Distribution Of Helicity 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.

Conserving Local Magnetic Helicity in Numerical Simulations

Magnetic helicity is robustly conserved in systems with very large magnetic Reynolds numbers, including most systems of astrophysical interest, and unlike kinetic and magnetic energy, it is not dissipated at small scales. This plays a major role in suppressing the kinematic large-scale dynamo and may also be responsible for driving the large-scale dynamo through the magnetic helicity flux. Numerical simulations of astrophysical systems typically lack sufficient resolution to enforce global magnetic helicity over several dynamical times. In these simulations, magnetic helicity is lost either through numerical errors or through the action of an unrealistically large resistivity. Errors in the internal distribution of magnetic helicity are equally important and typically larger. Here, we propose an algorithm for enforcing strict local conservation of magnetic helicity in the Coulomb gauge in numerical simulations, so that their evolution more closely approximates that of real systems.

The connection between the equatorial temperature bias and north–south helicity segregation in numerical simulations of the geodynamo

SUMMARY In recent numerical simulations of the geodynamo the dynamo action is driven, primarily, by the effects of helicity, with differential rotation playing only a secondary role. These dynamos display a number of robust features, such as: (i) thin convective columns outside the tangent cylinder whose azimuthally averaged helicity, $\langle h \rangle = \langle {{{\bf u}} \cdot \nabla \times {{\bf u}}} \rangle $, is left-handed in the north and right-handed in the south, (ii) approximately 2-D motion in the equatorial regions, with negligible axial velocity,$\langle {{u}_z} \rangle \approx 0$, (iii) positive radial current at mid-latitudes and negative radial current in the equatorial regions, (iv) a radial outflow in the equatorial regions and (v) elevated temperatures near the equator. We seek the relationship between all five of these observations. First, we note that $\langle {{u}_z} \rangle \approx 0$ near the equator follows from the skew-symmetric distribution of helicity, while a negative radial current at the equator is a generic feature of helicity-driven dynamos which have positive (negative) helicity in the south (north). Next, we confirm an earlier suggestion that the equatorial outflow is driven by Lorentz forces associated with the negative radial current. Crucially, however, this outflow does not account for the elevated equatorial temperatures. Rather, the high temperature near the equator is primarily a consequence of anisotropic turbulent diffusion, which preferentially carries heat radially outward along the equator, this anisotropy being a consequence of the (approximately) 2-D flow near the equator. In short, we show that the high equatorial temperatures are a direct consequence of the skew-symmetric distribution of helicity. Finally, we recall that the high equatorial temperatures can themselves explain the observed helicity distribution, as buoyant anomalies near the equator trigger inertial waves which carry negative helicity upward and positive helicity downward. Thus, there is a direct, two-way coupling between the high equatorial temperatures and the helicity distribution.

Spectral distribution and dissipation of turbulent helicity in rotating channel flow

Spectral distribution and dissipation of turbulent helicity in rotating channel flow

On the relationship between tropical cyclone size and environmental helicity in the South China Sea

In this study, the impact of environmental factors on tropical cyclone (TC) outer-core size was investigated for both migrating and local TCs in the South China Sea during the period 2001–2019. Among all the thermodynamic and dynamic factors, the low-level environmental helicity showed the strongest positive correlation with TC outer-core size. Large helicity favors the development and organization of convection in TCs, and the corresponding strong inflow and large angular momentum fluxes into the system is beneficial for the maintenance and enlargement of TC outer-core size. Besides, the asymmetric distribution of helicity may account for the asymmetry of TC outer-core size. Therefore, the environmental helicity, as an integrated dynamic factor, can provide an alternative view on TC outer-core size.摘要本文利用2001–2019年间的ERA5再分析数据集和热带气旋 (TC) 最佳路径观测, 分析了中国南海TC的外围尺度与环境变量之间的关系. 研究发现, 低层环境螺旋度与TC外围尺度具有显著的正相关. 大的环境螺旋度有利于TC外围对流的增强和组织化, 与之对应的径向入流和角动量输送有利于TC外围尺度的维持或扩张. 此外, 螺旋度的非对称分布与TC外围尺度的非对称性结构也密切相关. 环境螺旋度作为一个包含TC外围对流强度和组织化程度等信息的综合动力因子, 为理解TC外围尺度变化提供了不同的视角.

