Kinematic dynamo wave in the vicinity of the solar poles

We consider a dynamo wave in the solar convective shell for the kinematic $\alpha\omega$-dynamo model. The spectrum and eigenfunctions of the corresponding equations are derived analytically with the aid of the WKB method. Our main aim here is to investigate the dynamo wave behavior in the vicinity of the solar poles. Explicit expressions for the incident and reflected waves are obtained. The reflected wave is shown to be relatively weak in comparison to the incident wave. The phase shifts and the ratio of amplitudes of the two waves are found.Comment: 20 pages, 2 EPS figure

Wavy stripes and squares in zero P number convection

A simple model to explain numerically observed behaviour of chaotically varying stripes and square patterns in zero Prandtl number convection in Boussinesq fluid is presented. The nonlinear interaction of mutually perpendicular sets of wavy rolls, via higher mode, may lead to a competition between the two sets of wavy rolls. The appearance of square patterns is due to the secondary forward Hopf bifurcation of a set of wavy rolls.Comment: 8 pages and 3 figures, late

Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers

This paper is a detailed report on a programme of simulations used to settle a long-standing issue in the dynamo theory and demonstrate that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>>1 and small magnetic Prandtl number Pm<<1. The dependence of the critical Rm_c vs. the hydrodynamic Reynolds number Re is obtained for 1<Re<6700. In the limit Pm<<1, Rm_c is ~3 times larger than for Pm>1. The stability curve Rm_c(Re) (and, it is argued, the nature of the dynamo) is substantially different from the case of the simulations and liquid-metal experiments with a mean flow. It is not as yet possible to determine numerically whether the growth rate is ~Rm^{1/2} in the limit Re>>Rm>>1, as should be the case if the dynamo is driven by the inertial-range motions. The magnetic-energy spectrum in the low-Pm regime is qualitatively different from the Pm>1 case and appears to develop a negative spectral slope, although current resolutions are insufficient to determine its asymptotic form. At 1<Rm<Rm_c, the magnetic fluctuations induced via the tangling by turbulence of a weak mean field are investigated and the possibility of a k^{-1} spectrum above the resistive scale is examined. At low Rm<1, the induced fluctuations are well described by the quasistatic approximation; the k^{-11/3} spectrum is confirmed for the first time in direct numerical simulations.Comment: IoP latex, 27 pages, 25 figures, 3 tables. Accepted by New J. Physic

Low-Prandtl-number B\'enard-Marangoni convection in a vertical magnetic field

The effect of a homogeneous magnetic field on surface-tension-driven B\'{e}nard convection is studied by means of direct numerical simulations. The flow is computed in a rectangular domain with periodic horizontal boundary conditions and the free-slip condition on the bottom wall using a pseudospectral Fourier-Chebyshev discretization. Deformations of the free surface are neglected. Two- and three-dimensional flows are computed for either vanishing or small Prandtl number, which are typical of liquid metals. The main focus of the paper is on a qualitative comparison of the flow states with the non-magnetic case, and on the effects associated with the possible near-cancellation of the nonlinear and pressure terms in the momentum equations for two-dimensional rolls. In the three-dimensional case, the transition from a stationary hexagonal pattern at the onset of convection to three-dimensional time-dependent convection is explored by a series of simulations at zero Prandtl number.Comment: 26 pages, 9 figure

Influence of topography on tide propagation and amplification in semi-enclosed basins

An idealized model for tide propagation and amplification in semi-enclosed rectangular basins is presented, accounting for depth differences by a combination of longitudinal and lateral topographic steps. The basin geometry is formed by several adjacent compartments of identical width, each having either a uniform depth or two depths separated by a transverse topographic step. The problem is forced by an incoming Kelvin wave at the open end, while allowing waves to radiate outward. The solution in each compartment is written as the superposition of (semi)-analytical wave solutions in an infinite channel, individually satisfying the depth-averaged linear shallow water equations on the f plane, including bottom friction. A collocation technique is employed to satisfy continuity of elevation and flux across the longitudinal topographic steps between the compartments. The model results show that the tidal wave in shallow parts displays slower propagation, enhanced dissipation and amplified amplitudes. This reveals a resonance mechanism, occurring when\ud the length of the shallow end is roughly an odd multiple of the quarter Kelvin wavelength. Alternatively, for sufficiently wide basins, also Poincaré waves may become resonant. A transverse step implies different wavelengths of the incoming and reflected Kelvin wave, leading to increased amplitudes in shallow regions and a shift of amphidromic points in the direction of the deeper part. Including the shallow parts near the basin’s closed end (thus capturing the Kelvin resonance mechanism) is essential to reproduce semi-diurnal and diurnal\ud tide observations in the Gulf of California, the Adriatic Sea and the Persian Gulf

