Spot activity on HD 89546 (FG UMa) from long‐term photometry

We present the analysis of 20 years of time‐series BV photometry of the SB1 RS CVn binary HD 89546. The system's yearly mean V brightness, the B – V color index, the photometric period, and the light curve amplitude all show clear cyclic variability with an ≈9‐year time scale. We also find some evidence for brightness variability on a time scale longer than the 20‐year time span of our observations, perhaps indicating a longer cycle analogous to the solar Gleissberg cycle. We estimate the unspotted V magnitude of HD 89546 to be 7.^m154, which is ≈0.^m2 brighter than the observed maximum brightness. Spot modelling of the system shows that spot temperature variations affect the observed B – V color as well as the V brightness. Two active longitudes are observed, centered around 180° and 360° longitude on the G9 III primary, each covering a longitude range of 120°. Furthermore, two inactive longitude zones are seen spanning only 60° between the two active longitudes. The longitudinal distribution of the spots exhibits no strong cyclic variability but does show rapid jumps of 120° that look like the flip‐flop phenomenon. We estimate the differential rotation coefficient of the star as k = 0.086 by considering the range of observed photometric period variations and assumed latitudinal spot variations over 45° (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gregor@night: The future high‐resolution stellar spectrograph for the GREGOR solar telescope

We describe the future night‐time spectrograph for the GREGOR solar telescope and present its science core projects. The spectrograph provides a 3‐pixel resolution of up to R = 87 000 in 45 échelle orders covering the wavelength range 390‐900 nm with three grating settings. An iodine cell can be used for high‐precision radial velocity work in the 500‐630 nm range. The operation of the spectrograph and the telescope will be fully automated without the presence of humans during night‐time and will be based on the successful STELLA control system. Future upgrades include a second optical camera for even higher spectral resolution, a Stokes‐V polarimeter and a link to the laser‐frequency comb at the Vacuum Tower Telescope. The night‐time core projects are a study of the angular‐momentum evolution of “The Sun in Time” and a continuation of our long‐term Doppler imaging of active stars (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rotational and magnetic instability in the diffusive tachocline

In this article we study the linear instability of the two-dimensional strongly stratified model for global MHD in the diffusive solar tachocline. Gilman and Fox [Gilman, P.A. and Fox, P., Joint instability of the latitudinal differential rotation and toroidal magnetic fields below the solar convection zone. Astrophys. J., 1997, 484, 439–454] showed that for ideal MHD, the observed surface differential rotation becomes more unstable than is predicted by Watson's [Watson, M., Shear instability of differential rotation in stars. Geophys. Astrophys. Fluid Dyn., 1981, 16, 285–298] nonmagnetic analysis. They showed that the solar differential rotation is unstable for essentially all reasonable values of the differential rotation in the presence of an antisymmetric toroidal field. They found that for the broad field case B _φ～sinθcosθ, θ being the co-latitude, instability occurs only for the azimuthal m?=?1 mode, and concluded that modes which are symmetric (meridional flow in the same direction) about the equator onset at lower field strengths than the antisymmetric modes. We study the effect of viscosity and magnetic diffusivity in the strongly stably stratified case where diffusion is primarily along the level surfaces. We show that antisymmetric modes are now strongly preferred over symmetric modes, and that diffusion can sometimes be destabilising. Even solid body rotation can be destabilised through the action of magnetic field. In addition, we show that when diffusion is present, instability can occur when the longitudinal wavenumber m?=?2.     

