The angular momentum transport in rotating turbulent convection

The angular momentum transport in rotating turbulent convection is simulated with the NIRVANA code for Taylor numbers up to 10⁶. The box consists of an unstable layer embedded in two stable overshoot layers. We find the expected anisotropies in the rotating anisotropic turbulence field: 〈u^′2_r〉 exceeds 〈u^′2_ϕ〉, and 〈u^′2_ϕ〉 exceeds 〈u^′2_θ〉. The resulting radial angular momentum transport is directed inwards and peaks in the middle of the convective layer. The resulting latitudinal angular momentum transport is equatorwards, peaks at the surface and is highly concentrated to the equatorial region. Apart from a factor of 2–3 the total amplitudes of the cross‐correlations are of the same order of magnitude. In the lower overshoot region (‘tachocline’) the cross‐correlations are negative. It is argued that the concentration of the latitudinal angular momentum transport towards the surface and towards the equator does not too strongly reduce its potential to produce rotation laws with accelerated equators. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Helical magnetorotational instability of Taylor‐Couette flows in the Rayleigh limit and for quasi‐Kepler rotation

The magnetorotational instability (MRI) of differential rotation under the simultaneous presence of axial and azimuthal components of the (current‐free) magnetic field is considered. For rotation with uniform specific angular momentum the MHD equations for axisymmetric perturbations are solved in a local short‐wave approximation. All the solutions are overstable for B_z · B_ϕ ≠ 0 with eigenfrequencies approaching the viscous frequency. For more flat rotation laws the results of the local approximation do not comply with the results of a global calculation of the MHD instability of Taylor‐Couette flows between rotating cylinders. – With B_ϕ and B_z of the same order the traveling‐mode solutions are also prefered for flat rotation laws such as the quasi‐Kepler rotation. For magnetic Prandtl number Pm → 0 they scale with the Reynolds number of rotation rather than with the magnetic Reynolds number (as for standard MRI) so that they can easily be realized in MHD laboratory experiments. – Regarding the nonaxisymmetric modes one finds a remarkable influence of the ratio B_ϕ/B_z only for the extrema. For B_ϕ ≫ B_z and for not too small Pm the nonaxisymmetric modes dominate the traveling axisymmetric modes. For standard MRI with B_z ≫ B_ϕ, however, the critical Reynolds numbers of the nonaxisymmetric modes exceed the values for the axisymmetric modes by many orders so that they are never prefered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Über turbulente Bewegungen,die von Temperaturschwankungen hervorgerufen werden – eine kritische Betrachtung zur Boussinesq-Approximation

This paper deals with fluctuating motions which are caused by a given stochastical temperature field acting in a gas with gravitation and T¯ = const. It results that the often used BOUSSINESQ approximation much underestimates the horizontal motions in case wide-spread temperature fluctuations occur. For sufficiently large scales the horizontal motion exceeds the vertical ones even in the case of the temperature field fluctuating completely isotropically. Scales of 1000 km and 1 day in the Earth atmosphere lead to the observed value u′_horiz/|u′_vertic ≈︁ 10. Finally besides the relation between density correlation and pressure correlation we determine the expression for the turbulent mass transport vanishing with the molecular viscosity.     

Nonlinear simulations of magnetic Taylor‐Couette flow with currentfree helical magnetic fields

Themagnetorotational instability (MRI) in cylindrical Taylor‐Couette flow with external helical magnetic field is simulated for infinite and finite aspect ratios. We solve the MHD equations in their small Prandtl number limit and confirm with timedependent nonlinear simulations that the additional toroidal component of the magnetic field reduces the critical Reynolds number from O (10⁶) (axial field only) to O (10³) for liquid metals with their small magnetic Prandtl number. Computing the saturated state we obtain velocity amplitudes which help designing proper experimental setups. Experiments with liquid gallium require axial field ∼50 Gauss and axial current ∼4 kA for the toroidal field. It is sufficient that the vertical velocity u_z of the flow can be measured with a precision of 0.1 mm/s.We also show that the endplates enclosing the cylinders do not destroy the traveling wave instability which can be observed as presented in earlier studies. For TC containers without and with endplates the angular momentum transport of the MRI instability is shown as to be outwards. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Third-order Jupiter — Saturn planetary theory

