Strong Shearing Motions Research Articles

Evolution of an Emerging Anti-Hale Region and its Associated Eruptive Solar Flares in NOAA AR 12882

Solar active regions that violate the Hale–Nicholson rule are rare, but once formed, they tend to be flare-productive. In this letter, we investigated the evolution of an anti-Hale region newly emerging from the active region AR 12882 with a regular Hale distribution. The entire active region became very active, producing two eruptive flares within 48 hr after the emergence of the anti-Hale region. Strong photospheric shear motions appeared in this anti-Hale region, changing its tilt angle from the north–south direction to the east–west direction. The flux emergence and shearing motions continuously injected magnetic energy and negative magnetic helicity into the upper atmosphere. Meanwhile, the upper coronal structure changed from double J-shaped to reverse S-shaped, forming a magnetic flux rope lying above the anti-Hale region. This magnetic flux rope erupted successfully, then re-formed and erupted successfully again, producing a C2.7 flare and an M1.6 flare, respectively. Moreover, a large cusp structure was observed to form next to the flaring region after the M1.6 flare. Accordingly, we conclude that the evolution of the emerging anti-Hale region provides sufficient magnetic energy and helicity for the flares, and the interaction between the emerging anti-Hale region and the preexisting Hale active region eventually promotes the flares to be eruptive.

Triple Decomposition of Velocity Gradient Tensor in Compressible Turbulence

The decomposition of the local motion of a fluid into straining, shearing, and rigid-body rotation is examined in this work for a compressible isotropic turbulence by means of direct numerical simulations. The triple decomposition is closely associated with a basic reference frame (BRF), in which the extraction of the biasing effect of shear is maximized. In this study, a new computational and inexpensive procedure is proposed to identify the BRF for a three-dimensional flow field. In addition, the influence of compressibility effects on some statistical properties of the turbulent structures is addressed. The direct numerical simulations are carried out with a Reynolds number that is based on the Taylor micro-scale of Reλ=100 for various turbulent Mach numbers that range from Mat=0.12 to Mat=0.89. The DNS database is generated with an improved seventh-order accurate weighted essentially non-oscillatory scheme to discretize the non-linear advective terms, and an eighth-order accurate centered finite difference scheme is retained for the diffusive terms. One of the major findings of this analysis is that regions featuring strong rigid-body rotations or straining motions are highly spatially intermittent, while most of the flow regions exhibit moderately strong shearing motions in the absence of rigid-body rotations and straining motions. The majority of compressibility effects can be estimated if the scaling laws in the case of compressible turbulence are rescaled by only considering the solenoidal contributions.

Star Formation Efficiencies at Giant Molecular Cloud Scales in the Molecular Disk of the Elliptical Galaxy NGC 5128 (Centaurus A)

Abstract We present ALMA CO (1−0) observations toward the dust lane of the nearest elliptical and radio galaxy, NGC 5128 (Centaurus A), with high angular resolution (∼1″, or 18 pc), including information from large to small spatial scales and total flux. We find a total molecular gas mass of 1.6 × 109 M ⊙ and reveal the presence of filamentary components more extended than previously seen, up to a radius of 4 kpc. We find that the global star formation rate is ∼1 M ⊙ yr−1, which yields a star formation efficiency (SFE) of 0.6 Gyr−1 (depletion time τ = 1.5 Gyr), similar to those in disk galaxies. We show the most detailed view to date (40 pc resolution) of the relation between molecular gas and star formation within the stellar component of an elliptical galaxy, from a scale of several kiloparsecs to the circumnuclear region close to the powerful radio jet. Although on average the SFEs are similar to those of spiral galaxies, the circumnuclear disk (CND) presents SFEs of 0.3 Gyr−1, lower by a factor of 4 than the outer disk. The low SFE in the CND is in contrast to the high SFEs found in the literature for the circumnuclear regions of some nearby disk galaxies with nuclear activity, probably as a result of larger shear motions and longer active galactic nucleus feedback. The higher SFEs in the outer disk suggest that only central molecular gas or filaments with sufficient density and strong shear motions will remain in ∼1 Gyr, which will later result in the compact molecular distributions and low SFEs usually seen in other giant ellipticals with cold gas.

