Shear flow driven counter rotating vortices in an inhomogeneous dusty magnetoplasma

The coupling of Shukla-Varma (SV) and convective cell modes is discussed in the presence of non-Boltzmannian electron response and parallel equilibrium shear flow. In the linear case, a new dispersion relation is derived and analyzed. It is found that the coupled SV and convective cell modes destabilize in the presence of electron shear flow. On the other hand, in the nonlinear regime, it is shown that Shukla-Varma mode driven counter rotating vortices can be formed for the system under consideration. It is found that these vortices move slowly by comparison with the ion acoustic or electron drift-wave driven counter rotating vortices. The relevance of the present investigation with regard to space plasmas is also pointed out.     

Vortices in strongly magnetized nonuniform electron-positron-ion plasmas

The nonlinear mode coupling equations for electrostatic and electromagnetic waves in strongly magnetized nonuniform electron-positron-ion plasmas are derived. It is found that a small fraction of stationary ions (or high-Z charged impurities) can be responsible for the formation of coherent vortices which are forbidden when the ions are absent. Such vortices might significantly affect the transport properties of electron-positron plasmas in external magnetic fields.     

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).     

Numerical simulations of the magnetic field distribution in a solar complex of activity

Powerful solar complexes of activity are supposed to result from the excitation of Rossby vortices within a thin layer beneath the convection zone. Numerical simulations demonstrate that Rossby vortices generate large-scale arc-like magnetic structures. It is shown that the most powerful complex of activity observed in June-July 1982 was likely to be a result of the excitation of a Rossby anticyclone rather than a cyclone.     

A case study of Kelvin-Helmholtz vortices on both flanks of the Earth's magnetotail

Kelvin-Helmholtz instability (KHI) is a fundamental fluid dynamical process that develops in a velocity shear layer. It is excited on the tail-flanks of the Earth's magnetosphere where the flowing magnetosheath plasma and the stagnant magnetospheric plasma sit adjacent to each other. This instability is thought to induce vortical structures and play an important role in plasma transport there. While KHI vortices have been detected, the earlier observations were performed only on one flank at a time and questions related to dawn-dusk asymmetry were not addressed. Here, we report a case where KHI vortices grow more or less simultaneously and symmetrically on both flanks, despite all the factors that may have broken the symmetry. Yet, energy distributions of ions in and around the vortices show a remarkable dawn-dusk asymmetry. Our results thus suggest that although the initiation and development of the KHI depend primarily on the macroscopic properties of the flow, the observed enhancement of ion energy transport around the dawn side vortices may be linked to microphysical processes including wave-particle interactions. Possible coupling between macro- and micro-scales, if it is at work, suggests a role for KHI not only within the Earth's magnetosphere (e.g., magnetopause and geomagnetic tail) but also in other regions where shear flows of magnetized plasma play important roles.     

Covariant formulation of the dynamical equations of quantum vortices in type II superconductors

We have derived the closed system of covariant equations which describe the motion of quantum vortices regarded as a two-2dimensional polarized liquid. We have obtained the covariant expressions of the forces acting on the vortices; from the equilibrium condition of these forces we have deduced the equation satisfied by the velocity field of the fluid. It is shown that this velocity field depends on the friction coefficient, the density of vortices and the superconducting current. From this closed system of equations we derived the relaxation equation when a variable magnetic field is applied. Published in Astrofizika, Vol. 50, No. 3, pp. 381–391 (August 2007).     

Simulations of high-latitude spots on Jupiter: Constraints on vortex strength and the deep wind

We combine high-resolution observations of the dynamical behavior of small vortices (diameters ?5000 km) located at latitude 60°N on Jupiter with forward modeling, using the EPIC atmospheric model, to address two open questions: the dependence of the zonal winds with depth, and the strength of vortices that are too small to apply cloud tracking to their internal structure. The observed drift rates of the vortices can only be reproduced in the model when the zonal winds increase slightly with depth below the cloud tops, with a vertical shear that is less than was measured at 7°N at the southern rim of a 5-μm hotspot by the Galileo Probe Doppler Wind Experiment (DWE). This supports the idea that Jupiter's vertical shear may vary significantly with latitude. Our simulations suggest that the morphology of the mergers between vortices mainly depends on their maximum tangential velocities, the best results occurring when the tangential velocity is close to the velocity difference of the alternating jets constraining the zone in which the vortices are embedded. We use this correlation, together with the high-resolution data available for the White Ovals, to derive an empirical relationship between the maximum tangential velocity of a jovian vortex and its size, normalized by the strength and size of the encompassing shear zone. The Great Red Spot stands out as a significant anomaly to this relationship, but interestingly it is becoming less so with time.     

