The stability of a velocity shear in the presence of an inhomogeneous magnetic field

The stability of a velocity shear in the presence of a parallel but non-uniform magnetic field is considered in general terms. Two special cases are then investigated; (i) the well known case of a plane interface at which a discontinuity in the magnetic field coincides with the velocity shear; (ii) an axially symmetric flow in which discontinuities in the magnetic and velocity fields occur at a cylindrical surface whose axis is parallel to the flow. In the first case the flow is stabilized if the rms Alfvén velocity of the magnetic field exceeds the shear velocity; a result consistent with that obtained by other writers. In the second case it is shown that the discontinuity in the magnetic field increases the stability of the system. The significance of this result for the stability of the flux ropes associated with sunspots in the solar convection zone is considered.     

Azimuthally symmetric magnetohydrodynamic and two-fluid equilibria with arbitrary flows

Magnetohydrodynamic (MHD) and two-fluid quasi-neutral equilibria with azimuthal symmetry, gravity and arbitrary ratios of (non-relativistic) flow speed to acoustic and Alfvén speeds are investigated. In the two-fluid case, the mass ratio of the two species is arbitrary, and the analysis is therefore applicable to electron–positron plasmas. The methods of derivation can be extended in an obvious manner to several charged species. Generalized Grad–Shafranov equations, describing the equilibrium magnetic field, are derived. Flux-function equations and Bernoulli relations for each species, together with Poisson's equation for the gravitational potential, complete the set of equations required to determine the equilibrium. These are straightforward to solve numerically. The two-fluid system, unlike the MHD system, is shown to be free of singularities. It is demonstrated analytically that there exists a class of incompressible MHD equilibria with magnetic field-aligned flow. A special subclass first identified by S. Chandrasekhar, in which the flow speed is everywhere equal to the local Alfvén speed, is compatible with virtually any azimuthally symmetric magnetic configuration. Potential applications of this analysis include extragalactic and stellar jets, accretion discs, and plasma structures associated with active late-type stars.     

Hydrodynamic instability of convectively unstable atmospheres in shear flow

Results are presented concerning the interaction between regions of convectively unstable fluid, bounded above and below by stable fluid, with a basic horizontal flow field, sheared in a vertical direction. The analysis is conveniently based on the definition of the mechanical energy flux associated with wave motion in a stratified compressible fluid, and enables bounds to be placed on the real and complex phase velocities of overstable modes, in addition to some general results on the net upward wave energy flux. It is shown that purely exponentially growing modes (with horizontal wavevectors spanwise to the shear) do not exist. A known sufficient condition for the stability of stable atmospheres is reproduced here with an interesting modification, and details of energy-flux discontinuities at certain singular points of the equations are given. The work is relevant to any astrophysical and geophysical situations in which convectively unstable regions and shear flows are likely to be together present, but the special motivation here is that of describing some aspects of the interaction between supergranular flow and granular convection.     

Instability of Zonal Flows in Rotating Spherical Shells: An Application to Jupiter

Measurements from the Galileo probe suggest that the zonal winds are deep rooted. Jupiter's high rotation rate makes it likely that the whole outer molecular H/He layer is involved in these long-lived jet flows. Assuming that the primary flows are geostrophic, and that the banded surface structure stretches right through the molecular H/He layer, we examine the conditions for such flows to be stable. As a first step, the linear stability of some prescribed banded zonal flows in a rotating spherical shell is explored. Incompressibility is assumed for simplicity, and the boundary condition is stress-free. We compare solutions for two aspect ratios, appropriate for the molecular H/He layers of Jupiter and Saturn, and two Ekman numbers (E=10⁻² and E=10⁻⁴). Convective and shear flow instabilities compete in our system. The convective instabilities are of the well-known columnar structure. Shear flow instabilities for the larger Ekman number are similar to the Taylor-Couette instability in rotating annuli. At the lower Ekman number, shear flow instabilities adopt a geostrophic character, assuming the form of rotating columns, similar to the convective instabilities. While the convective instability always sets in outside the tangent cylinder, shear instability can become unstable inside the tangent cylinder. If even a weak zonal flow is present inside the tangent cylinder, the flow is unstable to shear instability. This offers an explanation why the jovian zonal jet structure is much weaker at the higher latitudes that correspond to locations inside the tangent cylinder.     