Energy Origination and Triggering Mechanism of a Series of Homologous Confined Flares

Abstract Using the Hα data from the New Vacuum Solar Telescope at the Fuxian Solar Observatory together with multiwavelength images and magnetograms obtained by the Solar Dynamics Observatory, we study the detailed process of three homologous confined flares in active region NOAA 11861 on 2013 October 12. All of the three flares occurred at the same location, with similar morphologies and comparable classes. Through analyzing the evolution of magnetic field and flow field, we found an emergence of magnetic flux and a strong shearing motion between two opposite polarities near the following sunspot. The magnetic flux and the average transverse field strength exhibited a decrease before each eruption and reached the lowest point at the onset of each eruption. By calculating the shearing and the emergence energy in the photosphere, we found that the integral of energy injected from the photosphere, for a few hours, could provide enough energy for the flares. The reconnection between different loops was observed in Hα images during the occurrence of each flare. These results suggest that the emerging magnetic flux and the shearing motion in the photosphere can inject the energy to the sheared magnetic loops and the energy was finally released via magnetic reconnection to power the solar flares.

Triple decomposition of velocity gradient tensor in homogeneous isotropic turbulence

The triple decomposition of a velocity gradient tensor is studied with direct numerical simulations of homogeneous isotropic turbulence, where the velocity gradient tensor ∇u is decomposed into three components representing an irrotational straining motion (∇u)EL, a rigid-body rotation (∇u)RR, and a shearing motion (∇u)SH. Strength of these motions can be quantified with the decomposed components. A procedure of the triple decomposition is proposed for three-dimensional flows, where the decomposition is applied in a basic reference frame identified by examining a finite number of reference frames obtained by three sequential rotational transformations of a Cartesian coordinate. Even though more than one basic reference frame may be available for the triple decomposition, the results of the decomposition depend little on the choice of basic reference frame. In homogeneous isotropic turbulence, regions with strong rigid-body rotations or straining motions are highly intermittent in space, while most flow regions exhibit moderately strong shearing motions in the absence of straining motions and rigid-body rotations. In the classical double decomposition, the velocity gradient tensor is decomposed into a rate-of-rotation tensor Ωij and a rate-of-strain tensor Sij. Regions with large ω2=2ΩijΩij can be associated with rigid-body rotations and shearing motions while those with large s2=2SijSij can be associated with irrotational straining motions and shearing motions. Therefore, vortices with rigid-body rotations and shear layers in turbulence cannot be detected solely by thresholding ω or s while they can be identified simply with (∇u)RR and (∇u)SH in the triple decomposition, respectively. The thickness of the shear layer detected in the triple decomposition is about 8 times of Kolmogorov scale, while the velocity parallel to the layer changes rapidly across the layer, in which the velocity difference across the shear layer is of the order of the root-mean-squared velocity fluctuation.

Eruption of a multi-flux-rope system in solar active region 12673 leading to the two largest flares in Solar Cycle 24

Context. Solar active region (AR) 12673 in 2017 September produced the two largest flares in Solar Cycle 24: the X9.3 flare on September 6 and the X8.2 flare on September 10. Aims. We attempt to investigate the evolutions of the two large flares and their associated complex magnetic system in detail. Methods. Combining observations from the Solar Dynamics Observatory and results of nonlinear force-free field (NLFFF) modeling, we identify various magnetic structures in the AR core region and examine the evolution of these structures during the flares. Results. Aided by the NLFFF modeling, we identify a double-decker flux rope configuration above the polarity inversion line (PIL) in the AR core region. The north ends of these two flux ropes were rooted in a negative- polarity magnetic patch, which began to move along the PIL and rotate anticlockwise before the X9.3 flare on September 6. The strong shearing motion and rotation contributed to the destabilization of the two magnetic flux ropes, of which the upper one subsequently erupted upward due to the kink-instability. Then another two sets of twisted loop bundles beside these ropes were disturbed and successively erupted within five minutes like a chain reaction. Similarly, multiple ejecta components were detected as consecutively erupting during the X8.2 flare occurring in the same AR on September 10. We examine the evolution of the AR magnetic fields from September 3 to 6 and find that five dipoles emerged successively at the east of the main sunspot. The interactions between these dipoles took place continuously, accompanied by magnetic flux cancellations and strong shearing motions. Conclusions. In AR 12673, significant flux emergence and successive interactions between the different emerging dipoles resulted in a complex magnetic system, accompanied by the formations of multiple flux ropes and twisted loop bundles. We propose that the eruptions of a multi-flux-rope system resulted in the two largest flares in Solar Cycle 24.

