Kinetic Helicity Research Articles

Topological constraints in the reconnection of vortex braids

We study the relaxation of a topologically nontrivial vortex braid with zero net helicity in a barotropic fluid. The aim is to investigate the extent to which the topology of the vorticity field—characterized by braided vorticity field lines—determines the dynamics, particularly the asymptotic behavior under vortex reconnection in evolution at high Reynolds numbers (25 000). Analogous to the evolution of braided magnetic fields in plasma, we find that the relaxation of our vortex braid leads to a simplification of the topology into large-scale regions of opposite swirl, consistent with an inverse cascade of the helicity. The change of topology is facilitated by a cascade of vortex reconnection events. During this process, the existence of regions of positive and negative kinetic helicities imposes a lower bound for the kinetic energy. For the enstrophy, we derive analytically a lower bound given by the presence of unsigned kinetic helicity, which we confirm in our numerical experiments.

Constant-energetics control-based forcing methods in isotropic helical turbulence

A deterministic forcing method and stochastic forcing method are proposed to keep mean turbulence kinetic energy and mean helicity at ideal values. Using the proposed forcing methods, it is shown that characteristics common to energy and helicity dissipation rates, and results of direct numerical simulations, support the joint cascade scenario of energy and helicity.

Chaotic transients and hysteresis in an α 2 dynamo model

The presence of chaotic transients in a nonlinear dynamo is investigated through numerical simulations of the 3D magnetohydrodynamic equations. By using the kinetic helicity of the flow as a control parameter, a hysteretic blowout bifurcation is conjectured to be responsible for the transition to dynamo, leading to a sudden increase in the magnetic energy of the attractor. This high-energy hydromagnetic attractor is suddenly destroyed in a boundary crisis when the helicity is decreased. Both the blowout bifurcation and the boundary crisis generate long chaotic transients that are due, respectively, to a chaotic saddle and a relative chaotic attractor.

Subgrid-scale helicity equation model for large-eddy simulation of turbulent flows

A new one-equation eddy-viscosity model based on subgrid-scale (SGS) helicity is introduced in this paper for large-eddy simulation (LES) of turbulent flows. First, the governing equation of SGS helicity is deduced from the incompressible Navier–Stokes equations, and it reflects the transfer of the small-scale helicity that has been filtered out. We deduce a certain functional relation between the eddy viscosity and SGS helicity based on the kinetic energy and helicity spectra in the homogeneous and isotropic helical turbulence. For improving the accuracy, each unclosed term in the governing equation of SGS helicity is modeled independently, and the coefficients of these unclosed terms are constants or are determined dynamically. The new one-equation eddy-viscosity model is first tested and validated in the simulation of the homogeneous and isotropic helical turbulence. The a priori tests from the direct numerical simulation of forced homogeneous and isotropic turbulence show that the energy and helicity fluxes exhibit scale invariance in the inertial subrange. Additionally, the a posteriori tests demonstrate that the constant-coefficient and dynamic SGS helicity equation models can predict both the energy and helicity spectra more precisely than the common SGS models. For the LES of channel flow, the SGS helicity equation model can accurately predict the mean velocity, the turbulent stress, and the viscous shear stress and supply more abundant flow structures than the compared SGS model under the same grid resolution.

A 4D flow cardiovascular magnetic resonance study of flow asymmetry and haemodynamic quantity correlations in the pulmonary artery

Objective. In this paper we elucidate the asymmetric flow pattern and the haemodynamic quantity distributions and correlations in the pulmonary artery (PA) vasculature in healthy adults having structurally normal hearts, to provide reference on the flow characteristics in the PA and the right ventricle. Approach. Velocity data are acquired non-invasively from 18 healthy volunteers by 4D flow magnetic resonance imaging, resolved to 20 phases with spatial resolution 3 × 3 × 3 mm3. Interpolation is applied to improve the accuracy in quantifying haemodynamic quantities including kinetic energy, rotational energy, helicity and energy dissipation rate. These quantities are volumetrically normalised to remove size dependency, representing densities or local intensity. Main results. Flow asymmetry in the PA is quantified in terms of all the flow dynamic quantities and their correlations. The right PA has larger diameter and higher peak stroke velocity than the left PA. It also has the highest rotational energy intensity. Counter-rotating helical streams in the main PA appear to be associated with the unidirectional helical flow noticed in the left and the right PA near the peak systole. Significance. This study provides a fundamental basis of normal flow in the PA. It implies the validity to use these flow pattern-related quantitative measures to aid with the identification of abnormal PA flow non-invasively, specifically for detecting abnormalities in the pulmonary circulation and response to therapy, where haemodynamic flow is commonly characterised by increased vortical and helical formations.