A relativistic mixing-layer model for jets in low-luminosity radio galaxies

We present an analytical model for jets in Fanaroff & Riley Class I (FR I) radio galaxies, in which an initially laminar, relativistic flow is surrounded by a shear layer. We apply the appropriate conservation laws to constrain the jet parameters, starting the model where the radio emission is observed to brighten abruptly. We assume that the laminar flow fills the jet there and that pressure balance with the surroundings is maintained from that point outwards. Entrainment continuously injects new material into the jet and forms a shear layer, which contains material from both the environment and the laminar core. The shear layer expands rapidly with distance until finally the core disappears, and all of the material is mixed into the shear layer. Beyond this point, the shear layer expands in a cone and decelerates smoothly. We apply our model to the well-observed FR I source 3C 31 and show that there is a self-consistent solution. We derive the jet power, together with the variations of mass flux and entrainment rate with distance from the nucleus. The predicted variation of bulk velocity with distance in the outer parts of the jets is in good agreement with model fits to Very Large Array observations. Our prediction for the shape of the laminar core can be tested with higher-resolution imaging.     

Behavior of the Rayleigh-Taylor mode in a dusty plasma with rotational and shear flows

The stability of a dusty plasma with sheared rotational flows is investigated. Using the fluid model together with the Bayly nonmodal approach, the inhomogeneous partial differential equations governing short-wavelength perturbations at the center of a rotational flow field or vortex structure are obtained. The effects of flow eccentricity, strength of the flow shear, as well as concentration of dust grains on the stability of the perturbations are investigated numerically. It is found that flow shear can cause secondary Rayleigh-Taylor instability of a rotational flow.     

Magnetic and vertical shear instabilities in accretion discs

The stability properties of magnetized discs rotating with angular velocity Ω = Ω( s ,  z ), dependent on both the radial and the vertical coordinates s and z , are considered. Such a rotation law is adequate for many astrophysical discs (e.g., galactic and protoplanetary discs, as well as accretion discs in binaries). In general, the angular velocity depends on height, even in thin accretion discs. A linear stability analysis is performed in the Boussinesq approximation, and the dispersion relation is obtained for short-wavelength perturbations. Any dependence of Ω on z can destabilize the flow. This concerns primarily small-scale perturbations for which the stabilizing effect of buoyancy is strongly suppressed due to the energy exchange with the surrounding plasma. For a weak magnetic field, instability of discs is mainly associated with vertical shear, whilst for an intermediate magnetic field the magnetic shear instability, first considered by Chandrasekhar and Velikhov, is more efficient. This instability is caused by the radial shear which is typically much stronger than the vertical shear. Therefore the growth time for the magnetic shear instability is much shorter than for the vertical shear instability. A relatively strong magnetic field can suppress both these instabilities. The vertical shear instability could be the source of turbulence in protoplanetary discs, where the conductivity is low.     

Dynamical instability of laminar axisymmetric flows of ideal incompressible fluid

The instability of axisymmetric flows of ideal incompressible fluid with respect to infinitesimal perturbations with the nonconservation of angular momentum is investigated by numerically integrating the differential equations of hydrodynamics. The problem has been solved for two types of rotation profiles of an unperturbed flow: with zero and nonzero pressure gradients at the flow boundaries. Both rigid and free boundary conditions have been considered. The stability of axisymmetric flows with free boundaries is of great importance in disk accretion problems. Our calculations have revealed a crucial role of the flow pattern near the boundaries in the instability of the entire main flow. When the pressure gradient at the boundaries is zero, there is such a limiting scale of perturbations in azimuthal coordinate that longer-wavelength perturbations grow, while growing shorter-wavelength perturbations do not exit. In addition, for a fixed radial flow extent, there exists a nonzero minimum amplitude of the deviation of the angular velocity from the Keplerian one at which the instability vanishes. For a nonzero pressure gradient at the boundaries, the flow is unstable with respect to perturbations of any scale and at any small deviation of the angular velocity from the Keplerian one.     

