Long‐term evolution of the magnetic field generated by an ensemble of Rossby vortices

The evolution of the large‐scale component of the magnetic field generated by an ensemble of Rossby vortices is numerically simulated. The distribution of the Rossby vortices excited at the beginning of each Carrington rotation is determined from the analysis of Kitt Peak synoptic maps. Our model also considers 11‐year hydrodynamic and 22‐year magnetic field oscillations. In the vicinity of the Rossby vortices, the toroidal magnetic field is significantly amplified and the sign of the angle between the rope of the field lines and the equator is in accordance with observations for “normal” sunspots. We also suggest the possibility of the interpretation by our model of “abnormal” sunspot phenomena. We find that an inverse cascade, namely, the merging of Rossby vortices, gives rise to the formation of large‐scale hydrodynamic structures with a life‐time on the order of a solar cycle period. We conclude from this that the formation of such structures can thus explain the appearance of long‐lived, large‐scale component in the distribution of the magnetic field.     

Rossby vortices as sources of global magnetic structures on the Sun

A numerical simulation of the process of generation of the magnetic field by Rossby vortices, whose horizontal scale is comparable to the solar radius, has been carried out. Long-lived vortices form global magnetic structures that drift together with vortices. Differential rotation in latitude leads to a longer lifetime of cyclones and corresponding magnetic structures. The cyclone and the magnetic structure travel in longitude with the velocity close to a corresponding differential rotation velocity and drift slowly poleward. The interaction of cyclones located in close latitudes makes one of them move to higher latitudes and the poloidal component of the magnetic field to intensify during the interaction.The formation of large-scale vortices was simulated, when the initial condition was specified by a grid of small-scale vortices with a random amplitude distribution. Merging of vortices of the same sign leads to the formation of large-scale vortices whose size is determined by the geometry of the problem and by the differential rotation profile.     

Non-linear dynamics of the corotation torque

The excitation of spiral waves by an external perturbation in a disc deposits angular momentum in the vicinity of the corotation resonance (the radius where the speed of a rotating pattern matches the local rotation rate). We use matched asymptotic expansions to derive a reduced model that captures non-linear dynamics of the resulting torque and fluid motions. The model is similar to that derived for forced Rossby wave critical layers in geophysical fluid dynamics. Using the model we explore the saturation of the corotation torque, which occurs when the background potential (specific) vorticity is redistributed by the disturbance. We also consider the effects of dissipation. If there is a radial transport of potential vorticity, the corotation torque does not saturate. The main application is to the creation, growth and migration of protoplanets within discs like the primordial solar nebula. The disturbance also nucleates vortices in the vicinity of corotation, which may spark further epochs of planet formation.     

Rossby Wave Propagation and Generation in the Protoplanetary Nebula

The protoplanetary nebular analog to the planetary Rossby wave is developed. Linear dispersion relations are derived. It is found that the nebular Rossby wave propagates freely in the nebular azimuthal direction and slowly grows in the radial direction. Possible ramifications for the nebula are raised for the reverse transition of turbulence into Rossby waves and zonal jets via the Rhines mechanism (P. B. Rhines 1975, J. Fluid Mech.69, 417–443), specifically, the formation of long-lived vortices and the accretion of solid bodies.     

The origin of pulsar glitches

It is usually assumed that pulsar glitches are caused by the large-scale unpinning of superfluid neutron vortices in the solid crust of a neutron star and that vortex motion relative to the crust is highly dissipative at low velocities, owing to the excitation of long-wavelength Kelvin waves. The force per unit length acting on a vortex as a result of Kelvin wave excitation has been calculated for a polycrystalline structure using the free-vortex Green function. An approximate upper limit for the maximum pinning force has been obtained which, for the form of structure anticipated, is many orders of magnitude too small for consistency with the observed size and frequency of glitches. The corollary is that glitches do not originate in the crust: the necessary pinning may be given by the interaction between neutron and proton vortices in the liquid core of the star.     

Role of 3d-dispersive Alfven waves in coronal heating

Coronal heating is one of the unresolved puzzles in solar physics from decades. In the present paper we have investigated the dynamics of vortices to apprehend coronal heating problem. A three dimensional (3d) model has been developed to study propagation of dispersive Alfvén waves (DAWs) in presence of ion acoustic waves which results in excitation of DAW and evolution of vortices. Taking ponderomotive nonlinearity into account, development of these vortices has been studied. There are observations of such vortices in the chromosphere, transition region and also in the lower solar corona. These structures may play an important role in transferring energy from lower solar atmosphere to corona and result in coronal heating. Nonlinear interaction of these waves is studied in view of recent simulation work and observations of giant magnetic tornadoes in solar corona and lower atmosphere of sun by solar dynamical observatory (SDO).     