Scaling of magnetic dissipation and particle acceleration in ABC fields

Using particle-in-cell numerical simulations with electron–positron pair plasma, we study how the efficiencies of magnetic dissipation and particle acceleration scale with the initial coherence length $\lambda _0$ in relation to the system size $L$ of the two-dimensional ‘Arnold–Beltrami–Childress’ (ABC) magnetic field configurations. Topological constraints on the distribution of magnetic helicity in two-dimensional systems, identified earlier in relativistic force-free simulations, that prevent the high- $(L/\lambda _0)$ configurations from reaching the Taylor state, limit the magnetic dissipation efficiency to about $\epsilon _{\textrm {diss}} \simeq 60\,\%$ . We find that the peak growth time scale of the electric energy $\tau _{E,{\textrm {peak}}}$ scales with the characteristic value of initial Alfvén velocity $\beta _{A,{\textrm {ini}}}$ like $\tau _{E,\textrm {peak}} \propto (\lambda _0/L)\beta _{A,{\textrm {ini}}}^{-3}$ . The particle energy change is decomposed into non-thermal and thermal parts, with non-thermal energy gain dominant only for high initial magnetisation. The most robust description of the non-thermal high-energy part of the particle distribution is that the power-law index is a linear function of the initial magnetic energy fraction.

On the distribution of helicity in the tropical cyclone boundary layer from dropsonde composites

This study analyzes GPS dropsonde data in multiple tropical cyclones from 1997 to 2017 to investigate the boundary layer structure with a focus on helicity distribution. A helicity-based method for boundary layer height is developed and evaluated by comparing it to other boundary layer height scales including the inflow layer depth, height of the maximum tangential wind speed and thermodynamic mixed layer depth. Our dropsonde composites confirmed the radial variations of these boundary layer heights seen in previous studies. The results show that the boundary layer height defined by the maximum vertical gradient of helicity is closest to the height of the maximum tangential wind speed or jet height and is located between the inflow layer depth and thermodynamic mixed layer height in all intensity groups. All three kinematic height scales generally decrease with storm intensity at a given radius. These kinematic height scales converge in the major hurricane group, while the inflow layer depth is much larger than the other two height scales in the tropical storm group. The maximum normalized helicity is located at 100–200 m altitude which is close to the height of the maximum inflow. Both front-back and downshear-upshear asymmetries are observed in the 0–1 km layer integrated helicity in the inner core region of a storm, and the helicity on the front and downshear sides is larger in all intensity groups. The results also show that the helicity magnitude is generally larger in the boundary layer of stronger storms. Application of helicity to quantify turbulent characteristics in the boundary layer is discussed.

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.

Relative magnetic field line helicity

Context. Magnetic helicity is an important quantity in studies of magnetized plasmas as it provides a measure of the geometrical complexity of the magnetic field in a given volume. A more detailed description of the spatial distribution of magnetic helicity is given by the field line helicity, which expresses the amount of helicity associated to individual field lines rather than in the full analysed volume. Aims. Magnetic helicity is not a gauge-invariant quantity in general, unless it is computed with respect to a reference field, yielding the so-called relative magnetic helicity. The field line helicity corresponding to the relative magnetic helicity has only been examined under specific conditions so far. This work aims to define the field line helicity corresponding to relative magnetic helicity in the most general way. In addition to its general form, we provide the expression for the relative magnetic field line helicity in a few commonly used gauges, and reproduce known results as a limit of our general formulation. Methods. By starting from the definition of relative magnetic helicity, we derived the corresponding field line helicity, and we noted the assumptions on which it is based. Results. We checked that the developed quantity reproduces relative magnetic helicity by using three different numerical simulations. For these cases we also show the morphology of field line helicity in the volume, and on the photospheric plane. As an application to solar situations, we compared the morphology of field line helicity on the photosphere with that of the connectivity-based helicity flux density in two reconstructions of an active region’s magnetic field. We discuss how the derived relative magnetic field line helicity has a wide range of applications, notably in solar physics and magnetic reconnection studies.

Intermittency spectra of current helicity in solar active regions

We analyse the spatial distribution of current helicity in solar active regions. A comparison of current helicity maps derived from three different instruments (Helioseismic and Magnetc Imager on board the Solar Dynamics Observatory, SDO/HMI, Spectro-Polarimeter on board the Hinode, and Solar Magnetic Field Telescope at the Huairou Solar Observing Station, China, HSOS/SMFT) is carried out. The comparison showed an excellent correlation between the maps derived from the spaceborne instruments and moderate correlation between the maps derived from SDO/HMI and HSOS/SMFT vector magnetograms. The results suggest that the obtained maps characterize real spatial distribution of current helicity over an active region. To analyse intermittency of current helicity, we traditionally use the high-order structure functions and flatness function approach. The slope of a flatness function within some range of scales - the flatness exponent - is a measure of the degree of intermittency. SDO/HMI vector magnetograms for 3 ARs (NOAA 11158, 12494, and 12673) were used to calculate the flatness exponent time variations. All three ARs exhibited emergence of a new magnetic flux during the observational interval. The flatness exponent indicated the increase of intermittency 12-20 hours before the emergence of a new flux. We suppose that this behaviour can indicate subphotospheric fragmentation or distortion of the pre-existed electric current system by emerging magnetic flux.