Acceleration and ejection of ring vortices as a mechanism for formation of jet components in AGN

Exact solutions are obtained for the two-dimensional hydrodynamic equations for symmetric configurations of two and four vortices in the presence of an arbitrary flow with a point singularity. These solutions describe the dynamics of a dipole toroidal vortex in accretion and wind flows within the active nuclei of galaxies. It is shown that in a converging (accretion) flow, as they are compressed along their major radius, toroidal vortices are ejected with acceleration along the axis of symmetry of the active nucleus, to form the components of a bilateral jet. For a symmetric flow, the increase in the velocity of the vortices is determined by the monopole component of the flow, and, when there is an asymmetry in the flow, also by the dipole component of the flow, which controls the asymmetry of the ejection.     

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.     

Solitary waves of vortices

We study the propagation of solitary waves of vortices within a spherical shell which constitutes the uppermost layer of a solid planet. This solid-liquid configuration rotates with constant angular velocity about an axis which is fixed with respect to the solid surface. The fluid within the shell is inviscid, incompressible, and of constant density. The motion imparted by the planetary rotation upon this fluid mass is governed by the Laplace tidal equation from which the potential of the extraplanetary forces has been deleted. Consistent with this ocean model, we establish that the stream function of a solitary wave of vortices must satisfy a third-order partial differential equation. We obtain solutions to this wave equation by imposing the condition that the vertical component of vorticity be functionally related to the stream function. We find that this dependence must necessarily be of the exponential type and that the solution to the wave equation then reduces to a quadrature depending on some arbitrary parameters. We prove that we can always choose the values of these parameters in order to approximate the integral in question by means of an analytic function: we reach a representation of the stream function of a solitary wave of vortices in terms of hyperbolic functions of time and position.This paper is dedicated to the memory of Professor Zdenek Kopal.     

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.     

Curvature coupling of slow and Alfvén MHD waves in a magnetotail field configuration

It is argued that in the short perpendicular wavelength limit the incompressible Alfvén mode may be coupled to a compressional slow mode signal by background field inhomogeneity. The mechanism described here is entirely due to field curvature. We propose that such coupling could take place near the Equator in the terrestrial plasma sheet and be responsible for the hybrid nature of the polarization deduced for the vortices discovered by Hones and co-workers in the Earth's magnetotail.     

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.     

On structure formation in the universe

The formation of structures in the universe is one of the most challenging problems of cosmology. In this paper, an attempt to explain the formation of galaxies through the generation of vortices (with dissipation) in an uniformly expanding perfect fluid is made. The equation governing the mean square vorticity for a turbulent (isotropic and homogeneous) fluid is derived. It is shown that the mechanism of stretching vortices could enhance the mean square vorticity as a function of time. However, ultimately expansion and dissipation dominate and the solution for the mean square vorticity reaches the prediction by linear theory.     

The meteorological signatures of dust devils on Mars

This paper describes a method for identifying martian dust devils and convective vortices in meteorological data. We have combined analysis of terrestrial dust devil fieldwork, re-analysis of martian meteorological data and laboratory experiments to explore fully the meteorological signature of dust devils. Both martian and terrestrial dust devils have similar characteristics implying a common formation mechanism. Terrestrial fieldwork therefore provides vital data that can be used to aid in the identification of their martian counterparts. Finally, a martian surface instrument package is suggested that will best detect dust devils and convective vortices without the need for visual confirmation.     

A Mechanism for the Local Production of Faculae

We offer a new viewpoint that can explain some of the recently obtained high-resolution observations of granules and faculae. Examining the data of Scharmer, Gudiksen, Kiselman et al. (2002) we observe many granules undergo an evolution that results in faculae emerging from within their boundaries, and moving towards and into intergranular lanes. These faculae have a characteristic hairpin substructure. The evolving morphology can be closely described by a fluid dynamic instability we call the “vortex/shear layer” (VSL) interaction. It occurs in all granules whose underlying structure has vorticity when they emerge into the photosphere through the sub-photospheric turbulent boundary layer (SPTBL). The VSL results in the creation of vortices from the distributed vorticity of the SPTBL. The subsequent stretching of these vortices results in high amplification of vorticity, and the concurrent high amplification of the background magnetic field. Magnetic field lines spiral around the vortices, as well as being stretched along their axis. Thus, the VSL is also the origin of a coherent local dynamo. The spiral sheathing of high magnetic flux results in a simple explanation for the “hot wall” effect. The VSL also creates the “dark lanes” observed by Lites, Scharmer, Berger et al. (2004) and groupings of bright hairpins/vortex sheet ensembles, which look like the ribbon faculae (Berger, Rouppe van der Voort, Lofdahl et al., 2004). The SPTBL results in emerging tilted granules, which when combined with the VSL create the three-dimensionality which Lites, Scharmer, Berger et al. (2004), also observed. Both the VSL and the SPTBL result, on average, in a west side bias of hairpin faculae and granular three-dimensionality. An erratum to this article is available at .     

