Author name code: getling ADS astronomy entries on 2022-09-14 author:"Getling, Alexander" ------------------------------------------------------------------------ Title: Spatial Scales and Time Variation of Solar Subsurface Convection Authors: Getling, Alexander V.; Kosovichev, Alexander G. Bibcode: 2022arXiv220804642G Altcode: Spectral analysis of the spatial structure of solar subphotospheric convection is carried out for subsurface flow maps constructed using the time--distance helioseismological technique. The source data are obtained from the Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) from 2010 May to 2020 September. A spherical-harmonic transform is applied to the horizontal-velocity-divergence field at depths from 0 to 19~Mm. The range of flow scales is fairly broad in shallow layers and narrows as the depth increases. The horizontal flow scales rapidly increase with depth, from supergranulation to giant-cell values, and indicate the existence of large-scale convective motions in the near-surface shear layer. The results can naturally be interpreted in terms of a superposition of differently scaled flows localized in different depth intervals. There is some tendency toward the emergence of meridionally elongated (banana-shaped) convection structures in the deep layers. The total power of convective flows is anticorrelated with the sunspot-number variation over the solar activity cycle in shallow subsurface layers and positively correlated at larger depths, which is suggestive of the depth redistribution of the convective-flow energy due to the action of magnetic fields. Title: Helioseismic Monitoring of Solar Subsurface Dynamics and Activity Authors: Kosovichev, Alexander; Pipin, Valery; Getling, Alexander; Stejko, Andrey; Stefan, John; Guerrero, Gustavo Bibcode: 2022cosp...44.3215K Altcode: Uninterrupted helioseismic data from Michelson Doppler Imager (MDI) onboard Solar and Heliospheric Observatory (SoHO) and from Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) have provided unique information about flows and structures evolving on various temporal and spatial scales inside the Sun. The data cover the past two solar cycles and the rising phase of the current solar cycle. In particular, our analysis of variations of the internal differential rotation reveals "extended" cyclic variations of migrating zonal flows ("torsional oscillations") through the whole convection zone. The observed patterns of subsurface flow acceleration provide evidence of hydromagnetic dynamo waves, which control the strength of sunspot cycles, and potentially carry information about the future solar cycles. Similarly, "extended" cyclic variations of the subsurface meridional circulation, detected by local helioseismic techniques, reflect the evolution of subsurface magnetic fields and emerging magnetic flux. Furthermore, to monitor emerging active regions, we develop a "deep-focus" helioseismic diagnostics, which allows us to detect large emerging active regions before they become visible on the surface. We present recent advances in helioseismic monitoring of solar activity and discuss helioseismic constraints on models of global solar variability and space weather forecasting. Title: Advances and Challenges in Observations and Modeling of the Global-Sun Dynamics and Dynamo Authors: Kosovichev, A. G.; Guerrero, G.; Stejko, A. M.; Pipin, V. V.; Getling, A. V. Bibcode: 2022arXiv220310721K Altcode: Computational heliophysics has shed light on the fundamental physical processes inside the Sun, such as the differential rotation, meridional circulation, and dynamo-generation of magnetic fields. However, despite the substantial advances, the current results of 3D MHD simulations are still far from reproducing helioseismic inferences and surface observations. The reason is the multi-scale nature of the solar dynamics, covering a vast range of scales, which cannot be solved with the current computational resources. In such a situation, significant progress has been achieved by the mean-field approach, based on the separation of small-scale turbulence and large-scale dynamics. The mean-field simulations can reproduce solar observations, qualitatively and quantitatively, and uncover new phenomena. However, they do not reveal the complex physics of large-scale convection, solar magnetic cycles, and the magnetic self-organization that causes sunspots and solar eruptions. Thus, developing a synergy of these approaches seems to be a necessary but very challenging task. Title: Spatial Spectrum of Solar Convection from Helioseismic Data: Flow Scales and Time Variations Authors: Getling, Alexander V.; Kosovichev, Alexander G. Bibcode: 2022arXiv220100638G Altcode: We analyze spectral properties of solar convection in the range of depths from 0 to 19~Mm using subsurface flow maps obtained by the time-distance heiioseismology analysis of solar-oscillation data from the Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) from May 2010 to September 2020. The results reveal a rapid increase of the horizontal flow scales with the depth, from supergranulation to giant-cell scales, and support the evidence of large-scale convection, previously detected by tracking the motion of supergranular cells on the surface. The total power of convective flows correlates with the solar activity cycle. During the solar maximum, the total power decreases in shallow subsurface layers and increases in the deeper layers. Title: Large-Scale Dynamics of Solar Subsurface Shear Layer: Theoretical Predictions and Helioseismic Inferences Authors: Kosovichev, Alexander; Getling, Alexander; Guerrero, Gustavo; Pipin, Valery; Stejko, Andrey Bibcode: 2021AGUFMSH53C..03K Altcode: Helioseismic observations show that the solar rotation rate sharply increases with depth in the outer 30 Mm-deep layers of the solar convection zone. This subsurface shear layer (SSL) plays a critical role in the formation of migrating activity belts (the butterfly diagram) and the emergence of active regions. Measurements of the rotation rate indicate that the magnetic field of sunspots and active regions is anchored in the subsurface shear layer. The magnetic structure of the SSL has not been directly measured by helioseismology, but it can be inferred by comparing variations of subsurface flows and sound-speed variations predicted by dynamo models with helioseismic measurements. To establish the connections between the flows and fields, we construct and analyze synoptic maps of subsurface flows in the SSL, obtained from time-distance helioseismic inversion during the whole Solar Cycle 24 and the rising phase of Cycle 25. The results reveal the extended solar-cycle pattern of variations of the meridional circulation, predicted by the dynamo models and previously known from surface and subsurface observations of zonal flows. We discuss the origin of the observed variations and their links to the magnetism and dynamics of the subsurface shear layer. Title: Multiscale Organization of Turbulent Convection in Global-Sun Simulations Authors: Guerrero, Gustavo; Stejko, Andrey; Kosovichev, Alexander; Getling, Alexander; Smolarkiewicz, Piotr Bibcode: 2021AGUFMSH55D1885G Altcode: Solar convection is at the core of fundamental phenomena such as differential rotation and meridional circulation and, ultimately, the solar dynamo. The governing mechanisms, amplitude, and dominant scales of convection in the solar interior remain under debate. Furthermore, the large Reynolds and Rayleigh numbers involved make it implausible to resolve all relevant scales using direct numerical simulation. In this work, we study solar convection through global, non-rotating, and non-magnetic implicit large-eddy simulations (ILES), using the 3D global hydrodynamic code EULAG. Our