Rotation Profile Research Articles

Characterization and optimization of weld properties due to the effect of different pin profiles for AA8011 – based friction stir welding

PurposeThis Friction stir welding study aims to weld thick AA8011 aluminium plates, and the interface joints created with a variety of tool pin profiles were examined for their effects on the welding process.Design/methodology/approachScanning electron microscopy and optical microscopy and X-ray diffraction were used to examine the macro and micro-structural characteristics, as well as the fracture surfaces, of tensile specimens. The mechanical properties (tensile, hardness tests) of the base metal and the welded specimens under a variety of situations being tested. Additionally, a fracture toughness test was used to analyse the resilience of the base metal and the best weldments to crack formation. Using a response surface methodology with a Box–Behnken design, the optimum values for the three key parameters (rotational speed, welding speed and tool pin profile) positively affecting the weld quality were established.FindingsThe results demonstrate that a defect-free junction can be obtained by using a cylindrical tool pin profile, increasing the rotational speed while decreasing the welding speeds. The high temperature and compressive residual stress generated during welding leads to the increase in grain size. The grain size of the welded zone for optimal conditions is significantly smaller and the hardness of the stir zone is higher than the other experimental run parameters.Originality/valueThe work focuses on the careful examination of microstructures behaviour under various tool pin profile responsible for the change in mechanical properties. The mathematical model generated using Taguchi approach and parameters was optimized by using multi-objectives response surface methodology techniques.

SNAPPING HIP SYNDROME: A SYSTEMATIC REVIEW OF CURRENT SURGICAL MANAGEMENT AND A CASE REPORT OF AN OVERLOOKED CAUSE

IntroductionSnapping hip syndrome is a common condition affecting 10% of the population. It is due to the advance of the iliotibial band (ITB) over the greater trochanter during lower limb movements and often associated with hip overuse, such as in athletic activities. Management is commonly conservative with physiotherapy or can be surgical to release the ITB. Here we carry out a systematic review into published surgical management and present a case report on an overlooked cause of paediatric snapping hip syndrome.Materials & MethodsA systematic review looking at published surgical management of snapping hip was performed according to PRISMA guidelines. PubMed, MEDLINE, EMBASE, CINAHL and the Cochrane Library databases were searched for “((Snapping hip OR Iliotibial band syndrome OR ITB syndrome) AND (Management OR treatment))”. Adult and paediatric published studies were included as few results were found on paediatric snapping hip alone.Results1548 studies were screened by 2 independent reviewers. 8 studies were included with a total of 134 cases, with an age range of 14–71 years. Surgical management ranged from arthroscopic, open or ultrasound guided release of the ITB, as well as gluteal muscle releases. Common outcome measures showed statistically significant improvement pre- and post-operatively in visual analogue pain score (VAPS) and the Harris Hip Score (HHS). VAPS improved from an average of 6.77 to 0.3 (t-test p value <0.0001) and the HHS improved from an average of 62.6 to 89.4 (t-test p value <0.0001).ConclusionsAlthough good surgical outcomes have been reported, no study has reported on the effect of rotational profile of the lower limbs and snapping hip syndrome. We present the case of a 13-year-old female with snapping hip syndrome and trochanteric pain. Ultrasound confirmed external snapping hip with normal soft tissue morphology and radiographs confirmed no structural abnormalities. Following extensive physiotherapy and little improvement, she presented again aged 17 with concurrent anterior knee pain, patella mal-tracking and an asymmetrical out-toeing gait. CT rotational profile showed 2° of femoral neck retroversion and excessive external tibial torsion of 52°. Consequently, during her gait cycle, in order to correct her increased foot progression angle, the hip has to internally rotate approximately 35–40°, putting the greater trochanter in an anterolateral position in stance phase. This causes the ITB to snap over her abnormally positioned greater trochanter. Therefore, to correct rotational limb alignment, a proximal tibial de-rotation osteotomy was performed with 25° internal rotation correction. Post-operatively the patient recovered well, HHS score improved from 52.5 to 93.75 and her snapping hip has resolved. This study highlights the importance of relevant assessment and investigation of lower limb rotational profile when exploring causes of external snapping hip, especially where ultrasound and radiographs show no significant pathology.