The effect of cube-roughened walls on the response of rough-to-smooth (RTS) turbulent channel flows

Direct numerical simulations of cube-roughened rough-to-smooth channel flows are performed with the objective of studying the response of turbulence statistics in the developing flow over smooth walls. Non-equilibrium effects persist and the global recovery is slow and incomplete by the streamwise exit of the computational domains, which is at about 10 channel half heights. The estimated recovery distance in the outer regions of the flow is on the order of 50 channel half heights, but different statistics have disparate relxataion rates. The turbulence structure swiftly relaxes to a ‘near’ equilibrium very close to the wall. Within this wall layer, due to a strong mean shear, turbulence statistics and instantaneous motions resemble their fully-smooth equivalents. However, the reversion is not complete because it is interrupted by large structures that persist from the upstream roughness. As the flow encounters the step change in roughness, it expands producing strong mean-advection effects, which prevent the canonical log-law region from being established. The expansion of the mean flow also results in an adverse pressure gradient across the channel. It recovers gradually, only becoming favourable near the exit of the computational domains.

Homologous White Light Solar Flares Driven by Photospheric Shear Motions

Abstract We describe the peculiarity of two recurrent white light flares that occurred on 2017 September 06, in the super active region NOAA 12673, with a time interval, between their peaks, of about 3 hr. These events of the X2.2 and X9.3 GOES classes are very important, not only for their high level of emission and for the visible effects on the lower layers of the solar atmosphere, which are discernible as clear white light ribbons, but also for the strong horizontal photospheric motions, which seemed to drive them. In fact, we observed the displacement of a negative umbra located in the main delta spot of the active region for several hours before the flare occurrence. We measured velocities of up to 0.6 km s−1. The strong and persistent shear motion of the photospheric structures, together with the high intensity of the magnetic flux involved in these events, can be considered responsible for the new energy that is continuously supplied to the magnetic system. From the timing of the emissions at different wavelengths, we were able to provide some constraints for the modeling of such events.

THE LINK BETWEEN TURBULENCE, MAGNETIC FIELDS, FILAMENTS, AND STAR FORMATION IN THE CENTRAL MOLECULAR ZONE CLOUD G0.253+0.016

ABSTRACT Star formation is primarily controlled by the interplay between gravity, turbulence, and magnetic fields. However, the turbulence and magnetic fields in molecular clouds near the Galactic center may differ substantially compared to spiral-arm clouds. Here we determine the physical parameters of the central molecular zone (CMZ) cloud G0.253+0.016, its turbulence, magnetic field, and filamentary structure. Using column density maps based on dust-continuum emission observations with ALMA+Herschel, we identify filaments and show that at least one dense core is located along them. We measure the filament width and the sonic scale of the turbulence, and find . A strong velocity gradient is seen in the HNCO intensity-weighted velocity maps obtained with ALMA+Mopra. The gradient is likely caused by large-scale shearing of G0.253+0.016, producing a wide double-peaked velocity probability distribution function (PDF). After subtracting the gradient to isolate the turbulent motions, we find a nearly Gaussian velocity PDF typical for turbulence. We measure the total and turbulent velocity dispersion, and , respectively. Using magnetohydrodynamical turbulence simulations, we find that G0.253+0.016's turbulent magnetic field is only of the ordered field component. Combining these measurements, we reconstruct the dominant turbulence driving mode in G0.253+0.016 and find a driving parameter of , indicating solenoidal (divergence-free) driving. We compare this to spiral-arm clouds, which typically have a significant compressive (curl-free) driving component ( ). Motivated by previous reports of strong shearing motions in the CMZ, we speculate that shear causes the solenoidal driving in G0.253+0.016 and show that this reduces the star-formation rate by a factor of 6.9 compared to typical nearby clouds.