The construction of a third order J-S theory is presented. The Hori theory of planetary perturbations is employed. No Critical J-S terms due to the 2:5 commensurabilities and its multiples exist, when we take into account the periodic terms of order 0, 1, 2 with respect to the eccentricity- inclination. In this case the Lie series transformation degenerates and is meaningless. The J-S equations of motion for secular perturbations are solved when we neglect in our treatment, the Poisson terms of degree > 2 in the Poincaré canonical variables H _u , K _u , P _u Q _u (u = 1, 2). The Jacobi-Radau referential is adopted, and the theory is expressed in terms of the canonical variables of H. Poincaré.Now at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, U.S.A.     

Nonhelical mean‐field dynamos in a sheared turbulence

Mechanisms of nonhelical large‐scale dynamos (shear‐current dynamo and effect of homogeneous kinetic helicity fluctuations with zero mean) in a homogeneous turbulence with large‐scale shear are discussed. We have found that the shearcurrent dynamo can act even in random flows with small Reynolds numbers. However, in this case mean‐field dynamo requires small magnetic Prandtl numbers (i.e., when Pm < Pm^cr < 1). The threshold in the magnetic Prandtl number, Pm^cr = 0.24, is determined using second order correlation approximation (or first‐order smoothing approximation) for a background random flow with a scale‐dependent viscous correlation time τ_c = (νk 2)^–1 (where ν is the kinematic viscosity of the fluid and k is the wave number). For turbulent flows with large Reynolds numbers shear‐current dynamo occurs for arbitrary magnetic Prandtl numbers. This dynamo effect represents a very generic mechanism for generating large‐scale magnetic fields in a broad class of astrophysical turbulent systems with large‐scale shear. On the other hand, mean‐field dynamo due to homogeneous kinetic helicity fluctuations alone in a sheared turbulence is not realistic for a broad class of astrophysical systems because it requires a very specific random forcing of kinetic helicity fluctuations that contains, e.g., low‐frequency oscillations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral properties of hydromagnetic fluctuations near 4 and 5 a.u.

Power spectra of vector components of interplanetary magnetic field fluctuations near 4–5 a.u. during quiet intervals show a frequency dependence very close to f^s over the frequency range 4 × 10^?5 to 9 × 10^?3 Hz (corresponding to periods of 7 h-2 min). While the spectra are generally very close to power law in frequency, variations in slope among the spectra exceed those expected from random errors and may represent true temporal variations. Mean slopes corrected for systematic error are s = ? 1.50±0.02 (Pioneer 10, mean heliocentric distance 5.3 a.u.) and s = ? 1.52±0.02 (Pioneer 11, mean heliocentric distance 3.9 a.u.) and are consistent with several determinations of spectral slope for magnetic fluctuations near 1 a.u. Radial evolution of the perturbations is investigated by choosing data samples in which Pioneer 10 and 11 and the sun are nearly colinear. The dependence on heliocentric distance of σ_c², the composite vector variance, and of σ_c/B_mag, where B_mag is the mean magnitude of the magnetic field, show that the radial variation of fluctuation amplitude is highly variable in time with a dependence on heliocentric distance typically in the range R^?1 to R^?1.5. These observations are compared with theoretical models of outward propagating Alfven waves of solar origin and of MHD turbulence. The mean slopes agree well with that expected for turbulence. The significant variability observed in spectral slopes and in the radial dependence of fluctuation amplitude in data selected specifically for conditions of relative magnetic quiet is noteworthy and urges caution in modeling heliospheric magnetic microstructure in studies of galactic cosmic ray modulation.     

Effect of fluctuations in Doppler width on the center of strong absorption lines

Stochastic temperatures and turbulence are characterized by average velocities u _th and < u _turb  > ≡ u ₀ and fluctuations u￠_th {u'_{th}} and u′ (<u′ > = 0). Thus, the Doppler width of a line also has a fluctuating component Dl￠_D \Delta {\lambda '_D} . Observed spectra correspond to the radiative flux averaged over time and over a star’s surface, <H_λ>. Usually, only the average velocities u _th and u ₀ are taken into account in photospheric models and these yield the Doppler width Dl_D⁽⁰⁾ \Delta \lambda_D^{(0)} of a line in the customary way. The fluctuations Dl￠_D \Delta {\lambda '_D} mean that near a line center the average absorption coefficient < α_λ > is larger than the usual α_λ, which depends only on the average velocities u _th and u ₀. This enhances the absorption line near the center and is not explained by the photospheric models. This new statistical effect depends on the wavelength of the line. A comparison of observed lines with model profiles yields an estimate for the average level of fluctuations in the Doppler width, h = á | Dl￠_D | ñ

