Instability of planetary flows using Riemann curvature: a numerical study

ABSTRACT

The instability of ideal non-divergent zonal flows on the sphere is determined numerically by the instability criterion of Arnold (Ann. Inst. Fourier 1966, 16, 319) for the sectional curvature. Zonal flows are unstable for all perturbations besides for a small set which are in approximate resonance. The planetary rotation is stable and the presence of rotation reduces the instability of perturbations.     

母船垂荡导致ROV脐带缆参量共振的研究

研究有缆遥控潜水器(Remote Operated Vehicles)的脐带缆受到轴向激励所产生的大幅横向振动,即参量共振.ROV脐带缆的参激现象发生会影响ROV的安全性.针对ROV脐带缆的结构特性,推导出其在轴向激励力下的非线性振动方程.运用希尔无穷行列式的方法分析脐带缆的参量不稳定性.以稳定性图为基准分析脐带缆在多...     

The azimuthal magnetorotational instability (AMRI)

We consider the flow of an electrically conducting fluid between differentially rotating cylinders, in the presence of an externally imposed current-free toroidal field B₀(R_in/R) ê _ϕ . It is known that the classical, axisymmetric magnetorotational instability does not exist for such a purely toroidal imposed field.We show here that a nonaxisymmetric magnetorotational instability does exist, having properties very similar to the axisymmetric magnetorotational instability in the presence of an axial field. In the nonlinear regime the magnetic energy of the perturbances is shifted (in the sense of an inverse cascade) to the axisymmetric mode rather than to the modes with m > 1. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear simulations of magnetic instabilities in stellar radiation zones: The role of rotation and shear

Using the 3-dimensional ASH code, we have studied numerically the instabilities that occur in stellar radiation zones in presence of large-scale magnetic fields, rotation and large-scale shear. We confirm that some configurations are linearly unstable, as predicted by Tayler and collaborators, and we determine the saturation level of the instability. We find that rotation modifies the peak of the most unstable wave number of the poloidal instability but not its growth rate as much as in the case of the m = 1 toroidal instability for which it is changed to σ = /Ω. Further in the case with rotation and shear, we found no sign of the dynamo mechanism suggested recently by Spruit even though we possess the essential ingredients (Tayler's m = 1 instability and a large scale shear) supposedly at work. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The generation of non aspect sensitive plasma density irregularities by field aligned drifts in the lower ionosphere

A theory of the generation of plasma density irregularities with virtually no aspect sensitivity, in the lower ionosphere at high latitudes, by electron drifts aligned with the geomagnetic field, is presented. The theory is developed through fluid equations in which the destabilising mechanism involves positive feedback from electron collisional heating. When field aligned electron drift speeds exceed a few km s^–1, this effect destabilises waves with wavelengths in excess of a few tens of metres in the lower E-region, where collisional effects are sufficiently large. Furthermore, the threshold conditions are almost independent of the wave propagation direction and the unstable waves propagate at speeds well below the ion acoustic speed. The role that this new instability may play in recent radar backscatter observations of short scale irregularities propagating in directions close to that of the geomagnetic field, in the lower E-region is also considered.     

Relativistic anisotropic pair plasmas

The properties of waves able to propagate in a relativistic pair plasma are at the basis of the interpretation of several astrophysical observations. For instance, they are invoked in relation to radio emission processes in pulsar magnetospheres and to radiation mechanisms for relativistic radio jets. In such physical environments, pair plasma particles probably have relativistic, or even ultrarelativistic, temperatures. Besides, the presence of an extremely strong magnetic field in the emission region constrains the particles to one-dimensional motion: all the charged particles strictly move along magnetic field lines.
We take anisotropic effects and relativistic effects into account by choosing one-dimensional relativistic Jűttner–Synge distribution functions to characterize the distribution of electrons and/or positrons in a relativistic, anisotropic pair plasma. The dielectric tensor, from which the dispersion relation associated with plane wave perturbations of such a pair plasma is derived, involves specific coefficients that depend on the distribution function of particles. A precise determination of these coefficients, using the relativistic one-dimensional Jűttner–Synge distribution function, allows us to obtain the appropriate dispersion relation. The properties of waves able to propagate in anisotropic relativistic pair plasmas are deduced from this dispersion relation. The conditions in which a beam and a plasma, both ultrarelativistic, may interact and trigger off a two-stream instability are obtained from this same dispersion relation. Two astrophysical applications are discussed.     

Linear and non-linear theory of a parametric instability of hydrodynamic warps in Keplerian discs

We consider the stability of warping modes in Keplerian discs. We find them to be parametrically unstable using two lines of attack, one based on three-mode couplings and the other on Floquet theory. We confirm the existence of the instability and investigate its non-linear development in three dimensions, via numerical experiment. The most rapidly growing non-axisymmetric disturbances are the most nearly axisymmetric (low- m ) ones. Finally, we offer a simple, somewhat speculative model for the interaction of the parametric instability with the warp. We apply this model to the masing disc in NGC 4258 and show that, provided the warp is not forced too strongly, parametric instability can fix the amplitude of the warp.     

The population of faint transients in the Galactic Centre

BeppoSAX has detected a population of faint transient X-ray sources in the Galactic Centre. I show that a simple irradiated disc picture gives a consistent fit to the properties of this population, and that it probably consists of low-mass X-ray binaries (LMXBs) that have evolved beyond their minimum orbital periods of ∼80 min. Since all post-minimum systems are transient, and neutron star LMXBs are more common than black hole LMXBs in the Galaxy, the majority of these systems should contain neutron stars, as observed. This picture predicts that the Galactic Centre transients should have orbital periods in the range ∼80–120 min, and that most of them should repeat in the next few years. In this case, the total number of post-minimum transients in the Galaxy would be considerably smaller than the usual estimates of its total LMXB population. I discuss possible reasons for this.     

A spectroscopic study of V603 Aquilae: stellar parameters and continuumline variations

A time-resolved spectroscopic study of V603 Aql (Nova Aquilae 1918) is presented. An orbital period of P _orb=01385±00002, consistent with previous results, and a radial velocity semi-amplitude of K =20±3 km s¹ are obtained from the radial velocity variations of the H emission line. Similar K values are also found in H , H , and He  i emission lines. Using the measured FWHM of the H line and assuming that the derived semi-amplitude is that of the white dwarf, we deduce a most likely mass ratio of q =0.24±0.05 and stellar masses of M ₂=0.29±0.04 M and M ₁=1.2±0.2 M for the secondary and primary (the white dwarf) star, respectively. The dynamical solution also indicates a very low orbital inclination, i =13°±2°. We find that the continuum and line variations are modulated with both the positive and the negative superhump periods, indicating that they arise from similar regions of the accretion disc. Moreover, we find, for the first time from spectroscopy, evidence of negative superhumps in addition to the positive superhumps. Positive superhumps are explained within the disc instability model as caused by an eccentric disc surrounding the white dwarf, which is precessing (apsidal advance) because of tidal instabilities, causing the observed positive superhumps. A nodal precession in the accretion disc is currently believed to be the cause of the observed negative superhumps. The low value of q is consistent with the expected value for systems that show superhumps, in accordance with the eccentric disc model. We find no evidence of periodicity associated with the spin period.