Quasiperiodic waves at the onset of zero Prandtl number convection with rotation

We show the possibility of quasiperiodic waves at the onset of thermal convection in a thin horizontal layer of slowly rotating zero-Prandtl number Boussinesq fluid confined between stress-free conducting boundaries. Two independent frequencies emerge due to an interaction between a stationary instability and a self-tuned wavy instability in presence of coriolis force, if Taylor number is raised above a critical value. Constructing a dynamical system for the hydrodynamical problem, the competition between the interacting instabilities is analyzed. The forward bifurcation from the conductive state is self-tuned.Comment: 9 pages of text (LaTex), 5 figures (Jpeg format

Stochastic excitation of acoustic modes in stars

For more than ten years, solar-like oscillations have been detected and frequencies measured for a growing number of stars with various characteristics (e.g. different evolutionary stages, effective temperatures, gravities, metal abundances ...). Excitation of such oscillations is attributed to turbulent convection and takes place in the uppermost part of the convective envelope. Since the pioneering work of Goldreich & Keely (1977), more sophisticated theoretical models of stochastic excitation were developed, which differ from each other both by the way turbulent convection is modeled and by the assumed sources of excitation. We review here these different models and their underlying approximations and assumptions. We emphasize how the computed mode excitation rates crucially depend on the way turbulent convection is described but also on the stratification and the metal abundance of the upper layers of the star. In turn we will show how the seismic measurements collected so far allow us to infer properties of turbulent convection in stars.Comment: Notes associated with a lecture given during the fall school organized by the CNRS and held in St-Flour (France) 20-24 October 2008 ; 39 pages ; 11 figure

The chemical composition of Ultracompact Dwarf Galaxies in the Virgo and Fornax Clusters

We present spectroscopic observations of ultra compact dwarf (UCD) galaxies in the Fornax and Virgo Clusters made to measure and compare their stellar populations. The spectra were obtained on the Gemini-North (Virgo) and Gemini-South (Fornax) Telescopes using the respective Gemini Multi-Object Spectrographs. We estimated the ages, metallicities and abundances of the objects from mea- surements of Lick line-strength indices in the spectra; we also estimated the ages and metallicities independently using a direct spectral fitting technique. Both methods re- vealed that the UCDs are old (mean age 10.8 \pm 0.7 Gyr) and (generally) metal-rich (mean [Fe/H] = -0.8 \pm 0.1). The alpha-element abundances of the objects measured from the Lick indices are super-Solar. We used these measurements to test the hypothesis that UCDs are formed by the tidal disruption of present-day nucleated dwarf elliptical galaxies. The data are not consistent with this hypothesis because both the ages and abundances are significantly higher than those of observed dwarf galaxy nuclei (this does not exclude disruption of an earlier generation of dwarf galaxies). They are more consistent with the properties of globular star clusters, although at higher mean metallicity. The UCDs display a very wide range of metallicity (-1.7 <[Fe/H]< 0.0), spanning the full range of both globular clusters and dwarf galaxy nuclei. We confirm previous reports that most UCDs have high metalliticities for their luminosities, lying significantly above the canonical metallicitiy-luminosity relation followed by early-type galaxies. In contrast to previous work we find that there is no significant difference in either the mean ages or the mean metallicities of the Virgo and Fornax UCD populations.Comment: 15 pages (including references and appendix), 8 figures (including appendix

Activation of mTOR coincides with autophagy during ligation-induced atrophy in the rat submandibular gland

Salivary gland atrophy is a common consequence of pathology, including Sjögren's syndrome, irradiation therapy and obstructive sialadenitis. During severe atrophy of the rat submandibular gland caused by excretory duct ligation, the majority of acinar cells disappear through apoptosis, whereas ductal cells proliferate and dedifferentiate; yet, the gland can survive in the atrophic state almost indefinitely, with an ability to fully recover if deligated. The control mechanisms governing these observations are not well understood. We report that ∼10% of acinar cells survive in ligation-induced atrophy. Microarray and quantitative real-time PCR analysis of ligated glands indicated sustained transcription of acinar cell-specific genes, whereas ductal-specific genes were reduced to background levels. After 3 days of ligation, activation of the mammalian target of rapamycin (mTOR) pathway and autophagy occurred as shown by phosphorylation of 4E-BP1 and expression of autophagy-related proteins. These results suggest that activation of mTOR and the autophagosomal pathway are important mechanisms that may help to preserve acinar cells during atrophy of salivary glands after injury