Differential rotation and meridional flow of Arcturus

The spectroscopic variability of Arcturus hints at cyclic activity cycle and differential rotation. This could provide a test of current theoretical models of solar and stellar dynamos. To examine the applicability of current models of the flux transport dynamo to Arcturus, we compute a mean‐field model for its internal rotation, meridional flow, and convective heat transport in the convective envelope. We then compare the conditions for dynamo action with those on the Sun. We find solar‐type surface rotation with about 1/10th of the shear found on the solar surface. The rotation rate increases monotonically with depth at all latitudes throughout the whole convection zone. In the lower part of the convection zone the horizontal shear vanishes and there is a strong radial gradient. The surface meridional flow has maximum speed of 170 m/s and is directed towards the equator at high and towards the poles at low latitudes. Turbulent magnetic diffusivity is of the order 10¹⁵–10¹⁶ cm²/s. The conditions on Arcturus are not favorable for a circulation‐dominated dynamo (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling spatio‐temporal nonlocality in mean‐field dynamos

When scale separation in space or time is poor, the mean‐field α effect and turbulent diffusivity have to be replaced by integral kernels by which the dependence of the mean electromotive force on the mean magnetic field becomes nonlocal. Earlier work in computing these kernels using the test‐field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel for isotropic stationary turbulence is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean‐field equations are solved for oscillatory α –shear dynamos as well as α² dynamos with α linearly depending on position, which makes this dynamo oscillatory, too. In both cases, the critical values of the dynamo number is lowered due to spatio‐temporal nonlocality.When scale separation in space or time is poor, the mean‐field α effect and turbulent diffusivity have to be replaced by integral kernels by which the dependence of the mean electromotive force on the mean magnetic field becomes nonlocal. Earlier work in computing these kernels using the test‐field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel for isotropic stationary turbulence is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean‐field equations are solved for oscillatory α –shear dynamos as well as α² dynamos     

Horizontal flows concurrent with an X2.2 flare in the active region NOAA 11158

Horizontal proper motions were measured with local correlation tracking (LCT) techniques in active region NOAA 11158 on 2011 February 15 at a time when a major (X2.2) solar flare occurred. The measurements are based on continuum images and magnetograms of the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. The observed shear flows along the polarity inversion line were rather weak (a few 100 m s^–1). The counter‐streaming region shifted toward the north after the flare. A small circular area with flow speeds of up to 1.2 km s^–1 appeared after the flare near a region of rapid penumbral decay. The LCT signal in this region was provided by small‐scale photospheric brigthenings, which were associated with fast traveling moving magnetic features. Umbral strengthening and rapid penumbral decay was observed after the flare. Both phenomena were closely tied to kernels of white‐light flare emission. The white‐light flare only lasted for about 15 min and peaked 4 min earlier than the X‐ray flux. In comparison to other major flares, the X2.2 flare in active region NOAA 11158 only produced diminutive photospheric signatures (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cyclic light and period variations of the UV Leonis system

Solutions of the new standard V‐light curves for the EA type binary UV Leo are obtained using the PHOEBE code (0.31a version). Absolute parameters of the stellar components were then determined, enabling them to be positioned on the absolute magnitude‐color (l.e. M_V vs. B – V) isochrones diagram, based on which the age of the system is estimated to be >4×10⁹ yr. Also times of minima data (“O – C curve”) have been analyzed. Apart from an almost sinusoidal variation with a period of 29.63 yr, which modulates the orbital period, and was attributed to a third body orbiting around the system, other cyclic variation in the orbital period and also brightness, with time scales of 24.25 and 22.77 yr were found, respectively. We associate this with a magnetic activity cycle newly reported here for UV Leo (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear dynamical modeling of solar cycles using dynamo formulation with turbulent magnetic helicity

Abstract

We describe a sequence of two-dimensional numerical simulations of inflection point instability in a stably stratified shear flow near the ground. The fastest growing Kelvin-Helmholtz modes are studied in detail; in particular we investigate the growth inhibiting effect of the ground which is predicted by linear theory and the Reynolds number dependence of the process of growth to finite amplitude. We consider flows which are both above and below the critical Reynolds number (Re = 300) which has been reported by Woods (1969) to mark the boundary between flows which have turbulent final states and those which do not. A global energy budget reveals a fundamental difference in character of the finite amplitude billows in these two Reynolds number regimes. However, for relatively high Reynolds numbers (Re = 10³) we do not find any explicit evidence for secondary instability. Above the transition Reynolds number the modified mean flow induced by wave growth is characterized by a splitting of the original shear layer and of the in version in which it is embedded.     