simulations exhibit a pattern of multiscale convection, clearly visible on the domain surface (~0.96 R), generated by a solar-like density and entropy stratification. Scale-splitting is evident at various depths throughout the model, with the upper boundary of convective cells penetrating surface layers, resembling solar-like convection. A continuous and coherent multiscale structure of convective cells is observed throughout the convective interior. The power peak of convective scales continuously shrinks with height to a maximum spherical harmonic degree of l = 40-50 on the model surface, compatible with reports of giant cell observations. Simulations are performed from low to high resolution to explore whether integral properties of convection, such as the RMS velocity, temperature profiles, and turbulent spectra, become independent of the mesh size. Results are compared with current observations of surface and sub-surface solar convection. Title: 3D Helioseismic Forward-Modeling and Analysis of Meridional Circulation Authors: Stejko, Andrey; Kosovichev, Alexander; Pipin, Valery; Guerrero, Gustavo; Getling, Alexander; Smolarkiewicz, Piotr Bibcode: 2021AGUFMSH55D1870S Altcode: The 3D Global Acoustic Linearized Euler (GALE) code is used to explore the variance in helioseismic signatures that result from various profiles of meridional circulation. The structure of meridional circulation regulates the redistribution of angular momentum and magnetic flux that governs the solar cycle. Forward-modeling is a useful tool in exploring the structure of meridional circulation and its impact on global parameters and can help resolve the current controversy between single and double-cell circulation profiles. Profiles of meridional circulation are generated using mean-field dynamo models, which induce a reverse flow near the base of the convection zone, characteristic of double-cell meridional circulation, with the inclusion of turbulent pumping (-effect) resulting from a strong rotational gradient in the region. These models provide physics-based mechanisms for the low-end in potential differences between single- and double-cell meridional circulation profiles. The resulting flows are used as background velocities in the linearized acoustic GALE codesimulating the stochastic excitation of acoustic perturbations. Techniques in local helioseismology are then applied to measure flow signatures, showing that within the observational time-period of the HMI instrument onboard Solar Dynamics Observatory, it may not be possible to definitively distinguish between single-cell and double-cell meridional circulation structure. This analysis is extended to models of meridional circulation generated in convectively-driven non-linear 3D global-Sun simulations to explore the helioseismic differences generated by these models and compare them with observations. Title: The Origin Of The Extended Solar Cycle Authors: Kosovichev, A.; Pipin, V.; Getling, A. Bibcode: 2021AAS...23830405K Altcode: The extended 22-year solar cycle phenomenon, discovered in observations of the solar corona and variations of the solar differential rotation (torsional oscillations), represents a fundamental heliophysics problem linked to dynamo processes inside the Sun. As observed on the surface, the extended solar cycle starts during a sunspot maximum at high latitudes and consists of a relatively short polar branch (described as "rush to the poles") and a long equatorward branch that continues through the solar minimum and the next sunspot cycle. Helioseismic observations of the internal dynamics of the Sun during the last two solar activity cycles allow us to identify the dynamical processes associated with the extended solar cycle throughout the depth of the convective zone and to link them with dynamo models. Observational data obtained from the SoHO (1996-2010) and SDO (2010-2020) spacecraft represent measurements of the internal differential rotation, meridional circulation, and thermodynamic parameters. The data indicate that the development of a new extended solar cycle begins at about 60 degrees latitude at the base of the convective zone during the maximum of the previous cycle. Then, the process of magnetic field migration to the Sun's surface is divided into two branches: fast (in 1-2 years) migration to the poles in the high-latitude zone and slow migration to the equator at middle and low latitudes for ~ 10 years. The subsurface rotational shear layer (leptocline) plays a key role in the formation of the magnetic butterfly diagram. Both the zonal flows (torsional oscillations) and the meridional circulation reveal the 22-year pattern of the extended solar cycle. A self-consistent MHD model of the solar dynamo developed in the mean-field theory framework is in good qualitative and quantitative agreement with the helioseismic observations. The model shows that the extended solar-cycle phenomenon is caused by magnetic field quenching of the convective heat flux and modulation of the meridional circulation induced by the heat flux variations. The model explains why the solar minimum polar field predicts the next sunspot maximum and points to new possibilities for predicting solar cycles from helioseismological data. Title: Helioseismic Observations and Modeling of Solar Dynamo Authors: Kosovichev, Alexander G.; Getling, Alexander V.; Pipin, Valery V. Bibcode: 2021csss.confE.115K Altcode: Helioseismological observations of the internal dynamics of the Sun during the last two solar activity cycles make it possible to trace the development of solar dynamo processes throughout the depth of the convective zone and to link them with models of solar cycles. Observational data obtained from the SoHO (1996-2010) and SDO (2010-2020) spacecraft represent measurements of the internal differential rotation, meridional circulation, and thermodynamic parameters. The structure and dynamics of zonal and meridional plasma flows reveal the processes of generation and transfer of magnetic fields inside the Sun. The data analysis shows that active latitudes and regions of a strong polar field on the Sun's surface coincide with regions of deceleration of zonal currents ("torsional oscillations"). The observed structure of zonal flows and their latitudinal and radial migration in deep layers of the convective zone correspond to dynamo waves predicted by dynamo theories and numerical MHD models. The data indicate that the development of a new solar cycle begins at about 60 degrees latitude at the base of the convective zone during the maximum of the previous cycle. Then, the process of magnetic field migration to the Sun's surface is divided into two branches: fast (in 1-2 years) migration in the high-latitude zone and slow migration at middle and low latitudes for ~ 10 years. The subsurface rotational shear layer ("leptocline") plays a key role in the formation of the magnetic "butterfly diagram". Both the zonal flows ("torsional oscillations") and the meridional circulation reveal the 22-year pattern of the "extended" solar cycle, initially discovered from observations of Doppler velocities and the structure of the solar corona.A self-consistent MHD model of the solar dynamo developed in the mean-field theory framework is in good qualitative and quantitative agreement with the helioseismic observations. The model shows that the observed variations of the solar dynamics are associated with a magnetic field effect on convective heat transfer and the corresponding modulation of the meridional circulation. The model explains why the solar minimum polar field predicts the next sunspot maximum and points to new possibilities for predicting solar cycles from helioseismological data. Title: Evolution of Subsurface Zonal and Meridional Flows in Solar