Dynamic Phase Alignment in Inertial Alfvén Turbulence.

In weakly collisional plasma environments with sufficiently low electron beta, Alfvénic turbulence transforms into inertial Alfvénic turbulence at scales below the electron skin depth, k_{⊥}d_{e}≳1. We argue that, in inertial Alfvénic turbulence, both energy and generalized kinetic helicity exhibit direct cascades. We demonstrate that the two cascades are compatible due to the existence of a strong scale dependence of the phase alignment angle between velocity and magnetic field fluctuations, with the phase alignment angle scaling as cosα_{k}∝k_{⊥}^{-1}. The kinetic and magnetic energy spectra scale as ∝k_{⊥}^{-5/3} and ∝k_{⊥}^{-11/3}, respectively. As a result of the dual direct cascade, the generalized helicity spectrum scales as ∝k_{⊥}^{-5/3}, implying progressive balancing of the turbulence as the cascade proceeds to smaller scales in the k_{⊥}d_{e}≫1 range. Turbulent eddies exhibit a phase-space anisotropy k_{∥}∝k_{⊥}^{5/3}, consistent with critically balanced inertial Alfvén fluctuations. Our results may be applicable to a variety of geophysical, space, and astrophysical environments, including the Earth's magnetosheath and ionosphere, solar corona, and nonrelativistic pair plasmas, as well as to strongly rotating nonionized fluids.

Rotational dependence of turbulent transport coefficients in global convective dynamo simulations of solar-like stars

Context. For moderate and slow rotation, the magnetic activity of solar-like stars is observed to strongly depend on rotation, while for rapid rotation, only a very weak or no dependency is detected. These observations do not yet have a solid explanation in terms of dynamo theory. Aims. We aim to find such an explanation by numerically investigating the rotational dependency of dynamo drivers in solar-like stars, that is, stars that have a convective envelope of similar thickness to that of the Sun. Methods. We ran semi-global convection simulations of stars with rotation rates from 0 to 30 times the solar value, corresponding to Coriolis numbers, Co, of 0 to 110. We measured the turbulent transport coefficients contributing to the magnetic field evolution with the help of the test-field method, and compared with the dynamo effect arising from the differential rotation that is self-consistently generated in the models. Results. The trace of the α tensor increases for moderate rotation rates with Co0.5 and levels off for rapid rotation. This behavior is in agreement with the kinetic α based on the kinetic helicity, if one takes into account the decrease of the convective scale with increasing rotation. The α tensor becomes highly anisotropic for Co ≳ 1. Furthermore, αrr dominates for moderate rotation (1 < Co < 10), and αϕϕ for rapid rotation (Co ≳ 10). The effective meridional flow, taking into account the turbulent pumping effects, is markedly different from the actual meridional circulation profile. Hence, the turbulent pumping effect is dominating the meridional transport of the magnetic field. Taking all dynamo effects into account, we find three distinct regimes. For slow rotation, the α and Rädler effects are dominating in the presence of anti-solar differential rotation. For moderate rotation, α and Ω effects are dominant, indicative of αΩ or α2Ω dynamos in operation, producing equatorward-migrating dynamo waves with a qualitatively solar-like rotation profile. For rapid rotation, an α2 mechanism with an influence from the Rädler effect appears to be the most probable driver of the dynamo. Conclusions. Our study reveals the presence of a large variety of dynamo effects beyond the classical αΩ mechanism, which need to be investigated further to fully understand the dynamos of solar-like stars. The highly anisotropic α tensor might be the primary reason for the change of axisymmetric to non-axisymmetric dynamo solutions in the moderate rotation regime.

