Stellar Oscillons

We study the weakly nonlinear evolution of acoustic instability of a plane- parallel polytrope with thermal dissipation in the form of Newton's law of cooling. The most unstable horizontal wavenumbers form a band around zero and this permits the development of a nonlinear pattern theory leading to a complex Ginzburg-Landau equation (CGLE). Numerical solutions for a subcritical, quintic CGLE produce vertically oscillating, localized structures that resemble the oscillons observed in recent experiments of vibrated granular material.Comment: 12 Latex pages using aasms4.sty, 2 postscript figures, submitted to the proceedings of the Florida Workshop in Nonlinear Astrophysics and Physic

Shear and Mixing in Oscillatory Doubly Diffusive Convection

To investigate the mechanism of mixing in oscillatory doubly diffusive (ODD) convection, we truncate the horizontal modal expansion of the Boussinesq equations to obtain a simplified model of the process. In the astrophysically interesting case with low Prandtl number, large-scale shears are generated as in ordinary thermal convection. The interplay between the shear and the oscillatory convection produces intermittent overturning of the fluid with significant mixing. By contrast, in the parameter regime appropriate to sea water, large-scale flows are not generated by the convection. However, if such flows are imposed externally, intermittent overturning with enhanced mixing is observed.Comment: 24 pages, 16 figures, Accepted for publication in Geophysical and Astrophysical Fluid Dynamic

The effect of time-dependent γ-pumping on buoyant magnetic structures

In this paper, we explore for the first time the interactions of the net downward, time-dependent, γ-pumping overlying an imposed layer of magnetic fluid, in a polytropic atmosphere. Our calculations show that an equipartition of energy, between the magnetic and kinetic components, must be reached for buoyancy-driven magnetic structures to rise into the pumping region. However, structures do not rise unhindered, as in a previous investigation. We show that the evolution and other features of the emerging magnetic flux structures are significantly affected by the temporal variation of the γ-pumping. The rate of emerging structures, the strength of magnetic concentrations and the extent to how far magnetic field can travel were all found to depend on the timescale of the γ-pumping

Hydrodynamics of thermal granular convection

A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular convection, recently predicted in molecular dynamic simulations and observed in experiment. The limit of a dilute flow is considered. The problem is fully described by three scaled parameters. The convection occurs via a supercritical bifurcation, the inelasticity of the collisions being the control parameter. The theory is expected to be valid for small Knudsen numbers and nearly elastic grain collisions.Comment: 4 pages, 4 EPS figures, some details adde

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

Onset of thermal convection in a horizontal layer of granular gas

The Navier-Stokes granular hydrodynamics is employed for determining the threshold of thermal convection in an infinite horizontal layer of granular gas. The dependence of the convection threshold, in terms of the inelasticity of particle collisions, on the Froude and Knudsen numbers is found. A simple necessary condition for convection is formulated in terms of the Schwarzschild's criterion, well-known in thermal convection of (compressible) classical fluids. The morphology of convection cells at the onset is determined. At large Froude numbers, the Froude number drops out of the problem. As the Froude number goes to zero, the convection instability turns into a recently discovered phase separation instability.Comment: 6 pages, 6 figures. An extended version. A simple and universal necessary criterion for convection presente

On the compatibility of a flux transport dynamo with a fast tachocline scenario

The compatibility of the fast tachocline scenario with a flux transport dynamo model is explored. We employ a flux transport dynamo model coupled with simple feedback formulae relating the thickness of the tachocline to the amplitude of the magnetic field or to the Maxwell stress. The dynamo model is found to be robust against the nonlinearity introduced by this simplified fast tachocline mechanism. Solar-like butterfly diagrams are found to persist and, even without any parameter fitting, the overall thickness of the tachocline is well within the range admitted by helioseismic constraints. In the most realistic case of a time and latitude dependent tachocline thickness linked to the value of the Maxwell stress, both the thickness and its latitude dependence are in excellent agreement with seismic results. In the nonparametric models, cycle related temporal variations in tachocline thickness are somewhat larger than admitted by helioseismic constraints; we find, however, that introducing a further parameter into our feedback formula readily allows further fine tuning of the thickness variations.Comment: Accepted in Solar Physic

Search for Short-Term Periodicities in the Sun's Surface Rotation: A Revisit

The power spectral analyses of the Sun's surface equatorial rotation rate determined from the Mt. Wilson daily Doppler velocity measurements during the period 3 December 1985 to 5 March 2007 suggests the existence of 7.6 year, 2.8 year, 1.47 year, 245 day, 182 day and 158 day periodicities in the surface equatorial rotation rate during the period before 1996. However, there is no variation of any kind in the more accurately measured data during the period after 1995. That is, the aforementioned periodicities in the data during the period before the year 1996 may be artifacts of the uncertainties of those data due to the frequent changes in the instrumentation of the Mt. Wilson spectrograph. On the other hand, the temporal behavior of most of the activity phenomena during cycles 22 (1986-1996) and 23 (after 1997) is considerably different. Therefore, the presence of the aforementioned short-term periodicities during the last cycle and absence of them in the current cycle may, in principle, be real temporal behavior of the solar rotation during these cycles.Comment: 11 pages, 6 figures, accepted for publication in Solar Physic

Reflection and Ducting of Gravity Waves Inside the Sun

Internal gravity waves excited by overshoot at the bottom of the convection zone can be influenced by rotation and by the strong toroidal magnetic field that is likely to be present in the solar tachocline. Using a simple Cartesian model, we show how waves with a vertical component of propagation can be reflected when traveling through a layer containing a horizontal magnetic field with a strength that varies with depth. This interaction can prevent a portion of the downward-traveling wave energy flux from reaching the deep solar interior. If a highly reflecting magnetized layer is located some distance below the convection zone base, a duct or wave guide can be set up, wherein vertical propagation is restricted by successive reflections at the upper and lower boundaries. The presence of both upward- and downward-traveling disturbances inside the duct leads to the existence of a set of horizontally propagating modes that have significantly enhanced amplitudes. We point out that the helical structure of these waves makes them capable of generating an alpha-effect, and briefly consider the possibility that propagation in a shear of sufficient strength could lead to instability, the result of wave growth due to over-reflection.Comment: 23 pages, 5 figures. Accepted for publication in Solar Physic

Sensitivity of the g-mode frequencies to pulsation codes and their parameters

From the recent work of the Evolution and Seismic Tools Activity (ESTA, Lebreton et al. 2006; Monteiro et al. 2008), whose Task 2 is devoted to compare pulsational frequencies computed using most of the pulsational codes available in the asteroseismic community, the dependence of the theoretical frequencies with non-physical choices is now quite well fixed. To ensure that the accuracy of the computed frequencies is of the same order of magnitude or better than the observational errors, some requirements in the equilibrium models and the numerical resolutions of the pulsational equations must be followed. In particular, we have verified the numerical accuracy obtained with the Saclay seismic model, which is used to study the solar g-mode region (60 to 140$\mu$Hz). We have compared the results coming from the Aarhus adiabatic pulsation code (ADIPLS), with the frequencies computed with the Granada Code (GraCo) taking into account several possible choices. We have concluded that the present equilibrium models and the use of the Richardson extrapolation ensure an accuracy of the order of $0.01 \mu Hz$ in the determination of the frequencies, which is quite enough for our purposes.Comment: 10 pages, 5 figures, accepted in Solar Physic