Cycle 24 from Helioseismological Data Authors: Getling, Alexander V.; Kosovichev, Alexander G.; Zhao, Junwei Bibcode: 2021ApJ...908L..50G Altcode: 2020arXiv201215555G The results of determinations of the azimuthal and meridional velocities by time-distance helioseismology from Helioseismic and Magnetic Imager on board Solar Dynamics Observatory from 2010 May to 2020 September at latitudes and Stonyhurst longitudes from - 60° to + 60° and depths to about 19 Mm below the photosphere are used to analyze spatiotemporal variations of the solar differential rotation and meridional circulation. The pattern of torsional oscillations, or latitudinal belts of alternating "fast" and "slow" zonal flows migrating from high latitudes toward the equator, is found to extend in the time-latitude diagrams over the whole time interval. The oscillation period is comparable with a doubled solar-activity-cycle and can be described as an extended solar cycle. The zonal-velocity variations are related to the solar-activity level, the local-velocity increases corresponding to the sunspot-number increases and being localized at latitudes where the strongest magnetic fields are recorded. The dramatic growth of the zonal velocities in 2018 appears to be a precursor of the beginning of Solar Cycle 25. The strong symmetrization of the zonal-velocity field by 2020 can be considered another precursor. The general pattern of poleward meridional flows is modulated by latitudinal variations similar to the extended-solar-cycle behavior of the zonal flows. During the activity maximum, these variations are superposed with a higher harmonic corresponding to meridional flows converging to the spot-formation latitudes. Our results indicate that variations of both the zonal and meridional flows exhibit the extended-solar-cycle behavior, which is an intrinsic feature of the solar dynamo. Title: Peculiarities of the Dynamics of Solar NOAA Active Region 12673 Authors: Getling, A. V. Bibcode: 2019ApJ...878..127G Altcode: 2019arXiv190408367G The dynamics of active region (AR) 12673 is qualitatively studied using observational data obtained with the Helioseismic and Magnetic Imager of the Solar Dynamics Observatory on 2017 August 31-September 8. This AR was remarkable for its complex structure and extraordinary flare productivity. The sunspot group in this AR consisted of (1) an old, well-developed and highly stable, coherent sunspot, which had also been observed two solar rotations earlier, and (2) a rapidly developing cluster of umbral and penumbral fragments. Cluster (2) formed two elongated, arc-shaped chains of spot elements, skirting around the major sunspot (1), with two chains of magnetic elements spatially coinciding with the arcs. AR components (1) and (2) were in relative motion, cluster (2) overtaking spot (1) in westward motion, and their relative velocity agrees in order of magnitude with the velocity jump over the near-surface shear layer, or leptocline. The pattern of motion of the features about the main spot bears amazing resemblance to the pattern of a fluid flow about a roundish body. This suggests that spot (1) was dynamically coupled with the surface layers, while cluster (2) developed in deeper layers of the convection zone. The magnetic-flux emergence in cluster (2) appeared to be associated with fluid motions similar to roll convection. The mutual approach of components (1) and (2) gave rise to light bridges in the umbrae of sunspots with the magnetic field having the same sign on both sides of the bridge. Title: The Origin and Early Evolution of a Bipolar Magnetic Region in the Solar Photosphere Authors: Getling, A. V.; Buchnev, A. A. Bibcode: 2019ApJ...871..224G Altcode: 2018arXiv180506486G Finding the formation mechanisms for bipolar configurations of a strong local magnetic field under control of the relatively weak global magnetic field of the Sun is a key problem of the physics of solar activity. This study is aimed at discriminating whether the magnetic field or fluid motion plays a primary, active role in this process. The very origin and early development stage of Active Region 12548 are investigated based on Solar Dynamics Observatory/Helioseismic and Magnetic Imager observations of 2016 May 20-25. Full-vector magnetic and velocity fields are analyzed in parallel. The leading and trailing magnetic polarities are found to grow asymmetrically in terms of their amplitude, magnetic flux, and the time variation of these quantities. The leading-polarity magnetic element originates as a compact feature against the background of a distributed trailing-polarity field, with an already existing trailing-polarity magnetic element. No signs of strong horizontal magnetic fields are detected between the two magnetic poles. No predominant upflow between their future locations precedes the origin of this bipolar magnetic region (BMR); instead, upflows and downflows are mixed, with some prevalence of downflows. Any signs of a large-scale horizontal divergent flow from the area where the BMR develops are missing; in contrast, a normal supergranulation and mesogranulation pattern is preserved. This scenario of early BMR evolution is in strong contradiction with the expectations based on the model of a rising Ω-shaped loop of a flux tube of strong magnetic field, and an in situ mechanism of magnetic-field amplification and structuring should operate in this case. Title: Effects of variable thermal diffusivity on the structure of convection Authors: Shcheritsa, O. V.; Getling, A. V.; Mazhorova, O. S. Bibcode: 2016arXiv160402543S Altcode: The multiscale flow structure in the solar convection zone - the coexistence of such features as the granules, mesogranules, supergranules and giant cells - has not yet been properly understood. Here, the possible role of one physical factor - variations in the thermal diffusivity - in the formation of a multiscale convection structure is investigated. Thermal convection in a plane horizontal fluid layer is numerically simulated. The temperature dependence of thermal diffusivity is chosen so as to produce a sharp kink in the static temperature profile near the upper layer boundary. As a result, the magnitude of the (negative) static temperature gradient dTs/dz, being small over the most part of the layer thickness, reaches large values in a thin boundary sublayer. To identify the structures on different scales, we apply a smoothing procedure, computational-homology techniques and spectral processing to the temperature field. The flow is found to be a superposition of three cellular structures with three different characteristic scales. The largest (first-scale) convection cells, with central upflows, fill the whole layer thickness; most of these cells are divided by bridges, or isthmuses, into a few smaller (second-scale) ones, which are localised in the upper portion of the layer; finally, there are numerous tiny (third-scale) features that dot the horizontal sections of the layer located near its upper boundary and exhibit a tendency of gathering in the intercellular lanes of the first-scale cells. The third-scale cellular structures are advected by the first-scale and second-scale convective flows. The spatial spectrum of the flow does not directly indicate the presence of the second-scale and third-scale structures; however, they can be selected by using our processing techniques. On the whole, the simulated flow pattern qualitatively resembles that observed on the Sun. Title: Development of Active Regions: Flows, Magnetic-Field Patterns and Bordering Effect Authors: Getling, A. V.; Ishikawa, R.; Buchnev, A. A. Bibcode: 2016SoPh..291..371G Altcode: 2016SoPh..tmp....9G; 2015arXiv150601848G A qualitative analysis is given of the data on the full magnetic and velocity vector