A Large Eddy Simulation of Turbulent Compressible Convection: Differential Rotation in the Solar Convection Zone

We present results of two simulations of the convection zone, obtained by solving the full hydrodynamic equations in a section of a spherical shell. The first simulation has cylindrical rotation contours (parallel to the rotation axis) and a strong meridional circulation, which traverses the entire depth. The second simulation has isorotation contours about mid-way between cylinders and cones, and a weak meridional circulation, concentrated in the uppermost part of the shell. We show that the solar differential rotation is directly related to a latitudinal entropy gradient, which pervades into the deep layers of the convection zone. We also offer an explanation of the angular velocity shear found at low latitudes near the top. A non-zero correlation between radial and zonal velocity fluctuations produces a significant Reynolds stress in that region. This constitutes a net transport of angular momentum inwards, which causes a slight modification of the overall structure of the differential rotation near the top. In essence, the {\it thermodynamics controls the dynamics through the Taylor-Proudman momentum balance}. The Reynolds stresses only become significant in the surface layers, where they generate a weak meridional circulation and an angular velocity `bump'.Comment: 11 pages, 14 figures, the first figure was too large and is excluded. Accepted for publication in MNRA

Modeling the Observed Solar Cycle Variations of the Quasi-biennial Oscillation (QBO): Amplification by Wave Forcing

In several papers, the solar cycle (SC) effect in the lower atmosphere has been linked observationally to the Quasi-biennial Oscillation (QBO) of the zonal circulation, which is generated primarily by small-scale gravity waves (GW). Salby and Callaghan (2000) in particular analyzed the QBO, covering more than 40 years, and discovered that it contains a large SC signature at 20 km. With our Numerical Spectral Model (NSM), we conducted a 3D study to describe the QBO under the influence of the SC, and some results have been published (Mayr et al., GRL, 2005,2006). For a SC period of 10 years, the relative amplitude of radiative forcing is taken to vary exponentially with height, i.e., 0.2% at the surface, 2% at 50 km, 20% at 100 km and above. Applying spectral analysis to filter out and identify the SC signature, the model generates a relatively large modulation of the QBO, which reproduces the observations qualitatively. Our numerical results demonstrate that the modulation of the QBO, with constant phase relative to the SC, persist at least for 60 years. The same model run generates in the seasonal variations a hemispherically symmetric Equatorial Annual Oscillation (EAO, with 12-month period), which is confined to low latitudes like the QBO and is also modulated by the SC. Although the amplitude of the EAO is relatively small, its SC modulation is large, and it is in phase with that of the QBO. The SC modulated EAO is evidently the pathway and pacemaker for the solar influence on the QBO. To shed light on the dynamical processes involved, we present model results that show how the seasonal cycle induces the SC modulations of the EAO and QBO. Our analysis further demonstrates that the SC modulations of the QBO and EAO are amplified by the GW interaction with the flow. The GW momentum source clearly shows a SC modulation that is in phase with the corresponding modulations of the QBO and EAO. By tapping the momentum from the upward propagating GWs, the QBO and EAO apparently serve as conduits to amplify and transfer to lower altitudes the larger SC variations in the UV absorbed in the mesosphere. Our model also produces in the temperature variations of the QBO and EAO measurable SC modulations at polar latitudes near the tropopause, and such signatures have been reported in the literature. Contrary to conventional interpretation, however, we suggest that the effects are generated at least in part by the meridional circulation, and planetary waves presumably, which redistribute the energy from the equatorial region where wave forcing is very efficient and thereby amplifies the SC influence

Turbulent Compressible Convection with Rotation - Penetration above a Convection Zone

We perform Large eddy simulations of turbulent compressible convection in stellar-type convection zones by solving the Navi\'{e}r-Stokes equations in three dimensions. We estimate the extent of penetration into the stable layer above a stellar-type convection zone by varying the rotation rate ({\boldmath$\rm\Omega$}), the inclination of the rotation vector ($\theta$) and the relative stability ($S$) of the upper stable layer. The computational domain is a rectangular box in an f-plane configuration and is divided into two regions of unstable and stable stratification with the stable layer placed above the convectively unstable layer. Several models have been computed and the penetration distance into the stable layer above the convection zone is estimated by determining the position where time averaged kinetic energy flux has the first zero in the upper stable layer. The vertical grid spacing in all the model is non-uniform, and is less in the upper region so that the flows are better resolved in the region of interest. We find that the penetration distance increases as the rotation rate increases for the case when the rotation vector is aligned with the vertical axis. However, with the increase in the stability of the upper stable layer, the upward penetration distance decreases. Since we are not able to afford computations with finer resolution for all the models, we compute a number of models to see the effect of increased resolution on the upward penetration. In addition, we estimate the upper limit on the upward convective penetration from stellar convective cores.Comment: Accepted for Publication in Asttrophysics & Space Scienc

'Negative' surface differential rotation in stars having low Coriolis numbers (slow rotation or high turbulence)

A general picture of differential rotation in cool stars is that they are 'solar-like', with the equator spinning faster than the poles. Such surface differential rotation profiles have also been demonstrated by some three-dimensional simulations. In our numerical investigation of rotating convection (both regional and global), we found that this picture is not universally applicable. The equator may spin substantially slower than the poles (Omega equator - Omega pole)/Omega can reach 50%). The key parameter that determines the transition in behavior is the Coriolis number (inverse Rossby number). 'Negative' differential rotation of the equator (relative to the mean rotation) occurs if the Coriolis number is below a critical value

APPLICATION OF THE ALTERNATING DIRECTION IMPLICIT METHOD TO THE COMPUTATION OF TIME-DEPENDENT COMPRESSIBLE CONVECTIVE FLOWS.

Numerical experiments indicate that the time accuracy is most sensitive to the maximum CFL number and insensitive to other parameters. The Alternating Direction Implicit (ADI) method is a very efficient technique whose CPU time per step is almost competitive with explicit methods. The results of a systematic study of the time accuracy of the ADI method as applied to problems of internal convection are reported