Tilted and non-tilted Gödel-type universe

This paper explores the dynamics of Gödel-type geometry for tilted and non-tilted congruences. The kinematical as well as dynamical quantities are investigated for both congruences with non-vanishing nature of vorticity vector. The obtained vorticity is of kinematical type, i.e., not produced by a circular flow of superenergy on the plane orthogonal to the vorticity vector. We conclude that super-Poynting vector is non-zero for the tilted congruence linked with heat flux of fluid distribution while it vanishes in non-tilted case.     

Dynamical instability of laminar axisymmetric flows of ideal compressible fluid

The instability of axisymmetric flows of inviscid compressible fluid with respect to two-dimensional infinitesimal perturbations with the nonconservation of angular momentum is investigated by numerically integrating the differential equations of hydrodynamics. The compressibility is taken into account for a homentropic flow with an adiabatic index varying over a wide range. The problem has been solved for two angular velocity profiles of an initial axisymmetric flow. In the first case, a power-law rotation profile with a finite enthalpy gradient at the flow edges has been specified. For this angular velocity profile, we show that the instability of sonic and surface gravity modes in a nearly Keplerian flow, when a radially variable vorticity exists in the main flow, can be explained by the combined action of the Landau mechanism and mode coupling. We also show that including a radially variable vorticity makes the limiting exponent in the rotation law at which the unstable surface gravity modes vanish dependent on the fluid compressibility. In the second case, a Keplerian rotation law with a quasi-sinusoidal deviation has been specified in such a way that the enthalpy gradient vanished at the flow edges. We have found than the sonic modes are then stabilized and the flow is unstable only with respect to the perturbations that also exist in an incompressible fluid.     

Modelling the differential rotation of F stars

We model stellar differential rotation based on the mean-field theory of fluid dynamics. DR is mainly driven by Reynolds stress, which is anisotropic and has a non-diffusive component because the Coriolis force affects the convection pattern. Likewise, the convective heat transport is not strictly radial but slightly tilted towards the rotation axis, causing the polar caps to be slightly warmer than the equator. This drives a flow opposite to that caused by differential rotation and so allows the system to avoid the Taylor-Proudman state. Our model reproduces the rotation pattern in the solar convection zone and allows predictions for other stars with outer convection zones. The surface shear turns out to depend mainly on the spectral type and only weakly on the rotation rate. We present results for stars of spectral type F which show signs of very strong differential rotation in some cases. Stars just below the mass limit for outer convection zones have shallow convection zones with short convective turnover times. We find solar-type rotation and meridional flow patterns at much shorter rotation periods and horizontal shear much larger than on the solar surface, in agreement with recent observations. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On large-scale solar convection

We examine the effects of rotation about a vertical axis on thermal convection with a simple model in which an inviscid, incompressible fluid of zero thermal conductivity and electrical resistivity is contained in a thin annulus of rectangular cross-section. The initial steady state assumed is one of no motion relative to the rotating frame with constant (unstable) vertical temperature gradient and uniform toroidal magnetic field. Small periodic disturbances are then introduced and the linearized perturbation equations solved. We also determine the second-order mean circulations and magnetic fields that are forced by non-zero Reynolds and thermal stresses and magnetic field transports.The solutions have several properties which are relevant to large-scale solar phenomena if giant long-lived convection cells exist on the sun. In particular, the convective cells are tilted in latitude in the same sense as bipolar magnetic regions, and induce vertical magnetic fields with the same tilt. They transport momentum across latitude circles through Reynolds stresses and induced meridional circulations thus setting up a differential rotation. Cells which grow slowly compared to the rotation rate and have comparable dimensions in latitude and longitude transport momentum toward the equator. The cells also form a poloidal magnetic field from initial toroidal field, in a manner similar to that put forth by Parker.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Convection in the Presence of an Inclined Axis of Rotation with Applications to the Sun

Thermal convection in a horizontal fluid layer heated from below and rotating about an arbitrary axis is studied analytically with the attention focused on mean flows and drifts generated by the convection velocity field. Mean flows occur in both horizontal directions when the angle between the rotation vector and the vertical is finite but less than 90°. In the case of a hexagonal convection pattern, a wavelike drift is found in the presence of a horizontal component of rotation. Applications to solar convection are discussed. Considering the simplicity of the model the agreement with observations is surprisingly good.     

The effect of coriolis force on acceleration covariance in turbulent dusty flow with rotational symmetry

In this paper considering the turbulent dusty flow of an incompressible viscous fluid which is nearly isotropic and spatially homogeneous with an extra vector argument (rotation symmetry) the expression for acceleration covariance in the presence of the Coriolis force has been derived and solution has been obtained in terms of defining scalars.     

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.     