木星“大红斑”的旋转浅水实验模拟研究

在具有自由表面的旋转轨物面浅水实验系统上进行了可重复的系列模拟实验，在旋转随动坐标系中拍摄的照片和功率谱分析表明，确有大尺度持续存在的涡旋、漂移与演化产生，在一定条件下，呈现出一个自持的、长寿命的、沿与整体旋转方向相反方向漂移的反气旋孤立波涡旋（Rossby孤立波涡旋），这就是木星“大红斑”的实验室模型，实验结果证实，流体动力学不稳定主要来自于剪切和Coriolis力效应，由于远离平衡态的耗散系统的自组织，涌现出大尺度长寿命相干涡旋结构，受多次实验的启发，从流体动力学基本方程出发，在一定的实验条件下提出一个半经验模型，近似求出了Rossby孤立波涡旋解。     

A new look at the relationship between activity, dynamo number and Rossby number in late-type stars

The correlation between stellar activity, as measured by the indicator Δ R _HK, and the Rossby number Ro in late-type stars is revisited in light of recent developments in solar dynamo theory. Different stellar interior models, based on both mixing-length theory and the full spectrum of turbulence, are used in order to see to what extent the correlation of activity with Rossby number is model dependent, or otherwise can be considered universal. Although we find some modest model dependence, we find that the correlation of activity with Rossby number is significantly better than with rotation period alone for all the models we consider. Dynamo theory suggests that activity should scale with the dynamo number. A current model of the solar dynamo, the so-called interface dynamo, proposes that the amplification of the toroidal magnetic field by differential rotation (the ω -effect) and the production of the poloidal magnetic field from toroidal by helical turbulence (the α -effect) take place in different, adjacent layers near the base of the convection zone. A new scale analysis based on the interface dynamo shows that the appropriate dynamo number does not depend on the Rossby number alone, but also depends on an additional dimensionless factor related to the differential rotation. This leads to a new interpretation of the correlation between activity and Rossby number, which in turn leads to some conclusions about the magnitude of differential rotation in the dynamo layers of late-type main-sequence stars.     

The dynamics of jovian white ovals from formation to merger

In early 1998 two of the three, long-lived anticyclonic, jovian white ovals merged. In 2000 the two remaining white ovals merged into one. Here we examine that behavior, as well as the dynamics of three earlier epochs: the Formation Epoch (1939-1941), during which a nearly axisymmetric band broke apart to form the vortices; the Kármán Vortex Street Epoch (1941-1994), during which the white ovals made up the southern half of two rows of vortices, and their locations oscillated in longitude such that the white ovals often closely approached each other but did not merge; and the Pre-merger Epoch (1994-1997), during which the three white ovals traveled together with intervening cyclones from the northern row of the Kármán vortex street in a closely spaced group with little longitudinal oscillation. We use a quasi-geostrophic model and large-scale numerical simulation to explain the dynamics. Our models and simulations are consistent with the observations, but none of the observed behavior is even qualitatively possible without assuming that there are long-lived, coherent cyclones longitudinally interspersed with the white ovals. Without them, the white ovals approach each other and merge on a fast, advective timescale (4 months). A necessary ingredient that allows the vortices to travel together in a small packet without spreading apart is that the strong, eastward-flowing jetstream south of the white ovals is coincident with a sharp gradient in background potential vorticity. The jet forms a Rossby wave and a trough of the wave traps the white ovals. In our simulations, the three white ovals were trapped before they merged. Without being trapped, the amount of energy needed to perturb two white ovals so that they merge exceeds the atmosphere’s turbulent energy (which corresponds to velocities of ∼1 m s⁻¹) by a factor of ∼100. The mergers of the white ovals BC and DE were not observed directly, so there is ambiguity in labeling the surviving vortices and identifying which vortices might have exchanged locations. The simulation and modeling make the identifications clear. They also predict the fate of the surviving white oval and of the other prominent jovian vortex chains.     