Formation of vortices in the presence of sheared electron flows in the earth's ionosphere

It is shown that sheared electron flows can generate long as well as short wavelength (in comparison with the ion gyroradius) electrostatic waves in a nonuniform magnetplasma. For this purpose, we derive dispersion relations by employing two-fluid and hybrid models; in the two-fluid model the dynamics of both the electrons and ions are governed by the hydrodynamic equations and the guiding center fluid drifts, whereas the hybrid model assumes kinetic ions and fluid electrons. Explicit expressions for the growth rates and thresholds are presented. Linearly excited waves attain finite amplitudes and start interacting among themselves. The interaction is governed by the nonlinear equations containing the Jacobian nonlinearities. Stationary solutions of the nonlinear mode coupling equations can be represented in the form of a dipolar vortex and a vortex street. Conditions under which the latter arise are given. Numerical results for the growth rates of linearly excited modes as well as for various types of vortices are displayed for the parameters that are relevant for the F-region of the Earth's ionosphere. It is suggested that the results of the present investigation are useful in understanding the properties of nonthermal electrostatic waves and associated nonlinear vortex structures in the Earth's ionosphere.     

Relaxation of the Angular Velocity of the Vela Pulsar Following Its First Eight Glitches

The theory of the relaxation of pulsar angular velocity is compared with observational data for the first eight glitches of the Vela pulsar. Solutions of the inverse problem in relaxation theory are obtained in the regions of exponential and linear relaxation in the core of the neutron star. From these solutions, a distribution of vortices is found that results in the observed relaxation of the pulsar's angular velocity. It is shown that the pinning of neutron vortices plays the primary role in the region of exponential relaxation, while in the region of linear relaxation one must allow for the variation of the angular velocity of the superfluid component.     

Sheared ion flow driven nonlinear coherent structures in inhomogeneous electron-positron-ion quantum magnetoplasmas

Nonlinear equations governing the dynamics of finite amplitude drift-acoustic-waves are derived by taking into account sheared ion flow perpendicular to the ambient magnetic field in a quantum magnetoplasma comprised of electrons, positrons, and ions. It is shown that stationary solution of the nonlinear equations can be represented in the form of a counter-rotating vortex for a particular choice of the equilibrium profile. The counter rotating vortices are, however, observed to form on very short scales i.e., of the order of ion Larmor radius ρ _i in quantum plasmas. It is observed that the scalelengths over which these structures form get modified in the presence of quantum statistical and Bohm potential terms as well as the positron concentration. The relevance of the present investigation with regard to dense astrophysical environments is also pointed out.     

Vertical structure of Jupiter's troposphere from nonlinear simulations of long-lived vortices

Numerical simulations of jovian vortices at tropical and temperate latitudes, under different atmospheric conditions, have been performed using the EPIC code [Dowling, T.E., Fisher, A.S., Gierasch, P.J., Harrington, J., LeBeau, R.P., Santori, C.M., 1998. Icarus 132, 221-238] to simulate the high-resolution observations of motions and of the lifetimes presented in a previous work [Legarreta, J., Sánchez-Lavega, A., 2005. Icarus 174, 178-191] and infer the vertical structure of Jupiter's troposphere. We first find that in order to reproduce the longevity and drift rate of the vortices, the Brunt-Väisälä frequency of the atmosphere in the upper troposphere (pressures P∼1 to 7 bar) should have a lower limit value of 5×¹⁰⁻³ s⁻¹, increasing upward up to 1.25×¹⁰⁻² s⁻¹ at pressures P∼0.5 bar (latitudes between 15° and 45° in both hemispheres). Second, the vortices drift also depend on the vertical structure of the zonal wind speed in the same range of altitudes. Simulations of the slowly drifting Southern hemisphere vortices (GRS, White Ovals and anticyclones at 40° S) require a vertically-constant zonal-wind with depth, but Northern hemisphere vortices (cyclonic “barges” and anticyclones at 19, 41 and 45° N) require decreasing winds at a rate of ∼5 m s⁻¹ per scale height. However vortices drifting at a high speed, close to or in the peak of East or West jets and in both hemispheres, require the wind speed slightly increasing with depth, as is the case for the anticyclones at 20° S and at 34° N. We deduce that the maximum absolute vertical shear of the zonal wind from P∼1 bar up to P∼7 bar in these jets is ∼15 m s⁻¹ per scale height. Intense vortices with tangential velocity at their periphery ∼100 m s⁻¹ tend to decay asymptotically to velocities ∼40 to 60 m s⁻¹ with a characteristic time that depends on the vortex intensity and static stability of the atmosphere. The vortices adjust their tangential velocity to the averaged peak to peak velocity of the opposed eastward and westward jets at their boundary. We show through our simulations that large-scale and long-lived vortices whose maximum tangential velocity is ∼100 m s⁻¹ can survive by absorbing smaller intense vortices.