fields in a growing sunspot group, recorded nearly simultaneously with the Solar Optical Telescope on the Hinode satellite. Observations of a young bipolar subregion developing within AR 11313 were carried out on 9 - 10 October 2011. Our aim was to form an idea about the consistency of the observed pattern with the well-known rising-tube model of the formation of bipolar active regions and sunspot groups. We find from our magnetograms that the distributions of the vertical [Bv] and the horizontal [Bh] component of the magnetic field over the area of the magnetic subregion are spatially well correlated; in contrast, the rise of a flux-tube loop would result in a qualitatively different pattern, with the maxima of the two magnetic-field components spatially separated: the vertical field would be the strongest where either spot emerges, while the maximum horizontal-field strengths would be reached in between them. A specific feature, which we call the bordering effect, is revealed: some local extrema of Bv are bordered with areas of locally enhanced Bh. This effect suggests a fountainlike spatial structure of the magnetic field near the Bv extrema, which is also hardly compatible with the emergence of a flux-tube loop. The vertical-velocity field in the area of the developing active subregion does not exhibit any upflow on the scale of the whole subregion, which should be related to the rising-tube process. Thus, our observational data can hardly be interpreted in the framework of the rising-tube model. Title: Stratification-induced scale splitting in convection Authors: Shcheritsa, O. V.; Getling, A. V.; Mazhorova, O. S. Bibcode: 2015AdSpR..55..927S Altcode: 2014arXiv1401.8137S The coexistence of motions on various scales is a remarkable feature of solar convection, which should be taken into account in analyses of the dynamics of magnetic fields. Therefore, it is important to investigate the factors responsible for the observed multiscale structure of solar convection. In this study, an attempt is made to understand how the scales of convective motions are affected by the particularities of the static temperature stratification of a fluid layer. To this end, simple models are considered. The equations of two-dimensional thermal convection are solved numerically for a plane horizontal fluid layer heated from below, in an extended Boussinesq approximation that admits thermal-diffusivity variations. These variations specify the stratification of the layer. The static temperature gradient in a thin sublayer near the upper surface of the layer is assumed to be many times larger than in the remainder of the layer. In some cases, distributed heat sinks are assumed to produce a stably stratified region overlying the convective layer. Manifestations of the scale-splitting effect are noted, which depend on the boundary conditions and stratification; it becomes more pronounced with the increase of the Rayleigh number. Small-scale convection cells are advected by larger-scale flows. In particular, the phase trajectories of fluid particles indicate the presence of complex attractors, which reflect the multiscale structure of the flow. The effect of the stably stratified upper sublayer on the flow scales is also considered. Title: Doubts about the crucial role of the rising-tube mechanism in the formation of sunspot groups Authors: Getling, A. V.; Ishikawa, R.; Buchnev, A. A. Bibcode: 2015AdSpR..55..862G Altcode: 2014arXiv1401.8077G Some preliminary processing results are presented for a dataset obtained with the Solar Optical Telescope on the Hinode satellite. The idea of the project is to record, nearly simultaneously, the full velocity and magnetic-field vectors in growing active regions and sunspot groups at a photospheric level. Our ultimate aim is to elaborate observational criteria to distinguish between the manifestations of two mechanisms of sunspot-group formation - the rising of an Ω -shaped flux tube of a strong magnetic field and the in situ amplification and structuring of magnetic field by convection (the convective mechanism is briefly described).

Observations of a young bipolar subregion developing within AR 11313 were carried out on 9-10 October 2011. During each 2-h observational session, 5576-Å filtergrams and Dopplergrams were obtained at a time cadence of 2 min, and one or two 32-min-long spectropolarimetric fast-mode scans were done. Based on the series of filtergrams, the trajectories of corks are computed, using a technique similar to but more reliable than local correlation tracking (LCT), and compared with the magnetic maps. At this stage of the investigation, only the vertical magnetic field and the horizontal flows are used for a qualitative analysis.

According to our preliminary findings, the velocity pattern in the growing active region has nothing to do with a spreading flow on the scale of the entire bipolar region, which could be expected if a tube of strong magnetic field emerged. No violent spreading flows on the scale of the entire growing magnetic region can be identified. Instead, normal mesogranular and supergranular flows are preserved. Signs of small-scale structuring of the magnetic field can be detected in the area where new spots develop, and signs of the presence of separatrices between the magnetic polarities can be found, such that the surface flows converge to but not diverge from these separatrix curves. The observed scenario of evolution seems to agree with Bumba's inference that the development of an active region does not entail the destruction of the existing convective-velocity field. The convective mechanism appears to be better compatible with observations than the rising-tube mechanism.

In the umbras of the well-developed sunspots, flows converging to the umbra centres are revealed. Spreading streams are present around these spots. Title: Can subphotospheric magnetic fields be amplified and structured by a convective mechanism? Authors: Getling, Alexander; Mazhorova, Olga; Kolmychkov, Vyacheslav Bibcode: 2014cosp...40E.975G Altcode: Strong photospheric magnetic fields frequently originate at the knots of the network formed by intercellular lanes -- the peripheral parts of convection cells on various scales. This phenomenon is normally interpreted as a result of the “sweeping” of magnetic field lines by convective motions. On the other hand, magnetic elements can emerge in the inner parts of supergranules (Title, 2006), which may be an effect of the “winding” of magnetic field lines by circulating matter, as suggested by Tverskoi (1966) based on a simple kinematic model. In this study, magnetoconvection in a horizontal layer of incompressible fluid is simulated numerically. The initial magnetic field is assumed to be weak, uniform throughout the layer and horizontal. The interaction of quasi-ordered cellular convection with the magnetic field is shown to be able to produce bipolar (and also diverse more complex) configurations of a substantially amplified magnetic field. In some cases, bipolar magnetic structures change into unipolar ones. Such transitions are analysed. The formation of the magnetic features can be attributed to either the “winding” or “sweeping” of magnetic field lines. The operation of this mechanism is controlled by the very topology of the cellular flow and does not require strong initial fields. Under solar conditions, it should be manifest on various spatial scales. This work was supported by the Russian Foundation for Basic Research, project no. 12-02-00792-a. Title: Formation of sunspot groups: Do we see manifestations of the rising-tube mechanism? Authors: Getling, Alexander; Ishikawa, Ryohko; Buchnev, Aleksei Bibcode: 2014cosp...40E.974G Altcode: A comparison is made between the expected manifestations