Spherical harmonic analysis of steady photospheric flows

Steady photospheric flows can be represented by a spectrum of spherical harmonic modes. A technique is described in which full disc doppler velocity measurements are analysed using the spherical harmonic functions to determine the characteristics of this spectrum and the nature of these flows. Synthetic data is constructed for testing this technique. This data contains limb shift, rotation, differential rotation, meridional circulation, supergranules, giant cells and various levels of noise.The data is analysed in several steps. First, the limb shift is calculated by finding the average velocity in concentric rings about disc center. A polynomial representation of the limb shift is then removed from the data. Secondly, the rotation profile is calculated by finding an average slope in the velocity across the disc at each latitude position. This rotation profile is fit with Legendre polynomials and removed from the data. The third step is to find the meridional circulation by calculating the spherical harmonic transform for the axisymmetric poloidal modes and correcting for the effects of the limb shift analysis. The final step is to calculate the full spectrum of spherical harmonic components for the convective flows. Supergranules are separated from giant cells by spectral filtering for high (l >32) and low (l <32) wavenumbers, respectively.Some information about the spectrum is lost because only one hemisphere is seen, only the line-of-sight velocity is measured and the measurements contain noise. The lack of information about the motions on the backside of the Sun produces a broad smearing of the spectrum into nearby modes. The lack of information about the transverse velocity component produces a mixing between modes whose longitudinal wavenumbers differ by two and between the poloidal and toroidal components with the same wavenumber. In spite of this mode mixing much can be learned from this analysis. Solar rotation and differential rotation can be accurately measured and monitored for secular changes. Meridional circulations with small amplitudes can be measured and monitored and giant cells can be separated from supergranules.     

Electromagnetic rotating universes

We study the Einstein-Maxwell equations for a tilted Bianchi type-II space-time. The matter content is a perfect fluid, with equation of statep=(γ?1)ε, (1≤γ≤2). The field equations are solved for all values of γ in the limiting case of small vorticity. The source of rotation is an electromagnetic field, which from observational requirements must be a small quantity at the present time.     

Bianchi types of Lie point symmetries arising for differentially rotating stationary axisymmetric fluids

The Einstein field equations for a perfect fluid with two commuting Killing vectors, which span the fluid's four-velocity, are considered. A third space time symmetry, which is a homothetic or a Killing vector, can be used to reduce these equations to a system of ordinary differential equations. This symmetry restricts the form of the differential rotation Ω of the fluid. A Bianchi classification of the resulting Lie algebras is performed and related to the kinematical properties of the fluid.     

Approximate rotation curve solutions for the evolution of a viscous protogalactic disk

The problem of evolution of viscous protogalactic disks is examined. A modification of traditional turbulent viscosity theory is proposed which is based on the premise that the eddies are so small and numerous that each eddy can be considered to be large molecule. The radial flow term is omitted from the viscosity equation to make it tractable, and the radial flow is later reintroduced via the requirement of gravitational balance within the disk. The main result is a family of rotation curves that, as the system evolves, serially reproduces most types of observed rotation curves. With the use of Seiden's star formation theory, the present model produces an exponential-like luminosity profile whenever stars form and the viscous action ceases.Los Alamos National Laboratory is operated by the University of California for U.S. Dept. of Energy under contract W-7405-ENG-36.     

Magnetized accretion flows: effects of gas pressure

We study how axisymmetric magnetohydrodynamic (MHD) accretion flows depend on γ adiabatic index in the polytropic equation of state. This work is an extension of Mościbrodzka & Proga, where we investigated the γ dependence of two-dimensional Bondi-like accretion flows in the hydrodynamical (HD) limit. Our main goal is to study if simulations for various γ can give us insights into the problem of various modes of accretion observed in several types of accretion systems, such as black hole binaries (BHBs), active galactic nuclei (AGN) and gamma-ray bursts. We find that for  γ≳ 4/3  , the fast-rotating flow forms a thick torus that is supported by rotation and gas pressure. As shown before for  γ= 5/3  , such a torus produces a strong, persistent bipolar outflow that can significantly reduce the polar funnel accretion of a slowly rotating flow. For low γ, close to 1, the torus is thin and is supported by rotation. The thin torus produces an unsteady outflow which is too weak to propagate throughout the polar funnel inflow. Compared to their HD counterparts, the MHD simulations show that the magnetized torus can produce an outflow and does not exhibit regular oscillations. Generally, our simulations demonstrate how the torus thickness affects the outflow production. They also support the notion that the geometrical thickness of the torus correlates with the power of the torus outflow. Our results, applied to observations, suggest that the torus ability to radiatively cool and become thin can correspond to a suppression of a jet as observed in the BHBs during a transition from a hard/low to soft/high spectral state and a transition from a quiescent to hard/low state in AGN.     

Non-static conformally flat spherically symmetric perfect fluid distribution in Einstein-Cartan theory

In this paper we have obtained general solution representing conformally-flat, non-static spherically-symmetric perfect fluid distribution in Einstein-Cartan theory. In particular, the solution has been also discussed in co-moving coordinates. The explicit expressions for pressure, density, expansion, rotation, shear and non-vanishing components of flow vector have also been found.     

Time-Distance Helioseismology with f Modes as a Method for Measurement of Near-Surface Flows

Travel times measured for the f mode have been used to study flows near the solar surface in conjunction with simultaneous measurements of the magnetic field. Previous flow measurements of Doppler surface rotation, small magnetic feature rotation, supergranular pattern rotation, and surface meridional circulation have been confirmed. In addition, the flow in supergranules due to Coriolis forces has been measured. The spatial and temporal power spectra for a six-day observing sequence have been measured.     