USING A DIGITAL INCLINOMETER SIGNIFICANTLY IMPROVES THE ACCURACY OF DEROTATION OSTEOTOMY: A SIMULATION STUDY

IntroductionDerotation osteotomies are commonly performed in paediatric orthopaedic and limb reconstruction practice. The purpose of this study was to determine whether the use of a digital inclinometer significantly improves the accuracy in attaining the desired correction.Materials & MethodsWe designed an electronic survey regarding derotation femoral osteotomy (DFO) including methods of intra-operative angular correction assessment and acceptable margins of error for correction. This was distributed to 28 paediatric orthopaedic surgeons in our region. A DFO model was created, using an anatomic sawbone with foam covering. 8 orthopaedic surgeons each performed two 30-degree DFOs, one using K-wires and visual estimation (VE), and the other using a Digital Inclinometer (DI). Two radiologists reported pre and post procedure rotational profile CT scans to assess the achieved rotational correction.ResultsThere was a 68% response rate to the survey. The most popular methods of estimating intra-operative correction were reported to be K-wires and rotation marks on bone. The majority of respondents reported that a 6–10 degree margin of error was acceptable for a 30-degree derotation. This was therefore set as the upper limit for acceptable error margin in the simulation study. The mean error in rotation in the VE group of simulated DFO was 19.7 degrees, with error>5 degrees and error>10 degrees in 7 (88%) and 6 (75%) cases respectively. Mean error in DI group was 3.1 degrees, with error>5 degrees in 1 case (13%).ConclusionsOur results show that the compared to conventional techniques, the use of an inclinometer significantly improves the accuracy of femoral de-rotation and significantly reduces the incidence of unacceptable errors in correction. We would suggest that digital inclinometers be used to assess intra-operative correction during derotation osteotomies.

Modelling and evaluation of beach morphodynamic behavior: A case study of Dongsha Beach in eastern China

Beaches provide natural protection for coast and ecosystems. Storm surges and waves make significant impacts on the topographic changes of beaches, subsequently causing crises of coastal erosion and management. Beach protection and nourishment projects is growing considerably along the world. Five profiles of Dongsha Beach located in the southeast of Zhujiajian Island, eastern China, were measured and used to analyze the cross-shore profile changes, longshore sediment transport, beach rotation and equilibrium shoreline and profile. Delft3D Flow/Wave and XBeach models were established and calibrated to investigate the morphological responses of Dongsha Beach. It was found that: (1) the longshore sediment transport dominated the changes of erosion and accretion sediment volume compared to the cross-shore sediment transport; (2) the shoreline of Dongsha Beach was not in equilibrium condition compared to the profile equilibrium conditions; (3) the longshore sediment transportation was the main reason of the erosion because the shoreline changes caused by longshore sediment transport during the storm condition could not be restored during calm sea periods; (4) the correlation between wave induced currents and Hs2·T was good and the dominating wave direction was 90°. Finally, sediment nourishment projects named N1∼N3 were assumed and simulated to identify the optimum for the dynamic balance of Dongsha beach. Sediment sources with D50 of 0.5 mm should be chosen in sediment nourishment projects, and the nourished area should be selected in N1 or N3 of the beach. The numerical model established in this study could be a useful tool to predict the future erosion and accretion of beaches. This study can provide a useful understanding and reference especially for the embayed beach nourishment, making the beach management decisions more scientific and reasonable.

Characterization of Quasi-Keplerian, Differentially Rotating, Free-Boundary Laboratory Plasmas.