Distance law and formation of satellite systems

In the solar system satellite systems of Jupiter, Saturn and Uranus are typical ones. The distribution of the semi-major axis of satellite orbits in each system may be expressed by an empirical formula corresponding to the Titius-Bode law. We found that it can be written as a_n = B′ · Bⁿ, where B′ and B are constants. Values of B′ and B depend on formation conditions of each system. Satellites should be formed in the gas-satellitesimal disk around a planet and by aggregation of satellitesimals. The gas is the major component in the disk and its damping effect must play an important role in the process of aggregation of satellitesimals. It may be proved that radial small perturbation in the disk can cause the gravitational instability and the formation of gaseous rings with increased density, where satellitesimals can easy aggregat into satellites.     

Self‐similar evolutionary solutions for an accreting magneto‐fluid around a compact object with finite electrical conductivity

In this paper, we investigate the time evolution of an accreting magneto‐fluid with finite conductivity. For the case of a thin disk, the fluid equations along with Maxwell's equations are derived in a simplified, one‐dimensional model that neglects the latitudinal dependence of the flow. The finite electrical conductivity of the plasma is taken into account by Ohm's law; however, the shear viscous stress is neglected, as well as the self‐gravity of the disk. In order to solve the integrated equations that govern the dynamical behaviour of the magneto‐fluid, we have used a self‐similar solution. We introduce two dimensionless variables, S₀ and ε_ϱ, which represent the size of the electrical conductivity and the density behaviour with time, respectively. The effect of each of these on the structure of the disk is studied. While the pressure is obtained simply by solving an ordinary differential equation, the density, the magnetic field, the radial velocity, and the rotational velocity are presented analytically. The solutions show that the S0 and ε_ϱ parameters affect the radial thickness of the disk. Also, radial velocity and gas pressure are more sensitive to the electrical conductivity in the inner regions of disk. Moreover, the parameter ε_ϱ has a more significant effect on the physical quantities for small radii. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structure and stability of rotating fluid disks around massive objects. I. Newtonian formulation

In this paper we have presented a very general class of solutions for rotating fluid disks around massive objects (neglecting the self gravitation of the disk) with density as a function of the radial coordinate only and pressure being nonzero. Having considered a number of cases with different density and velocity distributions, we have analysed the stability of such disks under both radial and axisymmetric perturbations. For a perfect gas disk with γ= 5/3 the disk is stable with frequency (MG/r³)^1/2 for purely radial pulsation with expanding and contracting boundary. In the case of axisymmetric perturbation the critical γ_c for neutral stability is found to be much less than 4/3 indicating that such disks are mostly stable under such perturbations. On leave of absence from Government College, Jagdalpur 494005.     

The influence of turbulence on the solar p-mode frequencies I. Free-mode approximation

The influence of turbulence on the frequencies of free acoustic modes in convection zones is considered. The frequencies are modified via the speed of sound by the turbulence-induced alterations of the effective pressure: (i) by the correlated fluctuations of temperature and density and (ii) the pressure part of the Reynolds stress. The two effects shift the frequency of low l p-modes in opposite directions. In addition, the correlation of the density fluctuations with the random velocity — the eddy-mass flow — is also relevant. It is, in a steady state, balanced by a vertical mean velocity. The balance results in a rather small net effect completely disappearing for highly nonradial oscillations. Both effects of the density fluctuations produce a redshift of the low l p-mode frequencies. The Reynolds stress, however, makes a blueshift of the frequencies relative to that computed for a laminar gas. This effect dominates for subsonic turbulences. The applied second-order correlation-approximation, however, only holds for the lowest frequencies, where the KORONAS (solar minimum) data are indicating a blueshift. Of particular importance for the present concept is the expected cycle-variations of the lineshifts, i.e. the consideration of the magnetic modification of the various contributions. Observations may show whether the suggested modifications of the solar oscillation theory are correct.     