磁弧剪切动力学和日珥的形成

日珥的观测显示存在着强的磁场剪切分量,本文研究了剪切在日珥形成中的积极作用。首先计算一个二维偶极势场当脚根受对称剪切后产生怎样的物理现象。作了三种情形的数值模拟。计算表明产生蘑菇状流动是个普遍规律,在某些条件下将形成弧顶凹陷。为了说明蘑菇流的物理起因,我们探讨了演化初期的线性渐近解。保留一阶量下导出了剪切速度W_z和磁场剪切分量B_x的解析解,对二维流动V_x,V_y求出了近似解:流的振幅随时间指数增长。对于弧顶凹陷,给于了定性的说明:磁浮力-(1/c)J_xB_x和形变阻尼力(1/c)J_zB_x之间的相互作用导致弧预变平凹陷,并把剪切区磁力线打开成为开场。弧顶凹陷是形成日珥的重要条件。冕弧加热量的略微减小,产生初始的热不稳定性,在凹陷处物质凝聚温度降低,弧脚根处因色球受蒸发而流入的物质沿管上升进入弧顶陷阱,加剧了热不稳定性,物质进一步变密,温度再降,最终形成了日珥。     

Generalized photoclinometry for Mariner 9

The present investigation develops a new theory for the photoclinometric determination of topography when the photometric function of the planetary surface (or that which corresponds to the mean optical depth of emergent scattered solar radiation from an optically thick planetary atmosphere) is not restricted beyond the expectation that it is a function of phase angle, angle of incidence, and angle of emergence. Several versions of such an operational theory, which differ according to the auxiliary conditions employed to achieve mathematical determinacy, together with several approaches to the numerical analysis, have been evolved. The differences in the numerical methods arise from a variable trade-off between computing speed and stability and computer storage requirements. Although the computer encoding process is not yet fully operational, a first result has been worked out for an early frame in the Mariner 9 mission in which the dust-laden atmosphere appears to exhibit standing-wave patterns. Provided the assumption of homologous departures from plane-parallel atmospheric configuration is valid, the photoclinometric implication is that laminar flow lines in the optically viewable dust layer undergo a near-sinusoidal rise and fall of about 40 to 50m. Regardless of assumption, the resulting surface is a rigorous mean-emission surface.     

Differential rotation and meridional flow of Arcturus

The spectroscopic variability of Arcturus hints at cyclic activity cycle and differential rotation. This could provide a test of current theoretical models of solar and stellar dynamos. To examine the applicability of current models of the flux transport dynamo to Arcturus, we compute a mean‐field model for its internal rotation, meridional flow, and convective heat transport in the convective envelope. We then compare the conditions for dynamo action with those on the Sun. We find solar‐type surface rotation with about 1/10th of the shear found on the solar surface. The rotation rate increases monotonically with depth at all latitudes throughout the whole convection zone. In the lower part of the convection zone the horizontal shear vanishes and there is a strong radial gradient. The surface meridional flow has maximum speed of 170 m/s and is directed towards the equator at high and towards the poles at low latitudes. Turbulent magnetic diffusivity is of the order 10¹⁵–10¹⁶ cm²/s. The conditions on Arcturus are not favorable for a circulation‐dominated dynamo (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reconnection in the Solar Corona: Role of the Kelvin–Helmholtz Instability

We consider the stability of current sheets where a normal component of the field is present. It is well known that reconnection in such systems progresses orders of magnitude too slow to explain observations, even when full kinetic models are used. We consider here a new possible mechanism for fast reconnection in such systems. We consider the effect of the possible presence of velocity shear that can drive the Kelvin–Helmholtz instability (KHI). The effect of the KHI is shown to convert shear flow into compression flow that drives reconnection. Three scaling effects can be discerned in the simulations. First, the reconnection rate is directly controlled by the driving mechanism which is provided by the KHI. The result of this new mechanism is that fast reconnection can be achieved even in absence of anomalous resistivity. Second, the effect of varying the initial sheared flow along the main magnetic field direction enhances the reconnection process. Finally, the reconnection rate is insensitive to the value of resistivity.     

Stability analyses of two-temperature radiative shocks: formulation, eigenfunctions, luminosity response and boundary conditions

We present a general formulation for stability analyses of radiative shocks with multiple cooling processes, longitudinal and transverse perturbations, and unequal electron and ion temperatures. Using the accretion shocks of magnetic cataclysmic variables as an illustrative application, we investigate the shock instabilities by examining the eigenfunctions of the perturbed hydrodynamic variables. We also investigate the effects of varying the condition at the lower boundary of the post-shock flow from a zero-velocity fixed wall to several alternative types of boundaries involving the perturbed hydrodynamic variables, and the variations of the emission from the post-shock flow under different modes of oscillations. We found that the stability properties for flow with a stationary-wall lower boundary are not significantly affected by perturbing the lower boundary condition, and they are determined mainly by the energy-transport processes. Moreover, there is no obvious correlation between the amplitude or phase of the luminosity response and the stability properties of the system. Stability of the system can, however, be modified in the presence of transverse perturbation. The luminosity responses are also altered by transverse perturbation.     