Magnetically active stars in Taurus-Auriga: Activity and rotation

A sample of 70 magnetically active stars toward the Taurus-Auriga star-forming region has been investigated. The positions of the sample stars on the Rossby diagram have been analyzed. All stars are shown to be in the regime of a saturated dynamo, where the X-ray luminosity reaches its maximum and does not depend on the Rossby number. A correlation has been found between the lithium line equivalent width and the age of a solar-mass (from 0.7 to 1.2 M _⊙) pre-main-sequence star. The older the age, the smaller the Li line equivalent width. Analysis of the long-term photometric variability of these stars has shown that the photometric activity of the youngest stars is appreciably higher than that of the older objects from the sample. This result can be an indirect confirmation of the evolution of the magnetic field in premain-sequence stars from predominantly dipole and axisymmetric to multipole and nonaxisymmetric.     

Keck adaptive optics images of Jupiter’s north polar cap and Northern Red Oval

We present observations at near-infrared wavelengths (1-5 μm) of Jupiter’s north polar region and Northern Red Oval (NN-LRS-1). The observations were taken with the near-infrared camera NIRC2 coupled to the adaptive optics system on the 10-m W.M. Keck Telescope on UT 21 August 2010. At 5-μm Jupiter’s disk reveals considerable structure, including small bright rings which appear to surround all small vortices. It is striking, though, that no such ring is seen around the Northern Red Oval. In de Pater et al. [2010a. Icarus 210, 742-762], we showed that such rings also exist around all small vortices in Jupiter’s southern hemisphere, and are absent around the Great Red Spot and Red Oval BA. We show here that the vertical structure and extent of the Northern Red Oval is very similar to that of Jupiter’s Red Oval BA. These new observations of the Northern Red Oval, therefore, support the idea of a dichotomy between small and large anticyclones, in which ovals larger than about two Rossby deformation radii do not have 5-μm bright rings. In de Pater et al. [2010a. Icarus 210, 742-762], we explained this difference in terms of the secondary circulations within the vortices. We further compare the brightness distribution of our new 5-μm images with previously published radio observations of Jupiter, highlighting the depletion of NH₃ gas over areas that are bright at 5 μm.     

Jupiter's cyclones and anticyclones vorticity from Voyager and Galileo images

We have measured the internal velocity field in jovian synoptic-scale cyclones and anticyclones by tracking cloud elements in very high spatial resolution images obtained by the Voyager 1 and 2 (in 1979) and Galileo (1996-2000) spacecrafts. In total we have studied 24 different closed vortices (6 cyclones, 18 anticyclones) spanning a latitude range from ∼60° N to 60° S and with East-West sizes larger than ∼2000 km. The tangential component of the velocity as a function of the distance to the vortex center and position angle is used to retrieve the vorticity field. We find that the velocity increases in all the vortices from a nearly quiescent center to a maximum at the vortex periphery, with a record of about 180 m s⁻¹ for the GRS. The vorticity of cyclones and anticyclones increases in general toward their periphery with absolute values in the range from ∼2-14×¹⁰⁻⁵ s⁻¹. There is a marked tendency to increase the vortices vorticity with their latitude location. However the vorticity does not depend on the vortex size, circulation sense, or ambient background meridional wind shear. The vortex Rossby number ranges from ∼0.2 to 0.5. A study of the interaction between the Great Red Spot with other vortices show that the GRS does not change its vorticity upon their absorption. The two White Ovals mergers showed contradictory results, with greater vorticity in the case of BE, but lower vorticity in the case of BA, although data are poorer for this last case. We present the case of a short lived but large coherent cyclone at −59° that was embedded in a weakly anticyclone wind shear domain. We show that jovian vortices do not follow the simple Kida vortex relationship between vorticity and aspect ratio as it has been previously suggested.     

On the rotation–activity correlation for active binary stars

We present an investigation of rotation–activity correlations using International Ultraviolet Explorer ( IUE ) SWP measurements of the C  iv emission line at 1550Å for 72 active binary systems. We use a standard stellar evolution code to derive non-empirical Rossby numbers, R ₀, for each star in our sample and compare the resulting C  iv rotation–activity correlation to that found for empirically derived values of the Rossby number and that based on rotation alone. For dwarf stars our values of R ₀ do not differ greatly from empirical ones and we find a corresponding lack of improvement in correlation. Only a marginal improvement in correlation is found for evolved components in our sample. We discuss possible additional factors, other than rotation or convection, that may influence the activity levels in active binaries. Our observational data imply, in contrast to the theoretical predictions of convective motions, that activity is only weakly related to mass in evolved stars. We conclude that current dynamo theory is limited in its application to the study of active stars because of the uncertainty in the angular velocity-depth profile in stellar interiors and the unknown effects of binarity and surface gravity.     

