Contemporary three-dimensional physics-based simulations of the solar convection zone disagree with observations. They feature differential rotation substantially different from the true rotation inferred by solar helioseismology and exhibit a conveyor belt of convective “Busse” columns not found in observations. To help unravel this so-called “convection conundrum”, we use a three-dimensional pseudospectral simulation code to investigate how radially non-uniform viscosity and entropy diffusivity affect differential rotation and convective flow patterns in density-stratified rotating spherical fluid shells. We find that radial non-uniformity in fluid properties enhances polar convection, which, in turn, induces non-negligible lateral entropy gradients that lead to large deviations from differential rotation geostrophy due to thermal wind balance. We report simulations wherein this mechanism maintains differential rotation patterns very similar to the true solar profile outside the tangent cylinder, although discrepancies remain at high latitudes. This is significant because differential rotation plays a key role in sustaining solar-like cyclic dipolar dynamos. Full article

We continue our study of the transition of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence from non-equilibrium initial conditions to equilibrium using long-time numerical simulations on a ${128}^3$ periodic grid. A Fourier spectral transform method is used to numerically integrate the dynamical equations forward in time. The six runs that previously went to near equilibrium are here extended into equilibrium. As before, we neglect dissipation as we are primarily concerned with behavior at the largest scale where this behavior has been shown to be essentially the same for ideal and real (forced and dissipative) MHD turbulence. These six runs have various combinations of imposed rotation and mean magnetic field and represent the five cases of ideal, homogeneous, incompressible, and MHD turbulence: Case I (Run 1), with no rotation or mean field; Case II (Runs 2a and 2b), where only rotation is imposed; Case III (Run 3), which has only a mean magnetic field; Case IV (Run 4), where rotation vector and mean magnetic field direction are aligned; and Case V (Run 5), which has non-aligned rotation vector and mean field directions. Statistical mechanics predicts that dynamic Fourier coefficients are zero-mean random variables, but largest-scale coherent magnetic structures emerge and manifest themselves as Fourier coefficients with very large, quasi-steady, mean values compared to their standard deviations, i.e., there is ‘broken ergodicity.’ These magnetic coherent structures appeared in all cases during transition to near equilibrium. Here, we report that, as the runs were continued, these coherent structures remained quasi-steady and energetic only in Cases I and II, while Case IV maintained its coherent structure but at comparatively low energy. The coherent structures that appeared in transition in Cases III and V were seen to collapse as their associated runs extended into equilibrium. The creation of largest-scale, coherent magnetic structure appears to be a dynamo process inherent in ideal MHD turbulence, particularly in Cases I and II, i.e., those cases most pertinent to planets and stars. Furthermore, the statistical theory of ideal MHD turbulence has proven to apply at the largest scale, even when dissipation and forcing are included. This, along with the discovery and explanation of dynamically broken ergodicity, is essentially a solution to the ‘dynamo problem’. Full article

Transition of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence to near-equilibrium from non-equilibrium initial conditions is examined through new long-time numerical simulations on a ${128}^3$ periodic grid. Here, we neglect dissipation because we are primarily concerned with behavior at the largest scale which has been shown to be essentially the same for ideal and real (forced and dissipative) MHD turbulence. A Fourier spectral transform method is used to numerically integrate the dynamical equations forward in time and results from six computer runs are presented with various combinations of imposed rotation and mean magnetic field. There are five separate cases of ideal, homogeneous, incompressible, MHD turbulence: Case I, with no rotation or mean field; Case II, where only rotation is imposed; Case III, which has only a mean magnetic field; Case IV, where rotation vector and mean magnetic field direction are aligned; and Case V, which has nonaligned rotation vector and mean field directions. Dynamic coefficients are predicted by statistical mechanics to be zero-mean random variables, but largest-scale coherent magnetic structures emerge in all cases during transition; this implies dynamo action is inherent in ideal MHD turbulence. These coherent structures are expected to occur in Cases I, II and IV, but not in Cases III and V; future studies will determine whether they persist. Full article