We present results from pulsed-power driven differentially rotating plasma experiments designed to simulate physics relevant to astrophysical disks and jets. In these experiments, angular momentum is injected by the ram pressure of the ablation flows from a wire array Z pinch. In contrast to previous liquid metal and plasma experiments, rotation is not driven by boundary forces. Axial pressure gradients launch a rotating plasma jet upward, which is confined by a combination of ram, thermal, and magnetic pressure of a surrounding plasma halo. The jet has subsonic rotation, with a maximum rotation velocity 23±3 km/s. The rotational velocity profile is quasi-Keplerian with a positive Rayleigh discriminant κ^{2}∝r^{-2.8±0.8} rad^{2}/s^{2}. The plasma completes 0.5-2 full rotations in the experimental time frame (∼150 ns).

Exploring the internal rotation of the extremely low-mass He-core white dwarf GD 278 with TESS asteroseismology

Context. The advent of high-quality space-based photometry, brought about by missions such as Kepler/K2 and TESS, makes it possible to unveil the fundamental parameters and properties of the interiors of white dwarf stars, particularly extremely low-mass white dwarfs, using the tools of asteroseismology. Aims. We present an exploration of the internal rotation of GD 278, the first known pulsating extremely low-mass white dwarf to show rotational splittings within its periodogram. Methods. We assessed the theoretical frequency splittings expected for different rotation profiles and compared them to the observed frequency splittings of GD 278. To this aim, we employed an asteroseismological model representative of the pulsations of this star, obtained by using the LPCODE stellar evolution code and the LP-PUL non-radial pulsation code. We also derived a rotation profile that results from detailed evolutionary calculations carried out with the MESA stellar evolution code and used it to infer the expected theoretical frequency splittings. Results. We find that the best-fitting solution when assuming linear profiles for the rotation of GD 278 leads to angular velocity values at the surface and center that are only slightly differential, and still compatible with rigid rotation. Additionally, the values of the angular velocity at the surface and the center for the simple linear rotation profiles and for the rotation profile derived from evolutionary calculations are in very good agreement. Also, the resulting theoretical frequency splittings are compatible with the observed frequency splittings, in general, for both cases. Conclusions. The results obtained from the different approaches followed in this work to derive the internal rotation of GD 278 agree. The fact that they were obtained by employing two independent stellar evolution codes gives our results robustness. Our results suggest only a marginally differential behavior for the internal rotation in GD 278 and, considering the uncertainties involved, this is very compatible with the rigid case, as has been observed previously for white dwarfs and pre-white dwarfs. The rotation periods derived for this star are also in line with the values determined asteroseismologically for white dwarfs and pre-white dwarfs in general.

Testing angular momentum transport processes with asteroseismology of solar-type main-sequence stars

Context. Thanks to the so-called photometry revolution with the space-based missions CoRoT, Kepler, and TESS, asteroseismology has become a powerful tool to study the internal rotation of stars. The rotation rate depends on the efficiency of the angular momentum (AM) transport inside the star, and its study allows to constrain the internal AM transport processes, as well as improve our understanding of their physical nature. Aims. We compared the ratio of the rotation rate predicted by asteroseismology and starspot measurements of solar-type stars considering different AM transport prescriptions and investigated whether some of these prescriptions can be ruled out observationally. Methods. We conducted a two-step modelling procedure of four main-sequence stars from the Kepler LEGACY sample, which consists of an asteroseismic characterisation that serves as a guide for a modelling with rotating models, including a detailed and coherent treatment of the AM transport. The rotation profiles derived with this procedure were used to estimate the ratio of the mean asteroseismic rotation rate with the surface rotation rate from starspot measurements for each AM transport prescriptions. Comparisons between the models were then conducted. Results. In the hotter part of the Hertzsprung-Russell (HR) diagram (masses typically above ∼1.2 M⊙ at solar metallicity), models with only hydrodynamic transport processes and models with additional transport by magnetic instabilities are found to be consistent with previous measurements that observed a low degree (below 30%) of radial differential rotation between the radiative and convective zones. For these stars, which constitute a significant fraction of the Kepler LEGACY sample, a combination of asteroseismic constraints from the splitting of pressure modes and of the surface rotation rate does not allow us to conclude that an efficient AM transport is required in addition to transport by meridional circulation and shear instability alone. Even a model assuming local AM conservation cannot be ruled out. In the colder part of the HR diagram, the situation is different because of the efficient braking of the stellar surface by magnetised winds. We find a clear disagreement between the rotational properties of models that only include hydrodynamic processes and asteroseismic constraints, while models with magnetic fields correctly reproduce the observations, similarly to the solar case. Conclusions. This shows the existence of a mass regime corresponding to main-sequence F-type stars for which it is difficult to constrain the AM transport processes, unlike for hotter, Gamma Dor stars or colder, less massive solar analogues. The comparison between asteroseismic measurements and surface rotation rates enables us to easily rule out models with an inefficient transport of AM in the colder part of the HR diagram.