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.

Are planetary dynamos driven by helical waves?

In most numerical simulations of the Earth’s core the dynamo is located outside the tangent cylinder and, in a zero-order sense, takes the form of a classical$\unicode[STIX]{x1D6FC}^{2}$dynamo. Such a dynamo usually requires a distribution of helicity,$h$, which is asymmetric about the equator and in the simulations it is observed that, outside the tangent cylinder, the helicity is predominantly negative in the north and positive in the south. If we are to extrapolate the results of these simulations to the planets, we must understand how this asymmetry in helicity is established and ask if the same mechanism is likely to operate in a planet. In some of the early numerical dynamos, which were too viscous by a factor of at least$10^{9}$, as measured by the Ekman number, the asymmetric helicity distribution was attributed to Ekman pumping. However, Ekman pumping plays much less of a role in more recent, and less viscous, numerical dynamos, and almost certainly plays no significant role in the core of a planet. So the question remains: what establishes the asymmetric helicity distribution in the simulations and is this mechanism likely to carry over to planetary cores? In this paper we review the evidence that planetary dynamos, and their numerical analogues, might be maintained by helical waves, especially inertial waves, excited in and around the equatorial regions. This cartoon arises from the observation that there tends to be a statistical bias in the buoyancy flux towards the equatorial regions, and so waves are preferentially excited there. Moreover, upward (downward) propagating inertial waves carry negative (positive) helicity, which leads naturally to a segregation in$h$.

Helicity sources in a rotating convection

Convective flows from localized heater in a rotating layer were studied numerically in a three-dimensional non-stationary formulation. Distribution of helicity, its mean and fluctuating contributions were simulated for two specific regimes. In the first one the stable cyclonic vortex and intensive convective jet produce substantial amount of helicity near the axis of rotation. In the second one convective flow is more chaotic, cyclonic vortex appears at some distance from the center and as a result helicity is more dispersed in the lower layer of the fluid. Helicity in a described system is characterized by high level of pulsations. Spatial and temporal variations of helicity sources were analysed using equation for helicity balance. Time variations of viscous term and buoyancy term in helicity equation strongly exceed variations of other terms and the helicity time derivative. In a described system the buoyancy term is a source of helicity and viscous term is a sink. It was found that they are in antiphase and compensate each other.

Estimating helicity in the atmospheric boundary layer from acoustic sounding data

Distributions of the velocity-field helicity in the atmospheric boundary layer have been obtained from acoustic sounding data. The helicity of large-scale motions (0.3–0.6 m/s2) exceeds (by an order of magnitude) its independently measured turbulent values, which are close to helicity averaged over the layer (0.02–0.12 m/s2). In the absence of strong convection, there is good correlation between helicity and wind velocity squared at upper sounding levels of 400 to 600 m.

The global distribution of magnetic helicity in the solar corona

By defining an appropriate field line helicity, we apply the powerful concept of magnetic helicity to the problem of global magnetic field evolution in the Sun’s corona. As an ideal-magnetohydrodynamic invariant, the field line helicity is a meaningful measure of how magnetic helicity is distributed within the coronal volume. It may be interpreted, for each magnetic field line, as a magnetic flux linking with that field line. Using magneto-frictional simulations, we investigate how field line helicity evolves in the non-potential corona as a result of shearing by large-scale motions on the solar surface. On open magnetic field lines, the helicity injected by the Sun is largely output to the solar wind, provided that the coronal relaxation is sufficiently fast. But on closed magnetic field lines, helicity is able to build up. We find that the field line helicity is non-uniformly distributed, and is highly concentrated in twisted magnetic flux ropes. Eruption of these flux ropes is shown to lead to sudden bursts of helicity output, in contrast to the steady flux along the open magnetic field lines.

Vorticity in heavy-ion collisions

We study the event-by-event generation of flow vorticity in RHIC Au + Au collisions and LHC Pb + Pb collisions by using the HIJING model. Different definitions of the vorticity field and velocity field are considered. A variety of properties of the vorticity are explored, including the impact parameter dependence, the collision energy dependence, the spatial distribution, the event-by-event fluctuation of the magnitude and azimuthal direction, and the time evolution. In addition, the spatial distribution of the flow helicity is also studied.

Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

We report results on rotating stratified turbulence in the absence of forcing and with large-scale isotropic initial conditions using direct numerical simulations computed on grids of up to 40963 points. The Reynolds and Froude numbers are, respectively, equal to Re = 5.4 × 104 and Fr = 0.0242. The ratio of the Brunt-Väisälä to the inertial wave frequency, N/f, is taken to be equal to 4.95, a choice appropriate to model the dynamics of the southern abyssal ocean at mid latitudes. This gives a global buoyancy Reynolds number RB = ReFr2 ≈ 32, a value sufficient for some isotropy to be recovered in the small scales beyond the Ozmidov scale, but still moderate enough that the intermediate scales where waves are prevalent are well resolved. We concentrate on the large-scale dynamics, for which we find a spectrum compatible with the Bolgiano-Obukhov scaling. This scaling is also found for geostrophically balanced initial conditions on a run at a lower resolution and hence lower RB ≈ 4. Furthermore, we confirm that the Froude number based on a typical vertical length scale is of order unity, with strong gradients in the vertical. Two characteristic scales emerge from this computation and are identified from sharp variations in the spectral distribution of either total energy or helicity. A spectral break is also observed at a scale at which the partition of energy between the kinetic and potential modes changes abruptly, and beyond which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous in the flow, in the velocity and temperature fields, with local overturning events indicated by small local Richardson numbers and strong localized vortex tangles . Finally, a small large-scale enhancement of energy directly attributable to the effect of rotation is also observed.

Observational cross helicity on the solar surface

We analyzed the correlation of the solar magnetograms and Dopplergrams from SOHO/MDI and SDO/HMI respectively. It is found that the full disk correlation coefficient of Dopplergrams is more than 0.80 between SOHO/MDI and SDO/HMI. The full disk correlation coefficient of magnetograms is about 0.73 and is more than 0.95 for active regions only. We also analyzed the distribution of the cross helicity (velocity-magnetic-field correlation) on the solar surface. It is found that the latitude distributions of the cross helicity based on SOHO/MDI data and SDO/HMI data have similar tendencies, and in the analysis of solar active regions the amplitude of the horizontal component of the mean cross helicity is about two times the line-of-sight one.

Hemispheric Distribution of Subsurface Kinetic Helicity and Its Variation with Magnetic Activity

We study the hemispheric distribution of the kinetic helicity of subsurface flows in the near-surface layers of the solar convection zone and its variation with magnetic activity. We determine subsurface flows with a ring-diagram analysis applied to Global Oscillation Network Group (GONG) Dopplergrams and Dynamics Program data from the Michelson Doppler Imager (MDI) instrument onboard the Solar and Heliospheric Observatory (SOHO). We determine the average kinetic helicity density as a function of Carrington rotation and latitude. The average kinetic helicity density at all depths and the kinetic helicity, integrated over 2 – 7 Mm, follow the same hemispheric rule as the current/magnetic helicity proxies with predominantly positive values in the southern and negative ones in the northern hemisphere. This holds true for all levels of magnetic activity from quiet to active regions. However, this is a statistical result; only about 55 % of all locations follow the hemispheric rule. But these locations have larger helicity values than those that do not follow the rule. The average values of helicity density increase with depth for all levels of activity, which might reflect an increase of the characteristic size of convective motions with greater depth. The average helicity of subsets of high magnetic activity is about five times larger than that of subsets of low activity. The solar-cycle variation of helicity is thus mainly due to the presence or absence of active regions. During the rising phase of cycle 24, locations of high magnetic activity at low latitudes show a weaker hemispheric behavior compared to the rising phase of cycle 23.

Influence of initial conditions on the large-scale dynamo growth rate

To investigate the effect of energy and helicity on the growth of magnetic field, helical kinetic forcing was applied to the magnetohydrodynamic(MHD) system that had a specific distribution of energy and helicity as initial conditions. Simulation results show the saturation of a system is not influenced by the initial conditions, but the growth rate of large scale magnetic field is proportionally dependent on the initial large scale magnetic energy and helicity. It is already known that the helical component of small scale magnetic field(i.e., current helicity $<{\bf j}\cdot {\bf b}>$) quenches the growth of large scale magnetic field. However, $<{\bf j}\cdot {\bf b}>$ can also boost the growth of large scale magnetic field by changing its sign and magnitude. In addition, simulation shows the nonhelical magnetic field can suppress the velocity field through Lorentz force. Comparison of the profiles of evolving magnetic and kinetic energy indicates that kinetic energy migrates backward when the external energy flows into the three dimensional MHD system, which means the velocity field may play a preceding role in the very early MHD dynamo stage.