On Motions Near the Lagrange Equilibrium Point L 4 in the Case of Routh's Critical Mass Ratio

We deal with the planar restricted circular problem of three bodies. We study trajectories in a small neighborhood of the Lagrange equilibrium point L ₄ when mass ratio is close to Routh's value. In particular, we show that the case of proper degeneracy takes place and for most initial conditions trajectories are conditionally-periodic. We obtain an approximate representation of families of periodic solution emanating from the equilibrium point L ₄. We also show that in the case of instability of L ₄ the trajectories starting in a vicinity of L ₄ remain in a finite domain forever. We give an upper bound of this domain. To carry out our investigation, we analyze the dynamics of a general Hamiltonian system with two degrees of freedom in the case of 1 : 1 resonance in detail.This revised version was published online in October 2005 with corrections to the Cover Date.     

Validating the Flash Code: Vortex-Dominated Flows

As a component of the Flash Center’s validation program, we compare FLASH simulation results with experimental results from Los Alamos National Laboratory. The flow of interest involves the lateral interaction between a planar M _a = 1.2 shock wave with a cylinder of gaseous sulfur hexafluoride (SF₆) in air, and in particular the development of primary and secondary instabilities after the passage of the shock. While the overall evolution of the flow is comparable in the simulations and experiments, small-scale features are difficult to match. We focus on the sensitivity of numerical results to simulation parameters.     

A numerical solution of the dynamical instability of a thin accretion torus

We consider the non-axisymmetric, dynamical instability of a thin accretion torus with a non-zero shift of corotation radius. By numerical method we evaluated the wave number dependence of the linear rate of growth of instability and the co-rotation shift. The rate of growth is only slightly affected by the non-zero co-rotation shift, while the dispersion relation in the case of a shift is the same as that of the linear KdV equation. This shows that the “planet-like” solution found in numerical simulations of thin tori is very probably analogous to the soliton solution of the KdV equation.     

Weibel Turbulence in Laboratory Experiments and GRB/SN Shocks

It has recently been realized that the Weibel instability plays a major role in the formation and dynamics of astrophysical shocks of gamma-ray bursts and supernovae. Thanks to technological advances in the recent years, experimental studies of the Weibel instability are now possible in laser-plasma interaction devices. We, thus, have a unique opportunity to model and study astrophysical conditions in laboratory experiments – a key goal of the Laboratory Astrophysics program. Here we briefly review the theory of strong non-magnetized collisionless GRB and SN shocks, emphasizing the crucial role of the Weibel instability and discuss the properties of radiation emitted by (isotropic) electrons moving through the Weibel-generated magnetic fields, which is referred to as the jitter radiation. We demonstrate that the jitter radiation field is anisotropic with respect to the direction of the Weibel current filaments and that its spectral and polarization characteristics are determined by microphysical plasma parameters. We stress that the spectral analysis can be used for accurate diagnostics of the plasma conditions in laboratory experiments and in astrophysical GRB and SN shocks.     

Phenomenological Theory of the Photoevaporation Front Instability

The dynamics of photoevaporated molecular clouds is determined by the ablative pressure acting on the ionization front. An important step in the understanding of the ensuing motion is to develop the linear stability theory for an initially flat front. Despite the simplifications introduced by linearization, the problem remains quite complex and still draws a lot of attention. The complexity is related to the large number of effects that have to be included in the analysis: acceleration of the front, possible temporal variation of the intensity of the ionizing radiation, the tilt of the radiation flux with respect to the normal to the surface, and partial absorption of the incident radiation in the ablated material. In this paper, we describe a model where all these effects can be taken into account simultaneously, and a relatively simple and universal dispersion relation can be obtained. The proposed phenomenological model may prove to be a helpful tool in assessing the feasibility of the laboratory experiments directed towards scaled modeling of astrophysical phenomena. PACS Numbers: 98.38.Dq, 98.38.Hv, 52.38.Mf, 5257.FG, 52.72.+v     

EFFECT OF PERPENDICULAR A.C. ELECTRIC FIELD ON THE OBLIQUE WHISTLER MODE INSTABILITY IN THE EARTH’S MAGNETOSPHERE

The elements of dielectric tensor and dispersion relation for obliquely propagating whistler waves with finite in an infinite magnetoplasma are obtained for a kappa distribution in the presence of perpendicular a.c. electric field. Integrals and modified plasma dispersion functions are reduced in power series form. Numerical calculations have been performed to obtain temporal growth rate and real frequencies of the plasma waves for magnetospheric plasma, using linear theory of dispersion relation. The effect and modification introduced by the perpendicular a.c. electric field on the temporal growth rates, real frequencies and resonance condition are discussed for kappa and Maxwellian distributions. Our results and their interpretation are compared with known whistler observations obtained by ground-based techniques and satellite observations.     