ON THE INJECTION OF HELICITY BY THE SHEARING MOTION OF FLUXES IN RELATION TO FLARES AND CORONAL MASS EJECTIONS

An investigation of helicity injection by photospheric shear motions is carried out for two active regions(ARs), NOAA 11158 and 11166, using line-of-sight magnetic field observations obtained from the Helioseismic and Magnetic Imager on-board Solar Dynamics Observatory. We derived the horizontal velocities in the active regions from the Differential Affine Velocity Estimator(DAVE) technique. Persistent strong shear motions at the maximum velocities in the range of 0.6--0.9km/s along the magnetic polarity inversion line and outward flows from the peripheral regions of the sunspots were observed in the two active regions. The helicities injected in NOAA 11158 and 11166 during their six days' evolution period were estimated as $14.16\times10^{42}$Mx$^2$ and $9.5\times10^{42}$Mx$^2$, respectively. The estimated injection rates decreased up to 13% by increasing the time interval between the magnetograms from 12 min to 36 min, and increased up to 9% by decreasing the DAVE window size from $21\times18$ to $9\times6$ pixel$^2$, resulting in 10% variation in the accumulated helicity. In both ARs, the flare prone regions (R2) had inhomogeneous helicity flux distribution with mixed helicities of both signs and that of CME prone regions had almost homogeneous distribution of helicity flux dominated by single sign. The temporal profiles of helicity injection showed impulsive variations during some flares/CMEs due to negative helicity injection into the dominant region of positive helicity flux. A quantitative analysis reveals a marginally significant association of helicity flux with CMEs but not flares in AR 11158, while for the AR 11166, we found marginally significant association of helicity flux with flares but not CMEs, providing evidences of the role of helicity injection at localized sites of the events.

EVOLUTION OF MAGNETIC FIELD AND ENERGY IN A MAJOR ERUPTIVE ACTIVE REGION BASED ONSDO/HMI OBSERVATION

We report the evolution of magnetic field and its energy in NOAA active region 11158 over 5 days based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). Fast flux emergence and strong shearing motion led to a quadrupolar sunspot complex that produced several major eruptions, including the first X-class flare of Solar Cycle 24. Extrapolated non-linear force-free coronal fields show substantial electric current and free energy increase during early flux emergence near a low-lying sigmoidal filament with sheared kilogauss field in the filament channel. The computed magnetic free energy reaches a maximum of ~2.6e32 erg, about 50% of which is stored below 6 Mm. It decreases by ~0.3e32 erg within 1 hour of the X-class flare, which is likely an underestimation of the actual energy loss. During the flare, the photospheric field changed rapidly: horizontal field was enhanced by 28% in the core region, becoming more inclined and more parallel to the polarity inversion line. Such change is consistent with the conjectured coronal field "implosion", and is supported by the coronal loop retraction observed by the Atmospheric Imaging Assembly (AIA). The extrapolated field becomes more "compact" after the flare, with shorter loops in the core region, probably because of reconnection. The coronal field becomes slightly more sheared in the lowest layer, relaxes faster with height, and is overall less energetic.

The Magnetic Field, Horizontal Motion and Helicity in a Fast Emerging Flux Region which Eventually forms a Delta Spot

We studied the behavior of magnetic field, horizontal motion and helicity in a fast emerging flux region NOAA 10488 which eventually forms a δ spot. It is found that the rotation of photospheric footpoints forms in the earlier stage of magnetic flux emergence and the relative shear motion of different magnetic flux systems appears later in this active region (AR). Therefore the emerging process of the AR can be separated into two phases: rotation and shear. We have computed the magnetic helicity injected into the corona using the local correlation tracking (LCT) technique. Furthermore we determined the vertical component of current helicity density and the vertical component of induction electric fields Ez = (V× B)z in the photosphere. Particularly we have presented the comparison of the injection rate of magnetic helicity and the variation of the current helicity density. The main results are as follows: (1) The strong shear motion (SSM) between the new emerging flux system and the old one brings more magnetic helicity into the corona than the twisting motions. (2) After the maturity of the main bipolar spots, their twist decreases and the SSM becomes dominant and the major contributor of magnetic non-potentiality in the solar atmosphere in this AR. (3) The positions of the maxima of Ez (about 0.1 ∼ 0.2 V cm−1) shift from the twisting areas to the areas showing SSMs as the AR evolved from the rotation phase to the shear one, but no obvious correlation is found between the kernels of Hα flare and Ez for the M1.6 flare in this AR. (4) The coronal helicity inferred from the horizontal motion of this AR amounts to −6 × 1043 Mx2. It is comparable with the coronal helicity of ARs producing flares with coronal mass ejections (CMEs) or helicity carried away by magnetic clouds (MCs) reported in previous studies (Nindos, Zhang, and Zhang, 2003; Nindos and Andrews, 2004). In addition, the formation of the δ configuration in this AR belongs to the third formation type indicated by Zirin and Liggett (1987), i.e., collision of opposite polarities from different dipoles, and can be naturally explained by the SSM.

