Nonlinear modal analysis of penetrative convection

Abstract

The modal expansion procedure has been used to analyze penetrative convection that arises when a thin unstable layer is embedded between two stable regions. The Boussinesq approximation is applied in which the effect of compressibility and stratification are neglected. Various calculations have been made, with one and two modes, for Rayleigh numbers ranging from the critical value to more than 10⁵ times critical. The effect of decreasing the Prandtl number has also been investigated.

It is found that in the nonlinear regime, the convective motions penetrate substantially into the stable regions. The flux of kinetic energy plays a crucial role in such penetration, and its existence puts some requirements on the motions: in the single-mode case, they need to be three-dimensional. The extent of penetration amounts to about half of the thickness of the unstable layer on each side of it when the degree of instability and that of stability are comparable in the two domains; it increases as the stability of the outer region is lowered. The penetration depth appears to be independent of all other parameters defining the problem.     

Dynamo action in simulations of penetrative solar convection with an imposed tachocline

We summarize new and continuing three-dimensional spherical shell simulations of dynamo action by convection allowed to penetrate downward into a tachocline of rotational shear. The inclusion of an imposed tachocline allows us to examine several processes believed to be essential in the operation of the global solar dynamo, including differential rotation, magnetic pumping, and the stretching and organization of fields within the tachocline. In the stably stratified core, our simulations reveal that strong axisymmetric magnetic fields (of ∼ 3000 G strength) can be built, and that those fields generally exhibit a striking antisymmetric parity, with fields in the northern hemisphere largely of opposite polarity to those in the southern hemisphere. In the convection zone above, fluctuating fields dominate over weaker mean fields. New calculations indicate that the tendency toward toroidal fields of antisymmetric parity is relatively insensitive to initial magnetic field configurations; they also reveal that on decade-long timescales, the magnetic fields can briefly enter (and subsequently emerge from) states of symmetric parity.We have not yet observed any overall reversals of the field polarity, nor systematic latitudinal propagation. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solar shear flows deduced from helioseismic dense-pack samplings of ring diagrams

We report on large-scale horizontal flows in the solar convection zone and their variability in time and space using a local-helioseismology technique known as ring-diagram analysis. By performing this analysis on a dense mosaic of individual regions on the solar disk, i.e., a `Dense-Pack' sampling, and repeating the analysis periodically on several time scales, we are able to assess the variation of horizontal flows from day-to-day, week-to-week, and year-to-year. We find that although there are changes in the flows on all these time scales, there are also basic patterns that persist. On a daily time scale we observe that the flow is reduced in those areas which are occupied by large active regions. On somewhat longer time-scales we see bands of persistent fast and slow zonal flow that are identifiable as torsional oscillations. As we examine these bands during a series of years, we find that these bands migrate toward the equator as solar activity increases. Similarly, the latitudes at which the meridional flow reaches maximum follow these regions of fast zonal flow as they migrate equatorwards. These Dense-Pack samplings also reveal substantial differences in the zonal and meridional flow patterns in the northern and southern hemispheres.     

Buoyant Magnetic Loops Generated by Global Convective Dynamo Action

Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions in a simulation with solar stratification but rotating at three times the current solar rate. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much higher values than is possible through laminar processes. These amplified portions can rise through the convective layer by a combination of magnetic buoyancy and advection by convective giant cells, forming buoyant loops. We measure statistical trends in the polarity, twist, and tilt of these loops. Loops are shown to preferentially arise in longitudinal patches somewhat reminiscent of active longitudes in the Sun, although broader in extent. We show that the strength of the axisymmetric toroidal field is not a good predictor of the production rate for buoyant loops or the amount of magnetic flux in the loops that are produced.     

Deeply Penetrating Banded Zonal Flows in the Solar Convection Zone

We discuss the spectrum arising from synchrotron emission by fast cooling (FC) electrons, when fresh electrons are continually accelerated by a strong blast wave, into a power-law distribution of energies. The FC spectrum has so far been described by four power-law segments divided by three break frequencies nusa相似文献   

Local Fractional Frequency Shifts Used as Tracers of Magnetic Activity

Using data from SOI-MDI (Haber et al., 2000), we compute the local frequencies of high-degree p modes and f modes. The frequencies are obtained through ring-diagram mode fitting. The Dense-Pack data set consists of a mosaic of 189 overlapping tiles, each tracked separately at the surface rotation rate over 1664-min time intervals during the Dynamics Programs. Each tile is 16° square and the tile centers are separated by 7.5° in latitude and longitude. For each sampling day and for each tile, we have computed the frequency shift measured relative to the temporal and spatial average of the entire set of frequencies. The motion of active regions as they rotate across the solar disk is vividly traced by these measurements. Active regions appear as locations of large positive frequency shifts. If the shifts are averaged over the solar disk and are scaled down to the appropriate wave number regime, the magnitude and frequency dependence of the shifts are consistent with the measured changes in global oscillation frequencies that occur over the solar cycle. As with the frequency shifts of low-degree global oscillations, the frequency dependence of the shifts indicates that the physical phenomena inducing the shifts is confined to the surface layers of the Sun.     

Phase inversion of one-dimensional artificial seismic data

Oscillations of an inhomogeneous one-dimensional loop have been simulated for the purpose of examining the effect of excitation and damping on the sound-speed inversion based on phase analysis. It has been demonstrated that the procedure is robust against the realization noise arising from frequent, stochastic excitation of weakly damped waves, but that strong damping can spoil the inversion.     

Multi-Ridge Fitting for Ring-Diagram Helioseismology

Inferences of subsurface flow velocities using local domain ring-diagram helioseismology depend on measuring the frequency shifts of oscillation modes seen in acoustic power spectra. Current methods for making these measurements use maximum-likelihood fitting techniques to match a model of modal power to the spectra. The model typically describes a single oscillation mode, and each mode in a given power spectrum is fit independently. We present a new method that produces measurements with higher reliability and accuracy by fitting multiple modes simultaneously. We demonstrate that this method permits measuring sub-surface flows deeper into the Sun while providing higher uniformity in data coverage and velocity response closer to the limb of the solar disk. While the previous fitting method performs better for some measurements of low phase-speed modes, we find this new method to be particularly useful for high phase-speed modes and small spatial areas.