Instabilities of the tidally induced bottom boundary layer in the rotating frame and their mixing effect

To investigate the stability of the bottom boundary layer induced by tidal flow (oscillating flow) in a rotating frame, numerical experiments have been carried out with a two-dimensional non-hydrostatic model. Under homogeneous conditions three types of instability are found depending on the temporal Rossby number Ro_t, the ratio of the inertial and tidal periods. When Ro_t < 0.9 (subinertial range), the Ekman type I instability occurs because the effect of rotation is dominant though the flow becomes more stable than the steady Ekman flow with increasing Ro_t. When Ro_t > 1.1 (superinertial range), the Stokes layer instability is excited as in the absence of rotation. When 0.9 < Ro_t < 1.1 (near-inertial range), the Ekman type I or type II instability appears as in the steady Ekman layer. Being much thickened (100 m), the boundary layer becomes unstable even if tidal flow is weak (5 cm/s). The large vertical scale enhances the contribution of the Coriolis effect to destabilization, so that the type II instability tends to appear when Ro_t > 1.0. However, when Ro_t < 1.0, the type I instability rather than the type II instability appears because the downward phase change of tidal flow acts to suppress the latter. To evaluate the mixing effect of these instabilities, some experiments have been executed under a weak stratification peculiar to polar oceans (the buoyancy frequency N²  10⁻⁶ s⁻²). Strong mixing occurs in the subinertial and near-inertial ranges such that tracer is well mixed in the boundary layer and an apparent diffusivity there is evaluated at 150–300 cm²/s. This suggests that effective mixing due to these instabilities may play an important role in determining the properties of dense shelf water in the polar regions.     

黄土高原一次β中尺度大暴雨特征及成因分析

利用NCEP／NCAR逐日6h分析资料和常规观测资料,分析了2011年2月25日一28日山西连续降雪天气过程（以下简称2．25降雪）。①2．25降雪过程经历了三个阶段：2月25日为回流降雪阶段,26日一27日为倒槽冷锋与回流降雪共同影响降雪阶段,28日为低空切变线影响降雪阶段。②2．25降雪过程涵盖了华北地区大到暴雪的三个类型：回流类降雪、倒槽冷锋类降雪、低空切变线类降雪。③通过温湿场分析得出,对于低空切变线类降雪,对流层中层的湿核对降雪的开始有一定的指示意义。降雪未开始之前对流层中层有湿核,随着时间的推移,湿核向低层扩展,整个对流层中低层变为高湿区,降雪开始。当对流层中层变为干区,并向低层扩展,降雪过程结束。对于回流类降雪,低层回流对回流降雪起到冷垫的作用。④通过涡度场分析得出,对流层低层的负绝对涡度中心对其东侧的降水有指示意义,如果其东侧对流层低层配合有正涡度核,降雪强度较大,维持时间较长。⑤地面层出现的负绝对涡度中心说明近地面层有小高压系统的存在,这是因为低层回流冷垫作用形成的孤立小高压体。⑥28日降雪维持机制是条件性对称不稳定。     

一次缓慢东移的黄河气旋暴雨的诊断分析

利用NCEP/NCAR再分析资料和常规气象资料,对2001年6月28-29日发生在河南的一次黄河气旋暴雨过程进行了诊断分析。结果表明：黄河气旋的稳定少动是造成这次暴雨的直接原因,高层辐散与中层正涡度平流对黄河气旋形成和发展起了重要作用。这次过程的水汽主要来自副高东南侧的海上,孟加拉湾的水汽也有一定的贡献。暴雨区的中低层对称不稳定的存在,导致上升运动和水汽输送的加强,造成降水的增幅。     

湿位涡诊断分析在河南台风远距离降水中的应用

应用湿位涡理论,分析了两个发生在河南的台风远距离降水个例,讨论了湿位涡与台风远距离降水形成的关系。结果表明：两个个例中,河南具有有利于强降水发生的湿位涡特征;异常暴雨的发展与湿位涡的变化有很好的对应关系：湿位涡的异常区域对应着最强的降水,对流层高层ζMPV1（湿位涡的垂直分量）正值区与低层ζMPV2负值区相互作用,即高层下滑的干冷空气与中低层由东南急流输送的高温高湿空气交汇,容易储存和释放湿对流不稳定能量,有利于强降水产生。湿位涡理论在河南台风远距离降水诊断中有很好的应用前景。