Redshift distortions in one-dimensional power spectra

We present a model for one-dimensional (1D) matter power spectra in redshift space as estimated from data provided along individual lines of sight. We derive analytic expressions for these power spectra in the linear and nonlinear regimes, focusing on redshift distortions arising from peculiar velocities. In the linear regime, redshift distortions enhance the 1D power spectra only on small scales, and do not affect the power on large scales. This is in contrast to the effect of distortions on three-dimensional (3D) power spectra estimated from data in 3D space, where the enhancement is independent of scale. For CDM cosmologies, the 1D power spectra in redshift and real space are similar for wavenumbers $q<0.1h/Mpc$ where both have a spectral index close to unity, independent of the details of the 3D power spectrum. Nonlinear corrections drive the 1D power spectrum in redshift space into a nearly universal shape over scale $q<10h/Mpc$, and suppress the power on small scales as a result of the strong velocity shear and random motions. The redshift space, 1D power spectrum is mostly sensitive to the amplitude of the initial density perturbations. Our results are useful in particular for power spectra computed from the SDSS quasars sample.

The GPS strain rate field in the Aegean Sea and western Anatolia

The GPS velocity field of the Aegean Sea and western Anatolia is used to determine crustal deformation strain rates for the period 1988 to 1996. The zone from the Marmara Sea to the North Aegean Trough is associated with strong right‐lateral shear motion, with maximum strain rates of 170 nstrain/a. In the northern Aegean Sea the extensional deviatoric axes are oriented NNE‐SSW, associated with strain rates reaching 150 nstrain/a, and in western Anatolia varying around N‐S with rates of up to 95 nstrain/a. The extensional areas mostly coincide with active graben features. The south‐western Aegean Sea is almost strain‐free. In general, the areas of high geodetic strain rates are accompanied by distinct seismic clusters whereas the strain‐free regions are nearly aseismic.

The strain rate field in the eastern Mediterranean region, estimated by repeated GPS measurements

We use the combined GPS velocity field of the eastern Mediterranean for the period 1988 to 1996 to determine crustal deformation strain rates in a region comprising the Hellenic arc, the Aegean Sea, and western Anatolia. We interpret the velocity field and determine the strain rate tensor by the spatial derivatives of the collocated motion vectors. The region following the line Marmara Sea, North Aegean Trough, northern central Greece, and the central Ionian islands is associated with strong right-lateral shear motion, with maximum shear strain rates of 180 nano-strain/a (180×10 −9/a). In the central Aegean Sea, N–S-oriented extensional processes prevail, reaching 100 nano-strain/a. The southern Aegean is characterized by relatively small strain rates. Maximum extensional components of the strain rate tensor, reaching 150 nano-strain/a in a N–S direction, are found in central Greece. The Hellenic arc is associated with moderate arc-parallel extension and strong compression perpendicular to it. Projections of the strain rates parallel to the major fault zones reveal that the northern Aegean is governed by the westward continuation of the North Anatolian Fault Zone which is associated with strong dextral shearing (maximum 220 nano-strain/a), accompanied by numerous large earthquakes in this century.