of two mechanisms suggested to account for the formation of local photospheric magnetic fields, viz., the rising of an Omega-shaped flux tube of a strong magnetic field and the emph{in situ} amplification and structuring of magnetic field by convection. The ultimate aim of the study is to elaborate observational criteria to find out which mechanism controls the process in any given case. To this end, the full velocity and magnetic-field vectors in growing active regions and sunspot groups at a photospheric level were recorded nearly simultaneously. Observations of a young bipolar subregion developing within AR 11313 were carried out on 9-10 October 2011, with the Solar Optical Telescope on the emph{Hinode} satellite, which yielded 5576-Å filtergrams and Dopplergrams and also spectropolarimetric records of the magnetic-field vector. To determine the tangential-velocity field, a technique similar to but more reliable than local correlation tracking (LCT) was applied to the series of filtergrams, and the trajectories of corks were computed. According to our preliminary findings, the velocity pattern in the growing active region cannot be described as a spreading flow on the scale of the entire bipolar region, which could be expected if a tube of strong magnetic field emerged. Instead, normal mesogranular and supergranular flows are observed in agreement with Bumba’s inference that the development of an active region does not entail the destruction of the existing convective-velocity field. Between the magnetic polarities, curves can be found to which the surface flows converge rather than diverging from them under the action of a rising tube. The convective mechanism appears to be better compatible with observations than the rising-tube mechanism. In the umbras of the well-developed sunspots, flows converging to the umbra centres are revealed. Spreading streams are present around these spots. Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in cooperation with ESA and NSC (Norway). This work was supported by the Russian Foundation for Basic Research (project no. 12-02-00792-a). Title: Why can different flow scales coexist in solar convection? Authors: Getling, Alexander; Shcheritsa, Olga; Mazhorova, Olga Bibcode: 2014cosp...40E.976G Altcode: Solar convection demonstrates a remarkable multiscale structure (the coexistence of granules, mesogranules, supergranules and giant cells), which largely controls the structure and dynamics of photospheric magnetic fields. With the aim of comprehending the possible mechanisms of such scale splitting, the effect of particularities of the static temperature profile on the structure of convection are considered here. To this end, two-dimensional convection in a plane horizontal layer of an incompressible fluid heated from below is simulated numerically. The stratification of the layer is controlled by thermal-diffusivity variations. The static temperature gradient in a thin sublayer near the upper surface of the layer is assumed to be many times larger than in the remainder of the layer. In some cases, distributed heat sinks are assumed to produce a stably stratified region overlying the convective layer. Manifestations of the scale-splitting effect are observed, which depend on the boundary conditions and stratification. The multiscale structure of the flow is manifest most clearly in the presence of complex attractors in the pattern of phase trajectories of fluid particles. Small-scale convection cells are carried by larger-scale flows. This work was supported by the Russian Foundation for Basic Research, project no. 12-02-00792-a. Title: Concerning the multiscale structure of solar convection Authors: Getling, A. V.; Mazhorova, O. S.; Shcheritsa, O. V. Bibcode: 2013Ge&Ae..53..904G Altcode: The discrete scale spectrum of the convective flows observed on the Sun has not yet received a convincing explanation. Here, an attempt is made to find conditions for the coexistence of convective flows on various scales in a horizontal fluid layer heated from below, where the thermal diffusivity varies with temperature in such a way that the static temperature difference across a thin sublayer near the upper surface of the layer is many times larger than the temperature variation across the remainder of the layer. The equations of two-dimensional thermal convection are solved numerically in an extended Boussinesq approximation, which admits thermal-diffusivity variations. The no-slip conditions are assumed at the lower boundary of the layer; either no-slip or free-slip conditions, at the upper boundary. In the former case, stable large-scale rolls develop, which experience small deformations under the action of small structures concentrated near the horizontal boundaries. In the latter case, the flow structure is highly variable, different flow scales dominate at different heights, the number of large rolls is not constant, and a sort of intermittency occurs: the enhancement of the small-scale flow component is frequently accompanied by the weakening of the large-scale one, and vice versa. The scale-splitting effects revealed here should manifest themselves in one way or another in the structure of solar convection. Title: Convective mechanism of amplification and structuring of magnetic fields Authors: Getling, A. V.; Kolmychkov, V. V.; Mazhorova, O. S. Bibcode: 2013IAUS..294..137G Altcode: Magnetoconvection in a horizontal layer of incompressible fluid is simulated numerically. The initial magnetic field is assumed to be uniform and horizontal. The interaction of quasi-ordered cellular convection with the magnetic field is shown to be able to produce bipolar (and also diverse more complex) configurations of a substantially amplified magnetic field. The operation of this mechanism, which can be regarded as a modification of the mechanism suggested by Tverskoi (1966), is controlled by the very topology of the cellular flow, should be manifest on various spatial scales, and does not require strong initial fields. Magnetic configurations develop both in the central parts of convection cells, where circulatory fluid motion ``winds'' magnetic field lines, and in the network formed by their peripheral regions due to the ``sweeping'' of magnetic field lines. Title: The flow helicity in quasi-orderedcellular convection Authors: Getling, A. V. Bibcode: 2013IAUS..294..359G Altcode: The helicity of cellular convective flows in a horizontal layer of compressible fluid (gas) heated from below and rotating about a vertical axis is studied using finite-difference numerical simulations. The medium is assumed to be polytropically stratified. An initial thermal perturbation is introduced so as to produce a system of Bénard-type hexagonal convection cells. The flow gradually becomes less ordered, and the mean helicity grows initially and decreases sharply after the substantial chaotisation of the flow. Given the Rayleigh and Prandtl numbers, the maximum value reached by the mean helicity increases with the decrease of the polytrope index and has a maximum at a certain rotational velocity of the layer. Title: Toward understanding the multiscale spatial spectrum of solar convection Authors: Getling, A. V.; Mazhorova, O. S.; Shcheritsa, O. V. Bibcode: 2013IAUS..294..361G Altcode: Convection is simulated numerically based on two-dimensional Boussinesq equations for a fluid layer with a specially chosen stratification such that the convective instability is much stronger in a thin subsurface sublayer than in the remaining part of the layer. The developing convective flow has a small-scale component superposed onto a basic large-scale roll flow. Title: The helicity of the velocity field for cellular convection in a rotating layer Authors: Getling, A. V. Bibcode: 