Influence of the Solar Global Magnetic-Field Structure Evolution on CMEs

We consider the influence of the solar global magnetic-field structure (GMFS) cycle evolution on the occurrence rate and parameters of coronal mass ejections (CMEs) in Solar Cycles 23?–?24. It has been shown that, over solar cycles, CMEs are not distributed randomly, but they are regulated by evolutionary changes in the GMFS. It is proposed that the generation of magnetic Rossby waves in the solar tachocline results in the GMFS cycle changes. Each Rossby wave period favors a particular GMFS. It is proposed that the changes in wave periods result in GMFS reorganization and consequently in CME location, occurrence rate, and parameter changes. The CME rate and parameters depend on the sharpness of the GMFS changes, the strength of the global magnetic field, and the phase of a cycle.     

The characteristics of Rossby waves frequencies on planets of the Solar system

The Rossby waves frequencies for all planets of the Solar system have been computed and compared with the frequencies of Rossby waves on the Earth.     

A Ca ii H&K survey of γ Doradus candidates

In an investigation of the starspot hypothesis as it applies to the 'slowly variable' F-type dwarfs, we spectroscopically observed eight promising γ Doradus candidates to search for Ca  ii H&K emission. We found that there are no significant emission reversals in the cores of these resonance lines. Based on the ceiling flux calculations of the Ca  ii K line and on calculations of the Rossby number, we conclude that there is no support for the presence of strong magnetic activity and the starspot hypothesis in these objects.     

Relaxation of quantum vortices in type II superconductors and in neutron stars

The nonstationary dynamics of vortices in conventional type II superconductors and in neutron stars is examined in the Newtonian approximation. A relaxation equation is obtained for vortices approaching an equilibrium distribution after a change in an external magnetic field. The relaxation times are estimated for vortices in low-temperature superconductors and for proton vortices in the superconducting core of a neutron star. It is shown that the proton vortex system created by entrainment currents is rigidly coupled to the neutron vortices. Translated from Astrofizika, Vol. 52, No. 2, pp. 291–300 (May 2009).     

Evolutionary status of UV Piscium and its comparison with other short period RS CVn binaries

From the derived elements of UV Piscium, the evolutionary status of both of its components are compared with the Schaller et al. models and also with other main sequence systems having spectral types of late F to K range. From these models the ages of the components of UV Psc are determined. The Rossby number, which is a measure of chromospheric activity, has been derived from the convective turnover time scales and also from the age estimates.     

Vortex–interface interactions and generation of glitches in pulsars

We show that the crust–core interface in neutron stars acts as a potential barrier to the peripheral neutron vortices approaching the interface in the model in which these are coupled to the proton vortex clusters. This elementary barrier arises because of the interaction of vortex magnetic flux with the Meissner currents set up by the crustal magnetic field at the interface. The dominant part of the force is derived from the cluster–interface interaction. As a result of the stopping of the continuous neutron vortex current through the interface, angular momentum is stored in the superfluid layers in the vicinity of the crust–core interface during the interglitch period. Discontinuous annihilation of proton vortices at the boundary restores the neutron vortex current and spins up the observable crust on short time-scales, leading to a glitch in the spin characteristics of a pulsar.     

Analytical theory of tachocline transport at mid latitudes

We provide a theory of magnetic diffusion, momentum transport, and mixing in the solar tachocline by considering magnetohydrodynamics (MHD) turbulence on a β plane subject to a large scale shear (provided by the latitudinal differential rotation). In the strong magnetic field regime, we find that the turbulent viscosity and diffusivity are reduced by magnetic fields only, similarly to the two-dimensional MHD case (without Rossby waves). In the weak magnetic field regime, we find a crossover scale (L_R) from a Alfvén dominated regime (on small scales) to a Rossby dominated regime (on large scales). For parameter values typical of the tachocline, L_R is larger than the solar radius so that Rossby waves are unlikely to play an important role in the transport of magnetic field and angular momentum. This is mainly due to the enhancement of magnetic back-reaction by shearing which efficiently generates small scales, thus strong currents. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)