely independent of helicity. We also investigate the localness of the interscale interaction in the energy and helicity cascades for the LRA. We demonstrate that the helicity cascade is slightly non-local in scales compared with the energy cascade. This study provides a foundation on the modelling of non-mirror-symmetric turbulent flows.

Helicity spectra and topological dynamics of vortex links at high Reynolds numbers

Abstract

Chirality transfer and chiral turbulence in gauge theories

Chirality transfer between fermions and gauge fields plays a crucial role for understanding the dynamics of anomalous transport phenomena such as the Chiral Magnetic Effect. In this proceeding we present a first principles study of these processes based on classical-statistical real-time lattice simulations of strongly coupled QED (e2Nf = 64). Our simulations demonstrate that a chirality imbalance in the fermion sector triggers chiral plasma instabilities in the gauge field sector, which ultimately lead to the generation of long range helical magnetic fields via an self-similar turbulent cascade of the magnetic helicity.

Scale locality of helicity cascade in physical space

Scale locality is a key concept in turbulent cascade theory and is also associated with reflection symmetry. Vortex stretching is proven to participate in the helicity cascade process while destroying the conservative characteristic of enstrophy transfer in three-dimensional flows. Numerical evidence indicates that a turbulent structure with scale L will also largely transfer its helicity to structures with scales of around 0.3L. However, the scale locality of the helicity cascade is slightly weaker than that of the energy cascade in physical space. The weaker scale locality suggests that more scales should be involved for turbulent modeling of helical turbulence.

Inverse cascade of energy in helical turbulence

Using direct numerical simulation of hydrodynamic turbulence with helicity forcing applied at all scales, a near-maximum helical turbulent state is obtained, with an inverse energy cascade at scales larger than the energy forcing scale and a forward helicity cascade at scales smaller than the energy forcing scale. In contrast to previous studies using decimated triads, our simulations contain all possible triads. By computing the shell-to-shell energy fluxes, we show that the inverse energy cascade results from weakly non-local interactions among homochiral triads. Varying the helicity injection range of scales leads to necessary conditions to obtain an inverse energy cascade.

Magnetic field configurations in neutron stars from MHD simulations

ABSTRACT We have studied numerically the evolution of magnetic fields in barotropic neutron stars, by performing non-linear magnetohydrodynamical simulations with the code pluto. For both initially predominantly poloidal and toroidal fields, with varying strengths, we find that the field settles down to a mixed poloidal–toroidal configuration, where the toroidal component contributes between ${\rm 10}$ and $20 {{\ \rm per\ cent}}$ of the total magnetic energy. This is, however, not a strict equilibrium, as the instability leads to the development of turbulence, which, in turn, gives rise to an inverse helicity cascade, which determines the final ‘twisted torus’ setup. The final field configuration is thus dictated by the non-linear saturation of the instability, and is not stationary. The average energy of the poloidal and toroidal components, however, is approximately stable in our simulations, and a complex multipolar structure emerges at the surface, while the magnetic field is dipolar at the exterior boundary, outside the star.

Dual channels of helicity cascade in turbulent flows

Helicity, as one of only two inviscid invariants in three-dimensional turbulence, plays an important role in the generation and evolution of turbulence. From the traditional viewpoint, there exists only one channel of helicity cascade similar to that of kinetic energy cascade. Through theoretical analysis, we find that there are two channels in helicity cascade process. The first channel mainly originates from vortex twisting process, and the second channel mainly originates from vortex stretching process. By analysing the data of direct numerical simulations of typical turbulent flows, we find that these two channels behave differently. The ensemble averages of helicity flux in different channels are equal in homogeneous and isotropic turbulence, while they are different in other type of turbulent flows. The second channel is more intermittent and acts more like a scalar, especially on small scales. Besides, we find a novel mechanism of hindered even inverse energy cascade, which could be attributed to the second-channel helicity flux with large amplitude.

Cascade Processes in Rapid Rotation

The process of the kinetic energy and kinetic helicity transfer over the spectrum in an incompressible, rapidly rotating turbulent flow is considered. An analogue of the Fjortoft theorem for 3D rapidly rotating turbulence is proposed. It is shown that, similar to 2D turbulence, there are two cascades simultaneously: the inverse cascade of the kinetic energy and the direct cascade of the kinetic helicity, which in the case of 2D turbulence corresponds to the cascade of enstrophy. The proposed scenario is in agreement with our earlier calculations, some recent numerical simulations, and physical experiment on rotating turbulence.

Inverse cascade of hybrid helicity inBΩ-MHD turbulence

An inverse cascade of hybrid helicity is observed in direct numerical simulations of 3D magnetohydrodynamics with both an imposed magnetic field and a rotation rate. The impact of the tilt angle between the two axes and of the polarized forcing is discussed.

Effect of pressure on joint cascade of kinetic energy and helicity in compressible helical turbulence.

Direct numerical simulations of three-dimensional compressible helical turbulence are carried out at a grid resolution of 1024^{3} to investigate the effect of pressure, which is important for the joint cascade of kinetic energy and helicity in compressible helical turbulence. The principal finding is that the pressure term of the helicity equation [defined as Φ^{H}=p∂_{i}(ω_{i}/ρ)] has a smaller effect on the helicity cascade in the aspect of amplitude and a smaller effective range, which leads to a longer inertial subrange of the helicity cascade, in contrast to a kinetic energy cascade. In addition, we also find that the effective range of Φ^{H} is concentrated only in large scales statistically, which is similar to the effect of the pressure term of the kinetic energy equation (defined as Φ^{E}=p∂_{i}u_{i}). From the overall sense of the effect of Φ^{E} and Φ^{H} on the kinetic energy and the helicity, respectively, both of them play a role of dissipation especially in the compression region. We propose that high enough helicity can affect the process of energy transformation between kinetic energy and internal energy, which means that the absolute local helicity hinders the process of kinetic energy transferring to internal energy, and promotes internal energy transferring to kinetic energy. In addition, Φ^{H} plays a source role both for positive and negative helicity. We also study the mechanism of cancellations between compression and rarefaction regions, and we find that the impact of a shocklet on the helicity cascade can be ignored statistically.