2012ARep...56..395G Altcode: 2012AZh....89..441G The helicity of a cellular convective flow in a horizontal layer of a compressible fluid (gas) heated from below and rotating about the vertical axis is studied using finite-difference numerical simulations. The medium is assumed to be polytropically stratified. A thermal perturbation that produces a system of Bénard-type hexagonal convection cells is introduced at the initial time. Next, the cells are deformed by the action of the Coriolis force; however, at some stage of the evolution, the flow is nearly steady (at later times, the cells break down). For given Rayleigh and Prandtl numbers, the velocity-field helicity for this stage averaged over the layer increases with decreasing polytrope index (i.e., with increasing the curvature of the static entropy profile) and has a maximum at a certain rotational velocity of the layer. Numerical simulations of such quasi-ordered convective flows should reduce the uncertainties in estimates of the helicity, a quantity important for the operation of MHD dynamos. Title: Some structural features of the convective-velocity field in the solar photosphere Authors: Getling, A. V.; Buchnev, A. A. Bibcode: 2010ARep...54..254G Altcode: 2010AZh....87..286G An algorithm for measuring horizontal photospheric velocities previously employed to process aerospace images is adapted for problems in solar physics and realized in a computational code. It differs from the standard procedure of local correlation tracking in a special choice of trial areas (“targets”), whose displacements are determined bymaximizing the correlation between the original and various shifted positions of the target. Specifically, an area is chosen as a target in a certain neighborhood of each node of a predefined grid if either the contrast or the entropy of the brightness distribution reaches its maximum in this area. The horizontal velocities obtained are then interpolated to the positions of imaginary “corks” using the Delaunay triangulation and affine transformations specified by the deformation of the obtained triangles at the time step considered. The motion of the corks is represented by their trajectories. A superposition of flows on different scales, from mesogranular to supergranular, can clearly be seen. “Large mesogranules” with sizes of order 15 Mm are revealed. In many cases, these are stellate in shape. Areas of strong convergence of the horizontal flows are detected; this convergence is sometimes accompanied by swirling. Evidence is found for the possible coexistence of convection cells with different circulation directions, so-called l-type and g-type cells. Title: Do Long-Lived Features Really Exist in the Solar Photosphere? II. Contrast of Time-Averaged Granulation Images Authors: Brandt, P. N.; Getling, A. V. Bibcode: 2008SoPh..249..307B Altcode: 2008arXiv0802.0204B; 2008SoPh..tmp...64B The decrease in the rms contrast of time-averaged images with the averaging time is compared between four data sets: (1) a series of solar granulation images recorded at La Palma in 1993, (2) a series of artificial granulation images obtained in numerical simulations by Rieutord et al. (Nuovo Cimento25, 523, 2002), (3) a similar series computed by Steffen and his colleagues (see Wedemeyer et al. in Astron. Astrophys.44, 1121, 2004), (4) a random field with some parameters typical of the granulation, constructed by Rast (Astron. Astrophys.392, L13, 2002). In addition, (5) a sequence of images was obtained from real granulation images by using a temporal and spatial shuffling procedure, and the contrast of the average of n images from this sequence as a function of n is analysed. The series (1) of real granulation images exhibits a considerably slower contrast decrease than do both the series (3) of simulated granulation images and the series (4) of random fields. Starting from some relatively short averaging times t, the behaviour of the contrast in series (3) and (4) resembles the t−1/2 statistical law, whereas the shuffled series (5) obeys the n−1/2 law from n=2 on. Series (2) demonstrates a peculiarly slow decline of contrast, which could be attributed to particular properties of the boundary conditions used in the simulations. Comparisons between the analysed contrast-variation laws indicate quite definitely that the brightness field of solar granulation contains a long-lived component, which could be associated with locally persistent dark intergranular holes and/or with the presence of quasi-regular structures. The suggestion that the random field (4) successfully reproduces the contrast-variation law for the real granulation (Rast in Astron. Astrophys.392, L13, 2002) can be dismissed. Title: Widespread Occurrence of Trenching Patterns in the Granulation Field: Evidence for Roll Convection? Authors: Getling, A. V.; Buchnev, A. A. Bibcode: 2008SoPh..248..233G Altcode: 2007arXiv0709.3251G Time-averaged series of granulation images are analysed using COLIBRI, a purpose-adapted version of a code originally developed to detect straight or curvilinear features in aerospace images. The image-processing algorithm utilises a nonparametric statistical criterion that identifies a straight-line segment as a linear feature (lineament) if the photospheric brightness at a certain distance from this line on both sides is stochastically lower or higher than at the line itself. Curvilinear features can be detected as chains of lineaments, using a modified criterion. Once the input parameters used by the algorithm are properly adjusted, the algorithm highlights "ridges" and "trenches" in the relief of the brightness field, drawing white and dark lanes. The most remarkable property of the trenching patterns is a nearly universally present parallelism of ridges and trenches. Since the material upflows are brighter than the downflows, the alternating, parallel light and dark lanes should reflect the presence of roll convection in the subphotospheric layers. If the numerous images processed by us are representative, the patterns revealed suggest a widespread occurrence of roll convection in the outer solar convection zone. In particular, the roll systems could form the fine structure of larger scale, supergranular and/or mesogranular convection flows. Granules appear to be overheated blobs of material that could develop into convection rolls owing to instabilities of roll motion. Title: Generation of coupled global and local magnetic fields by a cellular MHD dynamo Authors: Getling, A. V.; Simitev, R. D.; Busse, F. H. Bibcode: 2007IAUS..239..482G Altcode: No abstract at ADS Title: Is solar convection responsible for the local amplification and structuring of magnetic fields? (Observational test of the hypothesis) Authors: Getling, A. V.; Bao, X. M. Bibcode: 2007IAUS..239..496G Altcode: No abstract at ADS Title: Quasi-regular structures in the solar photosphere (trenching in the brightness relief): Algorithmic treatment Authors: Getling, A. V.; Buchnev, A. A. Bibcode: 2007IAUS..239..499G Altcode: No abstract at ADS Title: Can cellular convection in a rotating spherical shell maintain both global and local magnetic fields? Authors: Getling, A. V.; Simitev, R. D.; Busse, F. H. Bibcode: 2007IJGA....7.1004G Altcode: 2007IJGA....7I1004G; 2006astro.ph.10753G [1] A convection-driven MHD dynamo in a rotating spherical shell, with clearly defined structural elements in the flow and magnetic field, is simulated numerically. Such dynamos can be called deterministic, in contrast to those explicitly dependent on the assumed properties of turbulence. The cases most interesting from the standpoint of studying the nature of stellar magnetism demonstrate the following features. On a global scale, the convective flows can maintain a "general" magnetic field with a sign-alternating dipolar component. Local (in many cases, bipolar) magnetic structures are associated with convection cells. Disintegrating local structures change into background fields, which drift toward the poles. From time to time, reversals of the magnetic fields in the polar regions occur, as "new" background fields expel the "old" fields. Title: Do Quasi-Regular Structures Really Exist in the Solar Photosphere? I. Observational Evidence Authors: Getling, A. V. Bibcode: 2006SoPh..239...93G Altcode: 2006SoPh..tmp...82G; 2006astro.ph.10698G Two series of solar-granulation images - the La Palma series of 5 June 1993 and the SOHO MDI series of 17 - 18 January 1997 - are analysed both qualitatively and quantitatively. New evidence is presented for the existence of long-lived, quasi-regular structures (first reported by Getling and Brandt, Astron. Astrophys. 