Recovery of steady rotational wave profiles from pressure measurements at the bed

We derive equations relating the pressure at a flat seabed and the free-surface profile for steady gravity waves with constant vorticity. The resulting set of nonlinear equations enables the recovery of the free surface from pressure measurements at the bed. Furthermore, the flow vorticity (unknown a priori) is determined solely from the bottom pressure as part of the recovery method. This approach is applicable even in the presence of stagnation points and its efficiency is illustrated via numerical examples.

Minuscule Corrections to Near-surface Solar Internal Rotation Using Mode Coupling

The observed solar oscillation spectrum is influenced by internal perturbations such as flows and structural asphericities. These features induce splitting of characteristic frequencies and distort the resonant-mode eigenfunctions. Global axisymmertric flow—differential rotation—is a very prominent perturbation. Tightly constrained rotation profiles as a function of latitude and radius are products of established helioseismic pipelines that use observed Dopplergrams to generate frequency-splitting measurements at high precision. However, the inference of rotation using frequency splittings does not consider the effect of mode coupling. This approximation worsens for modes with high angular degrees, as they become increasingly proximal in frequency. Since modes with high angular degrees probe the near-surface layers of the Sun, inversions considering coupled modes could potentially lead to more accurate estimates of rotation very close to the surface. In order to investigate if this is indeed the case, we perform inversions for solar differential rotation, considering coupling of modes for angular degrees 160 ≤ ℓ ≤ 300 in the surface gravity f-branch and first-overtone p modes. In keeping with the character of mode coupling, we carry out a nonlinear inversion using an eigenvalue solver. Differences in inverted profiles for frequency-splitting measurements from MDI and HMI are compared and discussed. We find that the corrections to the near-surface differential rotation profile, when accounting for mode-coupling effects, are smaller than 0.003 nHz and hence are insignificant. These minuscule corrections are found to be correlated with the solar cycle. We also present corrections to even-order splitting coefficients, which could consequently impact inversions for structure and magnetic fields.

Consequences of the rotational speed and profile of tool pin in microstructure and mechanical properties of AA8011/ZrO2 composite produced by FSW

Consequences of the rotational speed and profile of tool pin in microstructure and mechanical properties of AA8011/ZrO2 composite produced by FSW

A Computational Study on Magnetohydrodynamics Stagnation Point Flow of Micropolar Fluids with Buoyancy and Thermal Radiation due to a Vertical Stretching Surface

In current analysis, A numerical approach for magnetohydrodynamics Stagnation point flow of Micropolar fluid due to a vertical stretching Surface is reported. The impact of buoyancy forces is considered. In additions the effects of the thermal radiation and thermal conductivity with non-zero mass flux have been analyzed. we implement the dimensionless variable technique and the systems of coupled non-linear PDEs are transformed into ODEs by using the appropriate similarity technique. Moreover, by using package ND-Solve on Mathematica problem is numerically integrated with the help of shooting technique. Numerical approach for magnetohydrodynamics Stagnation point flow of thermal Radiative Micropolar fluid due to a vertical stretching Surface. The impact of thermophoresis and Brownian motion are considered. We implement the dimensionless variable technique and the systems of coupled non-linear PDEs are transformed into ODEs by using the appropriate similarity technique. To observe the influence of the physical parameters, graphically valuations are performed for numerous emerging parameters like Brownian motion, mixed convection parameters, thermophoresis diffusion, Hartman number, Radiation parameter, Prandtl number, Stretching parameter and other dimension less parameters. These several protuberant parameters of interest are engaged for velocity, temperature and nonlinear micro rotation profile and studied in detail.