On the helicity characteristics and induced emf of magnetic-Coriolis wave packets

SUMMARY In a rapidly rotating Boussinesq fluid, buoyant anomalies radiate low-frequency inertial wave packets that disperse along the rotation axis. The wave packets lead to axially elongated vortices, which propagate negative (positive) kinetic helicity upwards (downwards) with respect to the rotation vector. The kinetic helicity carried by the inertial wave packets is near-maximal relative to the velocity and vorticity fields. In classical mean-field theory, kinetic helicity is often associated with the α-effect, which is thought to be an important ingredient for planetary dynamos. The modification of inertial wave packets in the presence of a transverse uniform magnetic field is investigated here, motivated by small-scale dynamics in planetary cores, where a large-scale magnetic field affects fluid motions. We study numerically the dispersion of wave packets from an isolated buoyant source and from a random layer of buoyant anomalies, while varying the Lehnert number Le—the ratio of the frequencies of Alfvén and inertial waves. We find that for Le < 0.1, the vortices are columnar and continue to segregate kinetic helicity so that it is negative (positive) above (below) the buoyant source. Importantly, the wave packets induce an α-effect, which remains strong and coherent for Earth-like values of the Lehnert number (Le < 0.1). The interaction of wave packets emitted by multiple neighbouring buoyant sources results in an α-effect that is stronger than the α-effect induced by wave packets launched from an isolated buoyant source, and we provide an analytical explanation for this. The coherence of the α-effect induced by the wave packets, for Earth-like values of the Lehnert number, lends support to the α2 dynamo model driven by helical waves.

Cross-chirality transfer of kinetic energy and helicity in compressible helical turbulence

The regularity of chirality transfer is numerically investigated in compressible helical turbulent flows. It is found that the compressible component of velocity serves as a medium role for chirality transfer, and the expansion of fluid elements can lead to a stronger lack of mirror symmetry. These conclusions not only uncover the complexity of compressible chiral turbulence but also may serve as a possible controlling method for chiral turbulence.

Magnetic and Velocity Field Topology in Active Regions of Descending Phase of Solar Cycle 23

We analyse the topology of photospheric magnetic fields and sub-photospheric flows of several active regions (ARs) that are observed during the peak to descending phase of the solar cycle 23. Our analysis shows clear evidence of hemispheric preferences in all the topological parameters such as the magnetic, current and kinetic helicities, and the 'curl-divergence'. We found that 68\%(67\%) ARs in the northern (southern) hemisphere with negative (positive) magnetic helicities. Same hemispheric preference sign is found for the current helicities in 68\%(68\%) ARs. The hemispheric preferences are found to exist statistically for all the time except in few ARs observed during the peak and the end phases of the solar cycle. This means that magnetic fields are dominantly left(right)-helical in scales smaller than individual ARs of northern(southern) hemisphere. We found that magnetic and current helicities parameters show equator-ward propagation similar to the sunspot cycle. The kinetic helicity showed similar hemispheric trend to that of magnetic and current helicity parameters. There are 65\%(56\%) ARs with negative (positive) kinetic helicity as well as divergence-curl, at the depth of 2.4\,Mm, in the northern (southern) hemisphere. The hemispheric distribution of the kinetic helicity becomes more evident at larger depths, e.g., 69\%(67\%) at the depth of 12.6\,Mm. Similar hemispheric trend of kinetic helicity to that of the current helicity supports the mean field dynamo model. We also found that the hemispheric distribution of all the parameters increases with the field strength of ARs. The topology of photospheric magnetic fields and near surface sub-photospheric flow fields did not show good association but the correlation between them enhances with depths which could be indicating more aligned flows at deeper layers of ARs.

