Turbulent Elasticity of the Solar Convective Zone and the Taylor Number Puzzle

Previous work on the angular momentum balance and meridional circulation of the solar convective zone (SCZ) generally consists either of semianalytic approaches in which a simple turbulence model is adopted, or full direct numerical simulation (DNS) of the hydrodynamics or magnetohydrodynamics (MHD). In both instances the inclusion of magnetic fields has been troublesome. Also, both approaches have had difficulty reproducing the known angular velocity profile of the SCZ; this is the Taylor Number Puzzle. I discuss preliminary work in which I incorporate magnetic fields into a viscoelastic turbulence model for the SCZ and apply this to the problem of meridional circulation and angular momentum balance. I suggest that such an approach may help solve the Taylor Number Puzzle of the SCZ and bring theoretical predictions for the large-scale motion of the SCZ in line with observations. The Taylor number puzzle is this: in mean-field simulations of the combined system of meridional circulation and rotation of the solar convective zone (SCZ), one may come reasonably close to reproducing the observed rotation profile by making the Taylor number artificially small. If on the other hand one uses realistic values for the Taylor number, the meridional circulation is much larger in magnitude than otherwise. This results in a theoretical angular momentum profile that differs markedly from the observed profile. (Brandenburg et al. 1990) To be fair, the puzzle may have already been solved, at least to a degree. That is because the situation changes if one allows for various mechanisms that create a significant baroclinic vector, as baroclinicity appears as a source term in the meridional circulation. This baroclinicity could be generated by latitudinal variations in the thermal transport, anisotropy of the thermal diffusivity tensor, subadiabaticity of the solar tachocline, or some combination of these effects (Kitchatinov & Rüdiger 1995a,b; Rempel 2005; Meisch et al. 2006). Another possibility is that additional Reynolds stresses due to the anisotropic kinetic alpha (AKA) effect may be important to getting theory to match observation (Rekowski & Rüdiger 1998). Still, I take an alternative point of view that the solution lies in part neither in baroclinicity nor in Reynolds stresses, but in the physics of Maxwell stresses. Here I focus particularly on turbulent Maxwell stresses rather than integral-scale fields. The provenance of the Taylor number is laboratory fluid dynamics. The definition varies, but the most common expression given is that