Saturn's Seismic Rotation Revisited

Normal mode seismology is a promising means of measuring rotation in gas giant interiors, and ring seismology presents a singular opportunity to do so at Saturn. We calculate Saturn’s normal modes of oscillation and zonal gravity field, using nonperturbative methods for normal modes in the rigidly rotating approximation, and perturbative methods for the shifts that Saturn’s deep winds induce in the mode frequencies and zonal gravity harmonics. The latter are calculated by solving the thermogravitational wind equation in an oblate geometry. Comparing many such models to gravity data and the frequencies of ring patterns excited by Saturn’s normal modes, we use statistical methods to estimate that Saturn’s cloud-level winds extend inward along cylinders before decaying at a depth 0.125–0.138 times Saturn’s equatorial radius, or 7530–8320 km, consistent with analyses of Cassini’s gravity and magnetic field data. The seismology is especially useful for pinning down Saturn’s poorly constrained deep rotation period, which we estimate at 2π/ΩS = 634.7 minutes (median) with a 5/95% quantile range of 633.8–635.5 minutes. Outstanding residuals in mode frequencies at low angular degree suggest a more complicated deep interior than has been considered to date. Smaller but still significant residuals at high angular degrees also show that our picture for the thermal, composition, and/or rotation profile in Saturn’s envelope is not yet complete.

Dynamical dissipative and radiative flow of comparative an irreversibility analysis of micropolar and hybrid nanofluid over a Joule heating inclined channel

This report scrutinized the influence of radiation and Ohmic heating on the dissipative flow of micropolar and hybrid nanofluid within an inclined length 2h channel under convective boundary conditions. Primary flow equations are renewed as the system of NODEs with the assistance of proper similarity conversions. In two circumstances, hybrid fluid flow and micropolar fluid flow, a blend of shooting and Runge–Kutta 4th order strategy, is used to achieve the desired results. The critical consequences of the current study are Larger pressure gradient minimizes the fluid velocity, and a more significant inertia parameter minimizes the rotation profile in the case of Newtonian fluid flow but facilitates the same in the case of hybrid nanofluid flow. It is perceived that the escalation in Brinkmann number causes the amelioration in the fluid temperature, and the radiation parameter mitigates the same. Furthermore, it is discovered that the Grashoff number enhances the Bejan number at the centre of the channel but lessens the same at other areas. Finally, validation is executed to compare the current outcomes with the former results and perceive a good agreement.

Study of correlations between LOC/SOC transition, intrinsic toroidal rotation reversal and TEM/ITG bifurcation with different working gases in TCV

The effects of different working gases on the transition from linear ohmic confinement (LOC) regime to saturated ohmic confinement (SOC) regime and its relation to the intrinsic toroidal rotation reversal phenomenon were explored in the TCV tokamak. The energy confinement saturation was studied across D, H and He density ramps, and a range of ECRH injection power and through variations of ohmic plasma current. The occurrence of rotation reversal, concomitantly with the LOC–SOC transition, was observed only for certain cases, making us formally exclude a causal relation between the two phenomena. A strong correlation between the evolution of toroidal rotation profiles and electron density gradients was, however, observed, in agreement with previous works (Lebschy et al 2017 Nucl. Fusion 58 026013; Hornsby et al 2018 Nucl. Fusion 58 056008). Linear gyrokinetic simulations were performed to probe the turbulent regime of these discharges, showing a dominance of trapped electron mode (TEM) during the LOC phase and a mixture of TEM and ion temperature gradient (ITG) following the transition to SOC regime in D. Such a TEM/ITG bifurcation was less pronounced in H and He. MHD activity was monitored throughout the discharges and possible correlations between sawteeth instability activity, energy confinement time saturation and rotation reversal are highlighted.