A solar wind model with the power spectrum of Alfvénic fluctuations

A new solar wind model has been developed by including in the model the Alfvénic fluctuation power spectrum equation proposed by Tu et al. (1984). The basic assumptions of the model are as follows: (1) for heliocentric distances r > 10 R _⊙, the radial variation of the power spectrum of Alfvénic fluctuations is controlled by the spectrum equation (1), (2) for heliocentric distances r < 10 R _⊙, the radial variation of the fluctuation amplitude is determined by the Alfvén wave WKB solution, (3) no energy cascades from the low-frequency boundary of the Alfvénic fluctuation power spectrum into the fluctuation frequency range, and the energy which cascades from the high-energy boundary of the spectrum into the higher frequency range is transported to heat of the solar wind flow. Some solutions of this model which, on one hand, describe the major properties of the Alfvénic fluctuations and the high-speed flow observed by Helios in the space range between 0.3–1 AU and, on the other hand, are consistent with the observational constraints at the coronal base have been obtained under the following conditions: (1) the spectrum index of the fluctuations is near to -1 for almost the whole frequency range at 10 R _⊙, (2) the particle flux density at 1 AU is not greater than 3 × 10⁸ cm^?2 s^?1, (3) the solution is for spherically-symmetric flow geometry or the solution passes through the outermost of the three critical points of the rapidly diverging flow geometry with f _max = 7. Some solutions passing through the innermost critical point of the rapidly diverging flow geometry with f _max = 7 have been found, however, with too low pressure at the coronal base to compare with the observational constraints. Heat addition or other kind of momentum addition for r < 10 R _⊙ is required to modify this model to yield better agreement with observations. A cascade energy flux function which leads to Kolmogorov power law in the high-frequency range of Alfvénic fluctuations is presented in Appendix A. More detailed discussions about the characteristics, the boundary conditions and the solution of the spectrum equation (1) are given in Appendix B.     

Proper motions,absolute magnitudes and spatial distribution of Zirconium stars

The computational algorithm to determine the the proper motions of Zirconium stars on the basis of catalogues “Carte du Ciel” and on the recent photographic observations carried out with the 70cm Abastumani meniscus telescope is presented. It allowed to determine the proper motions of 288 stars in the region around α Per with a rms error of ± 0,004 arcsec/yr. Applying the method proper motions of 74 Zirconium stars and 146 control stars have been obtained. The error of proper motions obtained for the North Zone (δ > −2°) 109 AGK₃ control stars is ± 0.006 arcsec/yr. On the basis of proper motins absolute magnitudes were separately calculated for the MCLPZS and LASZS. For the MCLPZS the average absolute visual magnitude at maximum, corresponding to the mean period of P = 350 days, equals −3^ϕm.9. For the LASZS the mean absolute visual magnitude, corresponding to the apparent median ones equals −1^ϕm.9. Low luminosity (M_v = −1^ϕmϕ9) Zirconium stars escape rather far (at a distance of up to 2 kpc) to the South from the Galactic plane into the region l ∼ 240 – 260°, where its assumed to be a connection with the Large Magellanic Cloud (LMC) begins to appear. Low luminosity Zirconium stars are weakly correlated with position of the Galaxy spiral arms. The MCLPZS show a somewhat other distribution.     

Analysis of the light curve of the magnetic CP star HD 56022

An examination of the published observational data concerning the light curves of magnetic CP stars has shown that only one star — HD 56022 — shows a light curve with a very long phase interval of light constancy. Only for this type of variability it is imaginable that the equatorial symmetry of the surface brightness distribution could be excluded. However, the analysis of the light curve of HD 56022 in the colour u of the Strömgren system has indicated that the possibly equatorial position of the small bright spot is not in contradiction to this observed curve. From the analysis in u the maximum amplitude of a light curve at another wavelength, where the curve is in counterphase to the light curve in u, can be predicted. The amplitude of such a light curve must be much smaller than 0.1 mag. From unpublished observations of HD 56022 by the satellites TD-1 A and ANS we have determined the amplitude at $LD = 155 nm, where the light curve is in counterphase to that in u, to be 0.2 mag. The consequences from the contradiction between the model and the observations in UV are discussed.     