彗木相撞中的惯性引力波

苏梅克-列维9号彗星(SL9)与木星相撞后，在木星上观测到的以常速度(～450m／s)向外扩展的圆环意味着这是碰撞在木星大气中引起的线性波动．我们选取：非旋转、无粘性、密度分层、不可压缩的木星大气模型，而且木星大气以水平速度U=b az运动；给出初始扰动压力P(r；0)作为碰撞的初始条件，用流体力学方程组求解了彗木相撞中的惯性引力波．结果表明：当木星大气以速度U=U0(～170m／s)运动时，彗星碎片的大部分能量都用来产生内波，同时还得到彗星碎片的撞击深度H与水平相速Vp的关系式．当木星大气以速度为U=b az运动时，木星大气的扰动能量不再是在动能和势能间均分。     

The stability of non-separable barotropic and baroclinic shear flows

The linear stability with respect to three-dimensional perturbations of unbounded barotropic and baroclinic shear flows depending linearly on both transverse coordinates is studied. The Boussinesq approximation is used, but the usual hydrostatic approximation in the vertical is relaxed. Dissipation effects are ignored. A baroclinic flow can always be destabilized by sufficiently large horizontal anticyclonic shear. The results are relevant for the stability of differential rotation in radiative stars and accretion disks.     

Local instabilities of Alfvén waves in high speed streams

A two fluid stability analysis of an inhomogeneous solar wind plasma leads to prediction of possible instabilities of both Alfvénic and magnetoacoustic waves driven by local velocity gradients. The waves predicted to be possibly unstable have short wavelengths in comparison with the length scale of the gradients and, with different thresholds for the value of velocity shear, may have different directions of propagation with respect to the background magnetic field.We have performed a detailed study, based on Pioneer 6 magnetic and plasma data relative to several high speed streams in the solar wind, on the direction of propagation of the transverse waves which are found within the streams and on their association with velocity gradients within the stream structure. The analysis leads to the conclusion that the observed Alfvén waves may be consistent with the hypothesis of local generation through one of the above mentioned instabilities where velocity shear leads in fact to excitation of incompressible waves in directions almost parallel to the magnetic field.     

Active galactic nuclei flow velocities and the highest energy cosmic rays

The dependence of the maximum energy cosmic rays can reach via diffusive shock acceleration in AGN jets on flow speeds is discussed. It is shown that in highly inclined termination shocks where the speed of the de Hoffman-Teller frame is crucial, a good independent knowledge of the jet speed is required to properly assess the extent of the cosmic ray spectrum.     

The stability of 2D current sheet models of prominences

A necessary and sufficient condition for the ideal magnetohydrodynamic stability of 2D current sheet models of prominences suspended in a potential coronal field with line-tying is developed using the energy method. This condition takes the form of two simple coupled second-order differential equations which may be integrated along a field line to find marginal stability. The two conditions (85) and (86) of Anzer (1969) are now only sufficient for stability. Two current sheet models are investigated and it is shown that for a potential coronal field allowing perturbed electric currents to flow, line-tying can completely stabilize the equilibria for realistic heights.     

A Comparative Study of Jovian Cyclonic Features from a Six-Year (1994-2000) Survey

This work presents a six-year study aimed at characterizing the morphology and properties of the atmospheric features present in jovian cyclonic regions. It complements our previous analysis for the same period on the anticyclonic vortices (Morales-Juberias et al. 2002, Icarus 157, 76-90). The main difference between cyclonic and anticyclonic regions in Jupiter is that a variety of organized morphologies are present in the cyclonic areas, although they can be grouped consistently into five different types: filamentary turbulence related to the highest speed jets, organized folded filamentary regions, elongated areas with contours closed by a ribbon-like feature, discrete, closed brown cyclones (“barges”), and peculiar transient structures such as short wave trains and cyclonic cells. We present data on their color contrast, size, aspect ratio, distribution, lifetimes, relation to the jet system and to the anticyclones, and motions (global and internal to the features). Most cyclonic features show a rapid evolution, compared to the anticyclones, and tend to be dispersed zonally although some survive for a few years. We used the barges that are the most representative, long-lived, and extended type of cyclonic features to show that there exists a linear relationship between their relative velocity and the mean zonal flow speed, similar to that found in our previous work on the anticyclones. There is also some evidence that the drift rate of barges is related to the planetary minus flow vorticity gradient.