Constraining the rotation profile in a low-luminosity subgiant with a surface rotation measurement

ABSTRACT Rotationally induced mode splitting frequencies of low-luminosity subgiants suggest that angular momentum transport mechanisms are 1–2 orders of magnitude more efficient in these stars than predicted by theory. Constraints on the rotation profile of low-luminosity subgiants could be used to identify the dominant mechanism for angular momentum transport. We develop a forward model for the rotation profile given observed rotational splittings, assuming a step-like rotation profile. We identify a consistent degeneracy between the position of the profile discontinuity and the surface rotation rate. We perform mock experiments that show the discontinuity position can be better constrained with a prior on the surface rotation rate, which is informed by star spot modulations. We finally apply this approach to KIC 12508433, a well-studied low-luminosity subgiant, as an example case. With the observed surface rotation prior, we obtain a factor of 2 increase in precision of the position of strong rotation gradient. We recover the literature values of the core and surface rotation rates and find the highest support for a discontinuity in the radiative zone. Auxiliary measurements of surface rotation could substantially improve inferences on the rotation profile of low-luminosity subgiants with already available data.

Kinematic differences between multiple populations in Galactic globular clusters

Aims. The formation process of multiple populations in globular clusters is still up for debate. These populations are characterized by different light-element abundances. Kinematic differences between the populations are particularly interesting in this respect because they allow us to distinguish between single-epoch formation scenarios and multi-epoch formation scenarios. We derive rotation and dispersion profiles for 25 globular clusters and aimed to find kinematic differences between multiple populations to constrain their formation process. Methods. We split red-giant-branch (RGB) stars in each cluster into three populations (P1, P2, and P3) for the type-II clusters and two populations (P1 and P2) otherwise using Hubble photometry. We derived the global rotation and dispersion profiles for each cluster by using all stars with radial velocity measurements obtained from MUSE spectroscopy. We also derived these profiles for the individual populations of each cluster. Based on the rotation and dispersion profiles, we calculated the rotation strength in terms of ordered-over-random motion, (v/σ)HL, evaluated at the half-light radius of the cluster. We then consistently analyzed all clusters for differences in the rotation strength of their populations. Results. We detect rotation in all but four clusters. For NGC 104, NGC 1851, NGC 2808, NGC 5286, NGC 5904, NGC 6093, NGC 6388, NGC 6541, NGC 7078, and NGC 7089, we also detect rotation for P1 and/or P2 stars. For NGC 2808, NGC 6093, and NGC 7078 we find differences in (v/σ)HL between P1 and P2 that are larger than 1σ. Whereas we find that P2 rotates faster than P1 for NGC 6093 and NGC 7078, the opposite is true for NGC 2808. However, even for these three clusters the differences are still of low significance. We find that the rotation strength of a cluster generally scales with its median relaxation time. For P1 and P2 the corresponding relation is very weak at best. We observe no correlation between the difference in rotation strength between P1 and P2 and the cluster relaxation time. The stellar radial velocities derived from MUSE data that this analysis is based on are made publicly available.

Boundary Layers of Circumplanetary Disks around Spinning Planets. I. Effects of Rossby Waves

Gas giant planets are believed to accrete from their circumplanetary disks (CPDs). The CPDs usually involve accretion through the boundary layer (BL) in the vicinity of planets. Prior studies have concentrated on the BL of nonspinning planets. We investigate the influence of planetary spin on the wave behaviors within the BL. The rotation profile in such BLs would show a sharp transition from the rigid rotation to the Keplerian rotation. We examine the angular momentum transport in these BLs in terms of linear perturbation analysis. We find that the global inertia-acoustic mode associated with spinning planets would give rise to the inflow of angular momentum and the accretion of gas. In this work, we identify a new kind of global mode, namely the Rossby mode. The Rossby mode can lead to the outflow of angular momentum and the decretion of gas from a spinning planet. The Rossby mode provides a negative feedback that regulates the planetary spin and mass. We compare the growth rate of the two modes as a function of the width of BL, the Mach number, and the spin rate of planets. Our results reveal the underlying hydrodynamic mechanism of terminal spins and asymptotic mass of the giant planets.