A piezoelectric pseudoshear multilayer actuator

A type of high strain piezoelectric ceramic actuator, namely, pseudoshear multilayer actuator, is described. In this structure, a stack of prepoled rectangular piezoelectric transducer ceramic sheets are conductively bonded at alternate ends, while the bottom layer bonded on a fixed base. When driven, alternate layers elongate or shrink in the same direction through converse piezoelectric effect, which results in the actuator structure developing a strong shear motion about the face perpendicular to the bonding direction. Experimental results indicate that more than 50 μm displacement can be achieved from the top layer for an actuator consisting of 18 layers with dimensions of 25.57 mm×4.02 mm×0.51 mm (1×w×t). By reducing ceramic sheet thickness and using more layers, even large displacement can be obtained, and driving voltage can also be reduced while keeping the same field level. Nonlinear piezoelectric response under high driving field further enhances the displacement level.

Ion beam driven electrostatic shocks

Electrostatic shock waves have been detected during the injection of an artificial xenon ion beam into the collisionless ionospheric plasma. The beam was directed quasi‐perpendicular to the ambient magnetic field. The ion source was situated on a small ejectable payload. The properties of the plasma/ion beam interaction were recorded on the main payload as a function of the separation distance to the ion source. The shock structure develops at distances where the apparent azimuthal speed of the beam fan is comparable to the phase velocity of ion acoustic waves sustained by background O+ ions. The shock is characterized by a decrease in the local density up to about 10% of the background density, strong shear motion visible in the convection electric field, field‐aligned potential drops of the order of several tens of millivolts, increased electron temperatures, and fluxes of reflected ions. Probably suprathermal electron fluxes along the magnetic field were also present, but these have not been measured. The Mach number is determined to M = 1.09, and thus the shock is weak and turbulent as a result of ion acoustic turbulence which has been observed throughout the shock region. It is suggested that this turbulence is driven by an ion‐ion instability excited by reflected background ions. Estimates of the number density of reflected ions show that roughly 50% of the background ion population may be reflected from the shock potential. On a larger spatial scale these reflected ions may be responsible for the excitation of the observed lower hybrid and ion cyclotron harmonic waves in front of the leading edge of the beam. No shock has been found on the trailing edge of the beam, suggesting that different physical conditions apply there.

The nonlinear breakup of a magnetic layer: instability to interchange modes

Motivated by considerations of the solar toroidal magnetic field we have studied the behaviour of a layer of uniform magnetic field embedded in a convectively stable atmosphere. Since the field can support extra mass, such a configuration is top-heavy and thus instabilities of the Rayleigh-Taylor type can occur. For both static and rotating basic states we have followed the evolution of the interchange modes (no bending of the field lines) by integrating numerically the nonlinear compressible MHD equations. The initial Rayleigh-Taylor instability of the magnetic field gives instabilities to strong shearing motions, thereby exciting secondary Kelvin-Helmholtz instabilities which wrap the gas into regions of intense vorticity. The subsequent motions are determined primarily by the strong interactions between vortices which are responsible for the rapid disruption of the magnetic layer.

Nonlinear Anelastic Modal Theory for Solar Convection

AbstractPreliminary solar envelope models have been computed using the single-mode anelastic equations as a description of turbulent convection. This approach provides estimates for the variation with depth of the largest convective cellular flows, akin to giant cells, with horizontal sizes comparable to the total depth of the convection zone. These modal nonlinear treatments are capable of describing compressible motions occurring over many density scale heights. Single-mode anelastic solutions have been constructed for a solar envelope whose mean stratification is nearly adiabatic over most of its vertical extent because of the enthalpy (or convective) flux explicitly carried by the big cell; a sub-grid scale representation of turbulent heat transport is incorporated into the treatment near the surface. The single-mode equations admit two solutions for the same horizontal wavelength, and these are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. It is striking that the upward directed flows experience large pressure effects when they penetrate into regions where the vertical scale height has become small compared to their horizontal scale. The fluctuating pressure can modify the density fluctuations so that the sense of the buoyancy force is changed, with buoyancy braking actually achieved near the top of the convection zone. The pressure and buoyancy work in the shallow but unstable H+ and He+ ionization regions can serve to decelerate the vertical motions and deflect them laterally, leading to strong horizontal shearing motions. It appears that such dynamical processes may explain why the amplitudes of flows related to the largest scales of convection are so feeble in the solar atmosphere.