382, L5 (paper I), 2002), which no longer appear unusual in images averaged over 1 - 2-hour time intervals. Such structures appear as families of light and dark concentric rings or families of light and dark parallel strips ("ridges" and "trenches" in the brightness distributions). In some cases, rings are combined with radial "spokes" and can thus form "web" patterns. The characteristic width of a ridge or trench is somewhat larger than the typical size of granules. Running-average movies constructed from the series of images are used to seek such structures. An algorithm is developed to obtain, for automatically selected centres, the radial distributions of the azimuthally averaged intensity, which highlight the concentric-ring patterns. We also present a time-averaged granulation image processed with a software package intended for the detection of geological structures in aerospace images. A technique of running-average-based correlations between the brightness variations at various points of the granular field is developed and indications are found for a dynamical link between the emergence and sinking of hot and cool parcels of the solar plasma. In particular, such a correlation analysis confirms our suggestion that granules - overheated blobs - may repeatedly emerge on the solar surface. Based on our study, the critical remarks by Rast (Astron. Astrophys. 392, L13, 2002) on the original paper by Getling and Brandt (paper I) can be dismissed. Title: Cellular dynamo in a rotating spherical shell Authors: Getling, A. V.; Simitev, R. D.; Busse, F. H. Bibcode: 2005AN....326..241G Altcode: Magnetoconvection in a rotating spherical shell is simulated numerically using a code developed by Tilgner and Busse. The thermal stratification is convectively unstable in the outer part and stable in the inner part of the shell. Regimes are found in which the convective flow is weakly affected by rotation and preserves its cellular structure. The dipolar component of the large-scale magnetic field exhibits undamped oscillations. It appears that convection cells slightly modified by rotation can be building blocks of the global dynamo. The generation of the magnetic field is thus due to regular ``macroscopic'' flows, and their structure itself may ensure the presence of the α effect responsible for the action of the dynamo. Such dynamos can be called deterministic, in contrast to those in which the maintenance of the magnetic field is related to the statistical predominance of a certain sign of helicity in the turbulent velocity field. Investigation of conditions under which dynamos of this sort can operate could suggest a more definite answer to the question of the origin of solar and stellar magnetic fields. Title: Contrast of time-averaged images of the solar granulation Authors: Brandt, P. N.; Getling, A. V. Bibcode: 2004IAUS..223..231B Altcode: 2005IAUS..223..231B The time-averaged images of the solar granulation exhibit a slower decrease in contrast with the averaging time than do time-averaged images of numerically simulated granulation and time-averaged random fields with some parameters typical of granulation. This confirms the hints for long-lived structures in the granulation pattern. Title: Compressible magnetoconvection as the local producer of solar-type magnetic structures Authors: Dobler, W.; Getling, A. V. Bibcode: 2004IAUS..223..239D Altcode: 2005IAUS..223..239D Simulations of cellular magnetoconvection in a compressible fluid reveal the formation of magnetic structures with a substantial bipolar component as an inherent property of the topology of cellular flows. Title: Structure of solar convection: guesses and observational evidence Authors: Getling, A. V. Bibcode: 2004IAUS..223..247G Altcode: 2005IAUS..223..247G Signs of quasi-regular structures in time-averaged photospheric images are described. Title: Regular Photospheric Patterns (Trenching in the Brightness Relief) and Persistence of the Granular Field Authors: Getling, A. V.; Brandt, P. N. Bibcode: 2003ASPC..286..185G Altcode: 2003ctmf.conf..185G No abstract at ADS Title: Convective Mechanism for Formation of Solar Magnetic Bipoles Authors: Getling, A. V.; Ovchinnikov, I. L. Bibcode: 2003ASPC..286..139G Altcode: 2003ctmf.conf..139G No abstract at ADS Title: Quasi-regular structures of the solar photosphere Authors: Getling, A. V.; Brandt, P. N. Bibcode: 2002ESASP.506..617G Altcode: 2002ESPM...10..617G; 2002svco.conf..617G As we already reported, the simple procedure of time averaging, when applied to the photospheric brightness field, reveals quasi-regular structures of the photospheric and subphotospheric flows. Our analysis presented here shows that the decrease in the rms contrast of the averaged images with the increase of the averaging time τ is slower compared to the √τ law, which argues for the real persistence of the revealed structures as physical entities. The procedure of running-average-based correlation is suggested to seek coherence between the brightness variations at the points of emergence and sinking of granules. Some results of the correlation analysis confirm the notion that granules are overheated blobs of material carried by the convective circulation. Title: Solar convection as the producer of magnetic bipoles Authors: Getling, A. V.; Ovchinnikov, I. L. Bibcode: 2002ESASP.506..819G Altcode: 2002svco.conf..819G; 2002ESPM...10..819G A mechanism for the in situ formation of bipolar magnetic configurations, alternative to the well-known rising-tube mechanism, is considered. Cellular magnetoconvection is simulated numerically. The initial magnetic field is assumed to be fairly weak and directed horizontally. A pattern of small-amplitude hexagonal cells is specified initially. A hexagonal convection cell can substantially amplify the magnetic field and impart bipolar configurations to it. Depending on the parameters, the amplified field may form either a simple pair of magnetic islands, opposite in polarity, or a more complex superposition of bipoles. In particular, very compact magnetic elements of strong field can form. The resulting pattern of magnetic-field evolution is in better agreement with observations than the rising-tube model. Title: Regular structures of the solar photosphere. (Persistence of the granular field and trenching in the brightness relief) Authors: Getling, A. V.; Brandt, P. N. Bibcode: 2002A&A...382L...5G Altcode: The simple procedure of time averaging, when applied to the photospheric brightness field, reveals quasi-regular structures of the photospheric and subphotospheric flows. We use an 8-h sub-set of the series of photospheric images obtained on 5 June 1993 with the Swedish Vacuum Solar Telescope, La Palma. First, the averaged images are far from completely smeared and contain a multitude of bright, granular-sized blotches even if the averaging period is as long as 8 h. This suggests that granules prefer to originate