Small-Scale Analysis of Hydrodynamical Helicity Suppression in the Mean-Field Dynamo-Model

We compare the classical mean-field dynamo model proposed by Steenbeck, Krause, and Radler to describe the generation of large-scale magnetic fields and the Kazantsev model that describes the small-scale dynamo in an unbounded homogeneous and isotropic flow. We consider the subcritical regime of small magnetic Reynolds numbers whereby there is no rapid generation. The same regime can also be understood as a process in which the small-scale generation is stopped due to its intrinsic mechanisms. Within both approaches we examine what distinguishes the spectra of the linear and nonlinear processes under the suppression of hydrodynamic (kinetic) helicity or, in other words, compare the alpha-quenchings. We check whether averaging the induction equation over scales larger than the velocity field correlation length leads to the loss of any features in the spectrum near the dissipative scale. We study the various types of dynamo stabilization using which seems more justified physically than the standard alpha-quenching, but more difficult within large-scale models containing limited information about the random velocity field. In particular, we compare the integral suppression whereby the total energy is conserved and the spectral suppression that suggests the conservation of energy and helicity in each spectral shell without assuming their redistribution over the spectrum.

Chiral Radiation Transport Theory of Neutrinos

We construct the chiral radiation transport equation for left-handed neutrinos in the context of radiation hydrodynamics for core-collapse supernovae. Based on the chiral kinetic theory incorporating quantum corrections due to the chirality of fermions, we derive a general relativistic form of the chiral transfer equation with collisions. We show that such quantum corrections explicitly break the spherical symmetry and axisymmetry of the system. In the inertial frame, in particular, we find that the so-called side jump leads to quantum corrections in the collisions between neutrinos and matter. We also derive analytic forms of such corrections in the emission and absorption rates for the neutrino absorption process. These corrections result in the generation of kinetic helicity and cross helicity of matter, which should then modify the subsequent evolution of matter. This theoretical framework can be applied to investigate the impacts of the chirality of neutrinos on the evolution of core-collapse supernovae.

Mean field dynamo action in shear flows. I: fixed kinetic helicity

ABSTRACT We study mean field dynamo action in a background linear shear flow by employing pulsed renewing flows with fixed kinetic helicity and non-zero correlation time (τ). We use plane shearing waves in terms of time-dependent exact solutions to the Navier–Stokes equation as derived by Singh & Sridhar (2017). This allows us to self-consistently include the anisotropic effects of shear on the stochastic flow. We determine the average response tensor governing the evolution of mean magnetic field, and study the properties of its eigenvalues that yield the growth rate (γ) and the cycle period (Pcyc) of the mean magnetic field. Both, γ and the wavenumber corresponding to the fastest growing axisymmetric mode vary non-monotonically with shear rate S when τ is comparable to the eddy turnover time T, in which case, we also find quenching of dynamo when shear becomes too strong. When $\tau /T\sim {\cal O}(1)$, the cycle period (Pcyc) of growing dynamo wave scales with shear as Pcyc ∝ |S|−1 at small shear, and it becomes nearly independent of shear as shear becomes too strong. This asymptotic behaviour at weak and strong shear has implications for magnetic activity cycles of stars in recent observations. Our study thus essentially generalizes the standard αΩ (or α2Ω) dynamo as also the α effect is affected by shear and the modelled random flow has a finite memory.

Effect of intake manifold design on the mixing of air and bio-CNG in a port-injected dual fuel diesel engine

The awareness for an effective utilization of renewable energy and alternative fuels has been increasing. As alternative fuels, both liquid and gaseous biofuels have huge resources. A bio-CNG is a form of biogas with increased methane content. The present study comprises the development of intake manifold with the port fuel injector and investigate the mixing characteristics of air and bio-CNG. The aim of the study is to analyse the effect the R/D ratio on the flow behaviour and mixture formation of air and bio-CNG. The four configurations of intake manifold are investigated. The ratio of radius of curvature of manifold bend (R) to the diameter of manifold (D) is varied as 1, 1.5, 1.75 and 2. The port fuel injector for bio-CNG induction is placed at 200 mm from the manifold. The objective is to optimize the intake manifold to deliver the homogeneous mixture of air and bio-CNG inside the engine cylinder. As the bio-CNG is new age fuel, being produced to reduce the import of conventional CNG, the work for optimization of port injector and intake manifold are hardly available. The geometries are made in PTC-Creo 3.0, followed by CFD simulation in ANSYS Fluent. The different configurations are analysed for the comparison of the parameters such as, pressure, velocity, turbulence kinetic energy, helicity and mass fraction of CH4. The results show that the distribution of bio-CNG near the outlet of the manifold is uniform and homogeneous for the manifold with R/D ratio of 1.75 and 2.