Statistical dynamics of internal gravity waves-turbulence

Abstract

Numerical simulations of internal gravity waves-turbulence are carried out for the inviscid, viscous and forced-dissipative two-dimensional primitive equations using the spectral method. Some of the results are compared with the predictions of the eddy damped quasi-normal Markovian (EDQNM) closure for internal waves of Carnevale and Frederiksen, generalized for periodic boundary conditions and possible random forcing and dissipation. The EDQNM reduces to the Boltzman equation of resonant interaction theory in the continuum space limit and as the forcing and dissipation vanish. However, the limit is singular in the sense that as well as conserving total energy, E, and total cross-correlation between the vorticity and buoyancy fields, C, an additional conservation law, viz. z-momentum, P_z , occurs in the limit. This means that the resonant interaction equilibrium (RIE) solution of the Boltzmann equation differs from the statistical mechanical equilibrium (SME) solution of the EDQNM closure.

The statistical stability of the SME and RIE spectra for the primitive equations is tested by integrating the inviscid equations using initial realizations of these spectra with random phases. It is found that E and C are accurately conserved while P_z undergoes large amplitude variations. The approach to equilibrium of initial disequilibrium spectra is monitored by examining the evolution of the entropy. The increase and asymptotic approach to a constant value corresponding to complete chaos is consistent with the behaviour predicted by the EDQNM closure.

For the viscous decay and forced-dissipative experiments, the behaviour of the entropy is also consistent with that predicted by the EDQNM closure. There is approximate equipartition of potential and total kinetic energies throughout the integrations from initial conditions having equal potential and total kinetic energies and as well equal vertical and horizontal energies, but as expected, the ratio of horizontal to vertical kinetic energy increases with time to a value greater than unity.

With Laplacian viscous dissipation and thermal diffusivity, the statistical steady states produced in the forced-dissipative experiments have k^?3 power laws for k≧7. A comparison with the power laws for kinetic energy and passive scalar variance produced in a numerical simulation of the two-dimensional passive scalar problem is also presented.     

Non-linear marginal convection in a rotating magnetic system

Abstract

An inviscid, electrically conducting fluid is contained between two rigid horizontal planes and bounded laterally by two vertical walls. The fluid is permeated by a strong uniform horizontal magnetic field aligned with the side wall boundaries and the entire system rotates rapidly about a vertical axis. The ratio of the magnitudes of the Lorentz and Coriolis forces is characterized by the Elsasser number, A, and the ratio of the thermal and magnetic diffusivities, q. By heating the fluid from below and cooling from above the system becomes unstable to small perturbations when the adverse density gradient as measured by the Rayleigh number, R, is sufficiently large.

With the viscosity ignored the geostrophic velocity, U, which is aligned with the applied magnetic field, is independent of the coordinate parallel to the rotation axis but is an arbitrary function of the horizontal cross-stream coordinate. At the onset of instability the value of U taken ensures that Taylor's condition is met. Specifically the Lorentz force, which results from marginal convection must not cause any acceleration of the geostrophic flow. It is found that the critical Rayleigh number characterising the onset of instability is generally close to the corresponding value for the usual linear problem, in which Taylor's condition is ignored and U is chosen to vanish. Significant differences can occur when q is small owing to a complicated flow structure. There is a central interior region in which the local magnetic Reynolds number, R_m , based on U is small of order q and on exterior region in which R_m is of order unity.     

Convection in a rotating magnetic system and Taylor's constraint

Abstract

A system is considered in which electrically conducting fluid is contained between two rigid horizontal planes and bounded laterally by a circular cylinder. The fluid is permeated by a strong azimuthal magnetic field. The strength of the field increases linearly with distance from the vertical axis of the cylinder, about which the entire system rotates rapidly. An unstable temperature gradient is maintained by heating the fluid from below and cooling from above. When viscosity and inertia are neglected, an arbitrary geostrophic velocity, which is aligned with the applied azimuthal magnetic field and independent of the axial coordinate, can be superimposed on the basic axisymmetric state. In this inviscid limit, the geostrophic velocity which occurs at the onset of convection is such that the net torque on geostrophic cylinders vanishes (Taylor's condition). The mathematical problem which describes the ensuing marginal convection is nonlinear, and was discussed previously for the planar case by Soward (1986). Here new features are isolated which result from the cylindrical geometry. New asymptotic solutions are derived valid when Taylor's condition is relaxed to include viscous effects.     