Simple laminar dynamos

Although current interest in astrophysical dynamo theory is largely focussed on flows with both large‐ and small‐scale motions, historically the study of dynamos driven by laminar flows has been important. Some classical laminar flow dynamos are reviewed. These results were obtained in an asymptotic regime corresponding to small values of system parameters. Numerical simulations have since been used to extend these results outside of these asymptotic regimes; the asymptotic results remain useful approximations well outside of their formal regions of validity. By changing slightly the system geometries some interesting new results have recently been obtained The latter include the very simple “one‐roll” dynamo, with motions in a single meridional cell contained within a spherical volume of fluid, without differential rotation (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Light subsystem with a linear velocity field inside a gravitating sphere

We have obtained possible figures of equilibrium for a light subsystem with internal material flows of constant vorticity inside a gravitating homogeneous sphere. Along with ellipsoidal figures of equilibrium (light analogs of Riemann ellipsoids), we have obtained figures of equilibrium in the form of one-sheet and two-sheeted hyperboloids undergoing tilted rotation.Translated from Astrofizika, Vol. 38, No. 1, pp. 55–73, January–March, 1995.     

Slow rotational perturbations of Robertson-Walker universes

A slow rotation perturbation of Robertson-Walker universes filled with perfect fluid has been investigated. It is found that the unit-four vector of perfect fluid hasno angular velocity in the perturbed cosmological models. The slow rotation which is related to the dragging of the local inertial frames, is compatible only with the cases of positive and negative curvatures of the cosmological universe. The intrinsic velocity vector field of the Universe isexpanding as well asshearing.     

Westward rotation of the atmospheric angular momentum vector of Titan by thermal tides

The orientation of the atmospheric angular momentum vector of Titan and its temporal variation predicted by a general circulation model are analysed and interpreted. The atmospheric angular momentum vector is tilted by a few degrees from the polar axis and the vector rotates (precesses) westward with a constant period of 1 Titan day. The fast westward rotation is likely to be caused by migrating diurnal thermal tides. The tilt is almost cancelled out in the troposphere by the wavenumber 2 pattern of Saturn's gravitational tide, but is more pronounced in the stratosphere, where thermal tides are significant. The predicted tilt angle and the equatorial angular momentum vary with season and maximize when the hemispheric asymmetry of the axial angular momentum or superrotation attains its peak.     

Inflated flows on Daedalia Planum (Mars)? Clues from a comparative analysis with the Payen volcanic complex (Argentina)

Inflation is an emplacement process of lava flows, where a thin visco-elastic layer, produced at an early stage, is later inflated by an underlying fluid core. The core remains hot and fluid for extended period of time due to the thermal-shield effect of the surface visco-elastic crust. Plentiful and widespread morphological fingerprints of inflation like tumuli and lava rises are found on the Payen volcanic complex (Argentina), where pahoehoe lava flows extend over the relatively flat surface of the Pampean foreland and reach at least 180 km in length.The morphology of the Argentinean Payen flows were compared with lava flows on Daedalia Planum (Mars), using Thermal Emission Imaging System (THEMIS), Mars Orbiter Laser Altimeter (MOLA), Mars Orbiter Camera (MOC), Mars Reconnaissance Orbiter (MRO)/High-Resolution Imaging Science Experiment (HiRISE). THEMIS images were used to map the main geological units of Daedalia Planum and determine their stratigraphic relationships. MOLA data were used to investigate the topographic surface over which the flows propagated and assess the thickness of lava flows. Finally, MOC and MRO/HIRISE images were used to identify inflations fingerprints and assess the cratering age of the Daedalia Planum’ s youngest flow unit which were found to predate the caldera formation on top of the Arsia Mons. The identification of similar inflation features between the Daedalia Planum and the Payen lava fields suggests that moderate and long lasting effusion rates coupled with very efficient spreading processes could have cyclically occurred in the Arsia Mons volcano during its eruptive history. Consequently the effusion rates and rheological proprieties of Daedalia lava flows, which do not take into account the inflation process, can be overestimated. These findings raise some doubts about the effusion rates and lava rheological properties calculated on Martian flows and recommends that these should be used with caution if applied on flows not checked with high-resolution images and potentially affected by inflation. Further HiRISE data acquisition will permit additional analysis of the flow surfaces and will allow more accurate estimates of effusion rates and rheological properties of the lava flows on Mars particularly if this data is acquired under a favourable illumination.     

A 2D study of the effects of the size of a solid core on the equatorial flow in giant planets

Zonal winds simulated in two-dimensional computer models of turbulent convection in the equatorial plane of giant planets have greater surface amplitudes for cases with smaller solid cores, and therefore larger buoyancy driving, all other properties being equal. This differential rotation in radius is maintained by the convergence of angular momentum flux, which occurs because of the convective flow that develops due to the effects of planetary rotation and density stratification. The superposition of the convective flow and the stronger zonal flow produces wave-like, instead of cellular convection.