Possible H2staggered+ ultraviolet spectrum of Jupiter

An ultraviolet spectral probe for a hydrogen-rich planetary atmosphere, such as that of Jupiter, is suggested, utilizing discrete lines in the H₂^staggered+ 2pπ_u?1sσ_g electronic transition. For the Jovian atmosphere, the dominant mechanism for exciting H₂⁺ to its 2pπ_u state appears to be photoexcitation, principally through absorption of the solar Lyman-α line. We estimate that the Jovian column emission rate of the H₂⁺ 2pπ_u(ν′ = 2, J′ = 1) →1sσ_g(ν″ = 18,J″ = 0) fluorescent line at 1236.6 Å is if1 photon cmsu-2 secsu-1; i.e., that if1 photon secsu-1 of this radiation would strike a 15-cm diameter mirror in a Jupiter fly-by at an impact parameter of 3 × 10⁵km. The critical role of corrections to the Born-Oppenheimer approximation in the use of an H₂⁺ probe is discussed.     

Mass—luminosity relation and pulsational properties of Wolf—Rayet stars

The evolution of Population I stars with initial masses 70M _⊙ ≤ M _ZAMS ≤ 130M _⊙ is considered. The computations were performed under various assumptions about the mass loss rate and were terminated at the phase of gravitational contraction after core helium exhaustion. The mass loss rate at the helium burning phase, ?_3α , is shown to be the main parameter that determines the coefficients of the mass—luminosity relation for Wolf—Rayet stars. Several more accurate mass—luminosity relations for mass loss rates ? = f _3α ?_3α , where 0.5 ≤ f _3α ≤ 3, are suggested, along with the mass—luminosity relation that combines all of the evolutionary sequences considered. The results of the stellar evolution computations were used as initial conditions in solving the hydrodynamic equations describing the spherically symmetric motions of a self-gravitating gas. The outer layers of massive Population I stars are unstable against radial oscillations throughout the helium burning phase. The oscillation amplitude is largest at enhanced carbon and oxygen abundances in the outer stellar layers, i.e., at a lower initial stellar mass M _ZAMS or a lower mass loss rate during the entire preceding evolution. In the course of evolution, the radial oscillation amplitude decreases and the small nonlinearity of the oscillations at M < 10M _⊙ allow the integral of mechanical work W done by an elementary spherical layer of gas in a closed thermodynamic cycle to be calculated with the necessary accuracy. The maximum of the radial dependence of W is shown to be located in layers with a gas temperature T ～ 2 × 10⁵ K, where the oscillations are excited by the iron Z-bump κ-mechanism. Comparison of the radial dependences of the integral of mechanical work W and the amplitude of the radiative flux variations suggests that the nonlinear radial oscillations of more massive Wolf—Rayet stars are also excited by the κ-mechanism.     

Differential rotation and meridional flow in the solar convection zone and beneath

The influence of the basic rotation on anisotropic and inhomogeneous turbulence is discussed in the context of differential rotation theory. An improved representation for the original turbulence leads to a Λ‐effect which complies with the results of 3D numerical simulations. The resulting rotation law and meridional flow agree well with both the surface observations (∂Ω/∂r < 0 and meridional flow towards the poles) and with the findings of helioseismology. The computed equatorward flow at the bottom of convection zone has an amplitude of about 10 m/s and may be significant for the solar dynamo. The depth of the meridional flow penetration into the radiative zone is proportional to ν^0.5_core, where ν_core is the viscosity beneath the convection zone. The penetration is very small if the tachocline is laminar. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An extended investigation of Helios 1 and 2 observations: The interplanetary magnetic field between 0.3 and 1 AU

Helios-1 and 2 spacecraft allowed a detailed investigation of the radial dependence of the interplanetary magnetic field components between 0.3 and 1 AU. The behaviour of the radial component B _ris in a very good agreement with Parker's model (B _r r ^-2) and the azimuthal component B also shows a radial dependence which is close to theoretical predictions (B r ^-1). Experimental results for the normal component B and for the field magnitude B are consistent with those from previous investigations. The relative amplitude of the directional fluctuations with periods less than 12 hr is essentially independent of heliocentric distance, while their power decreases approximately as r ^–3 without any appreciable difference between higher and lower velocity regimes.Also at Laboratorio Plasma nello Spazio, CNR, Frascati.