MHD stability of a filament immersed in a solar bipolar magnetic region

Abstract

The stability properties of the filament model of Low (1981) are investigated. We use a two-dimensional formalism based on the magnetohydrodynamic energy principle of Bernstein et al. (1958). For the parameter range observed in quiescent prominences this model describes stable horizontal oscillations with periods of about 3–6 min. In other parameter ranges we find instability which is driven exclusively by compressional effects. The Lorentz force has a continuously stabilizing influence. In addition, it seems that gravity is practically unimportant for the stability state of the equilibrium.     

Hydromagnetic waves in a thin rotating spherical shell

We consider an electrically conducting fluid confined to a thin rotating spherical shell in which the Elsasser and magnetic Reynolds numbers are assumed to be large while the Rossby number is assumed to vanish in an appropriate limit. This may be taken as a simple model for a possible stable layer at the top of the Earth's outer core. It may also be a model for the thin shells which are thought to be a source of the magnetic fields of some planets such as Mercury or Uranus. Linear hydromagnetic waves are studied using a multiple scale asymptotic scheme in which boundary layers and the associated boundary conditions determine the structure of the waves. These waves are assumed to be of the form of an asymptotic series expanded about an ambient magnetic field which vanishes on the equatorial plane and velocity and pressure fields which do not. They take the form of short wave, slowly varying wave trains. The results are compared to the author's previous work on such waves in cylindrical geometry in which the boundary conditions play no role. The approximation obtained is significantly different from that obtained in the previous work in that an essential singularity appears at the equator and nonequatorial wave regions appear.     

Nonlinear alfvénic fluctuations in uniform magnetic background fields

Abstract

The two dimensional incompressible MHD equations describing the decay of a random initial velocity field in the presence of a uniform magnetic background field are solved numerically by a Chebyshev spectral method. The nonlinear interactions of standing Alfvén-waves of a given energy are studied for various Reynolds numbers and field strengths of the magnetic background field. Small scale structures are generated by these interactions, which increase the energy dissipation, however, the uniform background field suppresses the production of arbitrary small scales. Thus energy dissipation is found to be insignificant at sufficiently high Reynolds numbers. Anisotropies of the fluctuating field components are also studied. In the temporal evolution they appear first in the magnetic field. This is explained by the conservation of mean square vector potential in the limit of infinite conductivity.     

A depth-dependent study of the topographic rectification of tidal currents

Abstract

A depth-dependent model for the topographic rectification of tidal currents in a homogeneous rotating fluid is used to examine the dependence of the rectified mean flow on various tidal, topographic and frictional parameters. Friction is parameterized through a vertically-uniform, time-independent vertical eddy viscosity and a bottom stress law applied near the top of the constant stress layer. The model neglects the interaction of mean and tidal currents, assumes uniformity along isobaths, and is closed with the assumption of zero depth-averaged mean flow across isobaths.

In the limit of depth-independence, the model reduces to that considered by Huthnance (1973) and Loder (1980) which, for weak friction, favours anticyclonic mean circulation around shallow regions and Lagrangian flow which is significantly reduced from the Eulerian. With the inclusion of vertical structure, the magnitude of the anticyclonic flow is amplified suggesting that depth-independent models may underestimate the along-isobath flow. For strong friction the direction of the mean flow depends on the orientation of the tidal ellipse relative to the isobaths. The depthindependent model again underestimates the magnitude of the along-isobath flow, but this can be offset with an appropriate reduction of the bottom friction coefficient.

The cross-isobath mean flows are one to two orders of magnitude weaker than the along-isobath flows and generally have more vertical structure. There is also a significant Stokes drift in the cross-isobath direction. Although there is some tendency for the cross-isobath mean bottom current to be down the cross-isobath mean pressure gradient, it appears that it is not generally possible to infer this current from depth-independent models.     

Hamiltonian description of almost geostrophic flow

Abstract

Geostrophic flow in the theory of a shallow rotating fluid is exactly analogous to the drift approximation in a strongly magnetized electrostatic plasma. This analogy is developed and exhibited in detailed to derive equations for the slow nearly geostrophic motion. The key ingredient in the theory is the isolation, to whatever order in Rossby number desired, of the fast motion near the inertial frequency. One of the remaining degrees of freedom represents a new approximate constant of the motion for nearly geostrophic flow. This is the analogue of the familiar magnetic moment adiabatic invariant in the plasma problem.

The procedure is a Rossby number expansion of the Hamiltonian for the fluid expressed in Lagrangian, rather than Eulerian variables. The fundamental Poisson brackets of the theory are not expanded so desirable properties such as energy conservation are maintained throughout.