at certain sites, where they emerge repeatedly, and the granular field demonstrates a sort of persistence for many hours. Second, the resulting patterns display relatively regular structures, which can be revealed only if the averaging period is sufficiently long (the optimum seems to lie between 2 and 3 h). The averaged brightness relief is ``trenched'': it comprises systems of concentric rings and arcs as well as straight or slightly wavy lines and systems of parallel strips. The trenching patterns resemble the so-called target patterns observed in experiments on Rayleigh-Bénard convection. In addition, the brightness values at a local averaged-field maximum and at a nearby minimum exhibit a distinct tendency to vary in antiphase. Thus, a previously unknown type of self-organization is manifest in the solar atmosphere, and our findings support the suggestion that granules are associated with overheated blobs carried by the convective circulation. Title: Solar convection and sunspot formation mechanishm Authors: Getling, A. V. Bibcode: 2001A&AT...20..433G Altcode: The rising-flux-tube model of the formation of a bipolar sunspot group sharply disgrees with the normally observed features of the process. Meanwhile, these features can be successfully accounted for in terms of local magnetic-field amplification due to zellular convective motions of the solar plasma. Here, magnetoconvection in a plane horizontal fluid layer is simulated numberically magnetic field and a weak cellular flow are present. Convention can produce bipolar configurations of strongly amplified magnetic field. Indications are found for the nontrivial effect of flow freezing. The action of the convective mechanism may be controlled by the large-scale toroidal magnetic field of the Sun. Title: Convective Mechanism for the Formation of Photospheric Magnetic Fields Authors: Getling, A. V. Bibcode: 2001ARep...45..569G Altcode: The well-known model that attributes the formation of a bipolar sunspot group to the emergence of a flux tube disagrees sharply with the usual observed pattern of phenomena. At the same time, the observed patterns can be accounted for quite convincingly in terms of local magnetic-field amplification due to cellular convective motions of the solar plasma. In this study, magnetoconvection in a plane horizontal fluid layer is simulated numerically in the framework of the fully nonlinear, three-dimensional problem. A weak horizontal magnetic field and weak cellular flow are assumed to be present initially. Convection is shown to be capable of producing bipolar magnetic configurations of the strongly amplified magnetic field. Indications of magnetic freezing of the flow in the cell are found. The action of the amplification mechanism under study may be controlled by the large-scale toroidal magnetic field of the Sun. Title: Hydrodynamic Instabilities and Photospheric Structures Authors: Getling, A. V. Bibcode: 2000ARep...44...56G Altcode: The possible role of convective-flow instabilities in the formation of certain structures observed in the solar photospheric and subphotospheric layers is discussed. High-resolution video records suggest that the granulation field is structurally and dynamically ordered in accordance with the mesogranulation pattern. Thus, it strikingly resembles the so-called spoke patterns of convection observed experimentally. These patterns could be produced by some instability of the mesogranular flow. Mesogranules seem to be the main structural features of the velocity field, whereas granules behave as relatively passive elements—blobs of overheated material carried by the mesogranular flow. One possible mechanism for their origin is the development of a three-dimensional analogue of the one-blob or the two-blob instability known from studies of convection. In particular, if this interpretation is adopted, the phenomenon of exploding granules can be accounted for in a natural way. Title: Numerical modelling of the magnetospheric convection in the region of closed force lines of the magnetic field. Authors: Alekseeva, L. M.; Getling, A. V.; Savelev, V. V. Bibcode: 1982Ge&Ae..22..612A Altcode: No abstract at ADS Title: The convective zone of the sun. Authors: Getling, A. V. Bibcode: 1982IGAFS..61....3G Altcode: No abstract at ADS Title: On the scales of convection flows in a horizontal layer with radiative energy transfer Authors: Getling, A. V. Bibcode: 1980FizAO..16..529G Altcode: No abstract at ADS Title: Theories of solar activity. Authors: Getling, A. V.; Tverskoi, B. A. Bibcode: 1980IzSSR..44.2560G Altcode: A solar dynamo model is developed which takes into account the relationship between global and local magnetic fields. It is shown that the model can explain certain aspects of solar activity. In particular, local magnetic fields intensified by convection cells can be the cause of sunspot groups. The basic features of the dynamo model are in accord with the features of the solar cycle: i.e., the model indicates changes of the sign of background fields in polar regions in each 11-year cycle, as well as a correlation between spot-forming activity and toroidal fields (whose existence in subphotospheric layers is highly probable). Title: Standing acoustic-gravity waves in the high-latitude atmosphere with allowance for the rotation of the earth Authors: Alekseeva, L. M.; Getling, A. V.; Magnitskii, B. V. Bibcode: 1980Ge&Ae..20...72A Altcode: No abstract at ADS Title: Model of an Oscillatory Hydromagnetic Dynamo. II Authors: Getling, A. V.; Tverskoy, B. A. Bibcode: 1971Ge&Ae..11..330G Altcode: No abstract at ADS Title: A model of an oscillating hydromagnetic dynamo. II. Authors: Getling, A. V.; Tverskoj, B. A. Bibcode: 1971GeA....11..389G Altcode: 1971Ge&Ae..11..389G No abstract at ADS Title: Model of an Oscillatory Hydromagnetic Dynamo. I Authors: Getling, A. V.; Tverskoy, B. A. Bibcode: 1971Ge&Ae..11..176G Altcode: No abstract at ADS Title: A model of an oscillating hydromagnetic dynamo. I. Authors: Getling, A. V.; Tverskoj, B. A. Bibcode: 1971GeA....11..211G Altcode: 1971Ge&Ae..11..211G No abstract at ADS Title: Criteria of thermal (overheat) instability of a transparent radiating gas. Authors: Getling, A. V.; Kuzmin, V. V.; Tverskoj, B. A. Bibcode: 1971DoSSR.196...71G Altcode: No abstract at ADS Title: Magnetic Fields in the Convection Cells of the Supergranulation Zone. Authors: Getling, A. V. Bibcode: 1969SvA....12..967G Altcode: No abstract at ADS Title: Solution of a class of magnetohydrodynamic problems with strengthening of the magnetic field. Authors: Getling, A. V. Bibcode: 1969DoSSR.187..301G Altcode: No abstract at ADS Title: A Possible Mechanism for Producing Sunspot Magnetic Fields. Authors: Getling, A. V.; Tverskoi, B. A. Bibcode: 1968SvA....12..481G Altcode: No abstract at ADS Title: Magnetic Fields in the Convection Cells of the Supergranulation Zone. Authors: Getling, A. V. Bibcode: 1968AZh....45.1222G Altcode: No abstract at ADS Title: A Possible Mechanism for Producing Sunspot Magnetic Fields. Authors: Getling, A. V.; Tverskoi, B. A. Bibcode: 1968AZh....45..606G Altcode: No abstract at ADS Title: Propagation of Hydromagnetic Waves in a Slightly Inhomogeneous Medium Authors: Getling, A. V. Bibcode: 1967SvA....11..410G Altcode: No abstract at ADS Title: Propagation of Hydromagnetic Waves in a Slightly Inhomogeneous Medium Authors: Getling, A. V. Bibcode: 1967AZh....44..513G Altcode: No abstract at ADS Title: Hydromagnetic Waves in a Nonisentropic Medium in the Presence of a Gravitational Field Authors: Getling, A. V. Bibcode: 1965SvA.....9..451G Altcode: No abstract at ADS Title: Hydromagnetic Waves in a Nonisentropic Medium in the Presence of a Gravitational Field Authors: Getling, A. V. Bibcode: 1965AZh....42..568G Altcode: No abstract at ADS