Eddy diffusivity in convective hydromagnetic systems

An eigenvalue equation, for linear instability modes involving large scales in a convective hydromagnetic system, is derived in the framework of multiscale analysis. We consider a horizontal layer with electrically conducting boundaries, kept at fixed temperatures and with free surface boundary conditions for the velocity field; periodicity in horizontal directions is assumed. The steady states must be stable to short (fast) scale perturbations and possess symmetry about the vertical axis, allowing instabilities involving large (slow) scales to develop. We expand the modes and their growth rates in power series in the scale separation parameter and obtain a hierarchy of equations, which are solved numerically. Second order solvability condition yields a closed equation for the leading terms of the asymptotic expansions and respective growth rate, whose origin is in the (combined) eddy diffusivity phenomenon. For about 10% of randomly generated steady convective hydromagnetic regimes, negative eddy diffusivity is found.Comment: 18 pages. Added numerical reults. Submitted to European Physical Journal

The Effects of Rotation Rate on Deep Convection in Giant Planets with Small Solid Cores

We study how the pattern of thermal convection and differential rotation in the interior of a giant gaseous planet is affected by the presence of a small solid core as a function of the planetary rotation rate. We show, using 2D anelastic, hydrodynamic simulations, that the presence of a small solid core results in significantly different flow structure relative to that of a fully convective interior only if there is little or no planetary rotation.Comment: 12 pages, 3 figure

Perturbative Renormalization and Mixing of Quark and Glue Energy-Momentum Tensors on the Lattice

We report the renormalization and mixing constants to one-loop order for the quark and gluon energy-momentum (EM) tensor operators on the lattice. A unique aspect of this mixing calculation is the definition of the glue EM tensor operator. The glue operator is comprised of gauge-field tensors constructed from the overlap Dirac operator. The resulting perturbative calculations are performed using methods similar to the Kawai approach using the Wilson action for all QCD vertices and the overlap Dirac operator to define the glue EM tensor. Our results are used to connect the lattice QCD results of quark and glue momenta and angular momenta to the $\overline{\text{MS}}$ scheme at input scale $\mu$Comment: 26 pages, 6 figure

Carbon Ignition in Type Ia Supernovae: II. A Three-Dimensional Numerical Model

The thermonuclear runaway that culminates in the explosion of a Chandrasekhar mass white dwarf as a Type Ia supernova begins centuries before the star actually explodes. Here, using a 3D anelastic code, we examine numerically the convective flow during the last minute of that runaway, a time that is crucial in determining just where and how often the supernova ignites. We find that the overall convective flow is dipolar, with the higher temperature fluctuations in an outbound flow preferentially on one side of the star. Taken at face value, this suggests an asymmetric ignition that may well persist in the geometry of the final explosion. However, we also find that even a moderate amount of rotation tends to fracture this dipole flow, making ignition over a broader region more likely. Though our calculations lack the resolution to study the flow at astrophysically relevant Rayleigh numbers, we also speculate that the observed dipolar flow will become less organized as the viscosity becomes very small. Motion within the dipole flow shows evidence of turbulence, suggesting that only geometrically large fluctuations (~1 km) will persist to ignite the runaway. We also examine the probability density function for the temperature fluctuations, finding evidence for a Gaussian, rather than exponential distribution, which suggests that ignition sparks may be strongly spatially clustered.Comment: 16 pages, 9 figures, submitted to ApJ. A high resolution version of this paper, as well as movies, can be found at http://www.ucolick.org/~mqk/Carbo

Modeling convection and zonal winds in giant planets

Three basic modeling approaches have been used to numerically simulate fluid turbulence and the banded zonal winds in the interiors and atmospheres of giant planets: shallow-water models, deep-shell Boussinesq models and deep-shell anelastic models. We review these models and discuss the approximations and assumptions upon which they are based. All three can produce banded zonal wind patterns at the surface. However, shallow-water models produce a retrograde (i.e., westward) zonal jet in the equatorial region, whereas strong prograde (i.e., eastward) equatorial jets exist on Jupiter and Saturn. Deep-shell Boussinesq models maintain prograde equatorial jets by the classic method of vortex stretching of convective columnar flows; however, they neglect the effects of the large density stratification in these giant planets. Deep-shell anelastic models account for density stratification and maintain prograde equatorial jets by generating vorticity as rising fluid expands and sinking fluid contracts, without the constraint of long thin convective column

Heat transport in 3D anelastic simulations of the internal dynamics of giant planets without cores

Differential rotation, similar to that seen on our gas giants, is manifested at the surface of three-dimensional (3D) computer simulations of thermal convection in density-stratified rotating planets without solid cores. Below the surface, the flow forms short axially-aligned vortices, generated by fluid expanding as it rises and contracting as it sinks. The convergence of the nonlinear Reynolds stresses resulting from the vorticity generated by fluid flowing through the density stratification maintains the surface banded zonal flow without the classical vortex stretching of Taylor columns. These preliminary simulations demonstrate that large non-convecting cores are not required to obtain multiple zonal jets at the surface, and show greater convective heat flux towards the poles relative to that seen at the equator. This result could help explain the nearly uniform with latitude thermal emission observed at the surface of Jupite