On inviscid stratified parallel flows varying in two directions

Abstract

A stratified parallel flow in a potential force field is investigated. The density, the velocity, and the potential field of the flow are allowed to vary in two directions. Three sufficient conditions are derived for guaranteed stability of the flow. Two are the classical stability conditions in their respective directions. The third, measured by a newly defined Richardson number, is a result of the shear interaction and the pressure balance condition for stability. Like the classical Richardson number which is always positive preceding stability, this new number acts as a constraint on the other two stability conditions. In addition to the above stability criteria, a semi-ellipse theorem is derived for the present flow.     

Thermal convection in differentially rotating systems

Abstract

The onset of convection in a cylindrical fluid annulus is analyzed in the case when the cylindrical walls are rotating differentially, a temperature gradient in the radial direction is applied, and the centrifugal force dominates over gravity. The small gap approximation is used and no-slip conditions on the cylindrical walls are assumed. It is found that over a considerable range of the parameter space either convection rolls aligned with the axis of rotation or rolls in the perpendicular (azimuthal) direction are preferred. It is shown that by a suitable redefinition of parameters, results for finite amplitude Taylor vortices and for convection rolls in the presence of shear can be applied to the present problem. Weakly nonlinear results for transverse rolls in a Couette flow indicate the possibility of subcritical bifurcation for Prandtl numbers P less than 0.82. Heat and momentum transports are derived as functions of P and the problem of interaction between transverse and longitudinal rolls is considered. The relevance of the analysis for problems of convection in planetary and stellar atmospheres is briefly discussed.     

中中新世以来阿尔金断裂走滑未造成柴达木盆地整体旋转

通过柴达木盆地南八仙剖面磁性地层学研究,建立了部分上油砂山组磁极性序列,认为该剖面时代为7.5~9.0 Ma。从320块样品的古地磁数据分析,揭示了一组高温特征剩磁分量,在95%置信度下通过倒转检验(B级),说明这组高温分量很可能代表岩石形成时的原生剩磁,其特征剩磁方向为:地理坐标下为D_g=358.5°, I_g=40.5°, k=28.5,α₉₅=4.2,层面坐标下为D_s=1.0°, I_s=41.5°, k=34.0,α₉₅=3.8;相应的极位置为λ_p=75.9°N, φ_p=270.5°E, d_p=2.8°, d_m=4.6°。通过与同时代柴达木盆地及邻区的古地磁极对比,说明中中新世以来柴达木地块整体上没有经历明显旋转运动,阿尔金断裂活动致使肃北等毗邻断裂带地区发生了构造旋转。     

宏-细观结合的砂土单剪试验非共轴特性分析

针对传统本构理论无法描述土体单剪试验非共轴变形的不足,采用非共轴修正模型进行改进。模型基于材料状态相关临界状态理论,采用宏-细观结合的方法,将1个新的各向异性状态变量引入本构模型来描述砂土的各向异性。考虑细观组构张量和应力张量的几何关系的变化,模型可以描述砂土在主应力轴旋转条件下材料状态的变化,材料状态变化直接导致模型的硬化规律和剪胀性发生变化,因此,模型可以描述该条件下原生向异性对砂土变形的影响。引入非共轴理论对本构模型进行修正,建立了三维非共轴各向异性模型。单剪试验的加载条件会造成主应力轴相对土体沉积面发生旋转,修正模型不但能够描述砂土在主应力轴旋转条件下其原生各向异性对变形的影响,而且可以描述主应力轴旋转造成的应力诱发各向异性对土体变形的影响,因此,该模型能够对整个单剪试验的变形规律进行描述,而且物理意义清晰。通过铝棒堆积体和Toyoura砂单剪试验验证表明,非共轴修正各向异性模型能对单剪试验的整个变形过程进行较好的模拟。