The Supersonic Project: The Eccentricity and Rotational Support of SIGOs and DM GHOSts

A supersonic relative velocity between dark matter (DM) and baryons (the stream velocity) at the time of recombination induces the formation of low-mass objects with anomalous properties in the early universe. We widen the scope of the “Supersonic Project” paper series to include objects we term Dark Matter + Gas Halos Offset by Streaming (DM GHOSts)—diffuse, DM-enriched structures formed because of a physical offset between the centers of mass of DM and baryonic overdensities. We present an updated numerical investigation of DM GHOSts and Supersonically Induced Gas Objects (SIGOs), including the effects of molecular cooling, in high-resolution hydrodynamic simulations using the AREPO code. Supplemented by an analytical understanding of their ellipsoidal gravitational potentials, we study the population-level properties of these objects, characterizing their morphology, spin, radial mass, and velocity distributions in comparison to classical structures in non-streaming regions. The stream velocity causes deviations from sphericity in both the gas and DM components and lends greater rotational support to the gas. Low-mass (≲105.5 M ⊙) objects in regions of streaming demonstrate core-like rotation and mass profiles. Anomalies in the rotation and morphology of DM GHOSts could represent an early universe analog to observed ultra-faint dwarf galaxies with variations in DM content and unusual rotation curves.

Internal Kink Instabilities Driven by Poloidal Flow via Non-Resonant Excitation in Tokamaks

Non-resonant excitation due to plasma inertia may be dominant in inducing internal kink (IK) instabilities. Poloidal rotation can effectively modify plasma inertia and cause non-resonant excitation to occur. An extended dispersion relation including poloidal rotation is established to study the IK mode and the fishbone (FB) mode. It is found that in rotating plasmas, even for a stable IK mode (i.e., the perturbed potential energy of background plasma δWc is positive) and in the absence of energetic particles (EPs), poloidal rotation can drive the IK mode via non-resonant excitation. Moreover, the IK mode is easy to be driven by poloidal rotation in weak magnetic shear plasmas. Similar to toroidal rotation, when poloidal rotation frequency exceeds a threshold, the FB mode can transform into a branch of a non-resonant mode. The real frequency of the mode, being independent of the precessional frequency of EPs, is just equal to the poloidal rotation frequency. Thus, the non-resonant mode is characterized by the long-lived mode (LLM) observed in toroidal rotating plasmas. The critical gradient of the poloidal rotation profile plays a crucial role in causing the resonant mode to evolve into a non-resonant one; for instance, only for a very peaked poloidal rotation profile can the FB mode transform into the LLM. In addition, the diamagnetic drift frequency of thermal ions can stabilize the FB and the IK modes.

The mechanism of magnetic flux rope rotation during solar eruption

Solar eruptions often show the rotation of filaments, which is a manifestation of the rotation of erupting magnetic flux rope (MFR). Such a rotation of MFR can be induced by either the torque exerted by a background shear-field component (which is an external cause) or the relaxation of the magnetic twist of the MFR (an internal cause). For a given chirality of the erupting field, both the external and internal drivers cause the same rotation direction. Therefore, it remains elusive from direct observations which mechanism yields the dominant contribution to the rotation. In this paper, we exploit a full MHD simulation of solar eruption by tether-cutting magnetic reconnection to study the mechanism of MFR rotation. In the simulation, the MFR’s height–rotation profile suggests that the force by the external shear-field component is a dominant contributor to the rotation. Furthermore, the torque analysis confirms that it is also the only factor in driving the counterclockwise rotation. On the contrary, the Lorentz torque inside the MFR makes a negative effect on this counterclockwise rotation.