Kinetic Helicity and Lifetime of Activity Complexes During Solar Cycle 24

Abstract We study magnetic features on the solar surface that exist for several rotations during solar cycle 24. To identify them, we average synoptic maps over a range in latitude and stack the resulting longitudinal strips in time. We use synoptic maps of magnetograms obtained with the NSO/Synoptic Optical Long-term Investigations of the Sun instrument and create synoptic maps of the kinetic helicity of subsurface flows integrated over 2.0–7.1 Mm based on Solar Dynamics Observatory/Helioseismic and Magnetic Imager Dopplergrams. To distinguish between active and quiet regions, we sort the grid points of the synoptic maps by their activity level and divide the data into four subsets with 25% of activity each and into two subsets with the highest or lowest 12.5% of activity values. The kinetic helicity of these six subsets follows the hemispheric helicity rule with, on average, positive values in the southern and negative values in the northern hemisphere. However, the helicity of the subset with the highest activity is about four times higher than that of the other subsets, and the mid-quartile subsets show the weakest hemispheric helicity rule. We define the lifetime of complexes in each subset and find that for the high-activity subset, the amplitude of magnetic activity and kinetic helicity increases almost linearly with the lifetime of complexes. The distribution of flares closely resembles that of the high-activity subset. The flare-productive locations in long-lived complexes produce, on average, the same number of flares as those of short-lived complexes. However, long-lived complexes have a higher fractional number of these locations than the short-lived complexes and thus produce more flares not just because they live longer.

On uniqueness of transfer rates in magnetohydrodynamic turbulence

In hydrodynamic and MHD (magnetohydrodynamic) turbulence, formal expressions for the transfer rates rely on integrals over wavenumber triads $(\boldsymbol{k},\boldsymbol{p},\boldsymbol{q})$ satisfying $\boldsymbol{k}+\boldsymbol{p}+\boldsymbol{q}=0$ . As an example $S_{E}^{uu}(\boldsymbol{k}\mid \boldsymbol{p},\boldsymbol{q})$ denotes the kinetic energy transfer rate to the mode $\boldsymbol{k}$ , from the two other modes in the triad, $\boldsymbol{p}$ and $\boldsymbol{q}$ . However as noted by Kraichnan (Phys. Rev., vol. 111, 1958, pp. 1747–1747), in $S_{E}^{uu}(\boldsymbol{k}\mid \boldsymbol{p},\boldsymbol{q})$ , what fraction of the energy transferred to the mode $\boldsymbol{k}$ originated from $\boldsymbol{p}$ and which from $\boldsymbol{q}$ is unknown. Such an expression is thus incongruent with the customary description of turbulence in terms of two-scale energy exchange. Notwithstanding this issue, Dar et al. (Physica D, vol. 157 (3), 2001, pp. 207–225) further decomposed these transfers into separate contributions from $\boldsymbol{p}$ -to- $\boldsymbol{k}$ and $\boldsymbol{q}$ -to- $\boldsymbol{k}$ , thus introducing the concept of mode-to-mode transfers that they applied to MHD turbulence. Doing so, they had to set aside additional transfers circulating within each triad, but failed to calculate them. In the present paper we explain how to derive the complete expressions of the mode-to-mode transfers, including the circulating transfers. We do it for kinetic energy and kinetic helicity in hydrodynamic turbulence, for kinetic energy, magnetic energy and magnetic helicity in MHD turbulence. We find that the degree of non-uniqueness of the energy transfers derived from the induction equation is a priori higher than the one derived from the Navier–Stokes equations. However, separating the contribution of magnetic advection from magnetic stretching, the energy mode-to-mode transfer rates involving the magnetic field become uniquely defined, in striking contrast to the hydrodynamic case. The magnetic helicity mode-to-mode transfer rate is also found to be uniquely defined, contrary to kinetic helicity in hydrodynamics. We find that shell-to-shell transfer rates have the same properties as mode-to-mode transfer rates. Finally calculating the fluxes, we show how the circulating transfers cancel in accordance with conservation laws.

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.

Mean field solar surface dynamo in the presence of partially ionized plasmas and sub-surface shear layer

Abstract A non-linear α − Ω dynamo in the partially ionized turbulent plasma in the presence of sub-surface velocity shear is studied with mean-field electrodynamics. Such a dynamo is probably operational in the near-surface region of the Sun, where the presence of both neutrals and the velocity shear (due to sub-surface shear layer in the rotation profile) is observationally well established. In particular, we show that the inclusion of ambipolar diffusion leads to a saturation of magnetic field amplitudes in the α − Ω dynamo. We also demonstrate that the temporal evolution of large-scale global magnetic fields follows the well-known pattern similar to the ‘butterfly’ diagram displayed by sunspots. As usual the velocity shear converts part of the poloidal into the toroidal magnetic field which in turn is regenerated largely by the combined kinetic plus Hall helicity, thus closing the dynamo loop. In addition, by allowing temporal variation in the helicity and ambipolar diffusion coefficient we are able to reproduce the grand-minimum type behaviour of the solar dynamo. Details of theoretical model along with numerical computations of dynamo equations in the partially ionized plasma are outlined. The solar surface dynamo model envisaged in this work could operate in conjunction with the global dynamo present in the bulk of the convection zone.

Cross helicity sign reversals in the dissipative scales of magnetohydrodynamic turbulence

We perform direct numerical simulations of magnetohydrodynamic (MHD) turbulence with kinetic energy and cross helicity injections at large scales. We observe that the cross helicity changes sign as we go from large and intermediate scales to small scales. In addition, the magnetic reconnections are strongest at the regions where the cross helicity changes sign and becomes smallest in magnitude. Thus, our simulations provide an important window to explore the regions of magnetic reconnections in nonlinear MHD.

Chiral fermion asymmetry in high-energy plasma simulations

ABSTRACTThe chiral magnetic effect (CME) is a quantum relativistic effect that describes the appearance of an additional electric current along a magnetic field. It is caused by an asymmetry between the number densities of left- and right-handed fermions, which can be maintained at high energies when the chirality flipping rate can be neglected, for example in the early Universe. The inclusion of the CME in the Maxwell equations leads to a modified set of magnetohydrodynamical (MHD) equations. The CME is studied here in numerical simulations with the Pencil Code. We discuss how the CME is implemented in the code and how the time step and the spatial resolution of a simulation need to be adjusted in presence of a chiral asymmetry. The CME plays a key role in the evolution of magnetic fields, since it results in a dynamo effect associated with an additional term in the induction equation. This term is formally similar to the α effect in classical mean-field MHD. However, the chiral dynamo can operate without turbulence and is associated with small spatial scales that can be, in the case of the early Universe, orders of magnitude below the Hubble radius. A chiral effect has also been identified in mean-field theory. It occurs in the presence of turbulence, but is not related to kinetic helicity. Depending on the plasma parameters, chiral dynamo instabilities can amplify magnetic fields over many orders of magnitude. These instabilities can potentially affect the propagation of MHD waves. Our numerical simulations demonstrate strong modifications of the dispersion relation for MHD waves for large chiral asymmetry. We also study the coupling between the evolution of the chiral chemical potential and the ordinary chemical potential, which is proportional to the sum of the number densities of left- and right-handed fermions. An important consequence of this coupling is the emergence of chiral magnetic waves (CMWs). We confirm numerically that linear CMWs and MHD waves are not interacting. Our simulations suggest that the chemical potential has only a minor effect on the non-linear evolution of the chiral dynamo.