# Overview

The solar magnetic field and its variation in time has many consequences for the Sun-Earth Connection. The solar-cycle dependent ultraviolet flux, flares and large-scale magnetic features such as coronal holes, which drives the high speed solar wind, are all related to magnetic activity and have a significant terrestrial impact. The source of this activity is the interior solar magnetic field which is generated by a hydromagnetic dynamo. The key ingredients for the large-scale solar dynamo are turbulent convection influenced by rotation, the resultant differential rotation and the presence of magnetic fields. The generation and maintenance of the observed differential rotation and cyclic magnetic fields, and the appearance of fields at the surface as active regions, are still unsolved problems. The centrality of these issues to solar terrestrial physics is highlighted in Quest I of the NASA SEC Roadmap, and we believe that high-resolution numerical simulations hold the key to future progress. We therefore propose to continue our theoretical studies of turbulent rotating magnetoconvection, presently supported by NASA SPTP grant NAG5--2256, `Turbulent Solar Convection Coupled to Rotation and Magnetic Fields', and now extend them to deal with dynamics within full spherical shells and to address new issues raised by the data.

Less than two decades ago, basic theoretical considerations and low-resolution computations predicted that the solar interior rotation would be in a state with angular velocity $\Omega$ constant on cylinders aligned parallel to the rotation axis. Helioseismic data now reveals that $\Omega$ within the convection zone is constant on radii rather than on cylinders, and that just below the convection zone there is a thin shear layer, now called the tachocline, in which $\Omega$ makes a rapid transition from the differential rotation observed at the surface to nearly solid body rotation in the deeper radiative interior. Moreover, fully self-consistent dynamo models disagreed significantly with major properties of the solar cycle.

Why did such models turn out to be so wrong? The early calculations were necessarily laminar and therefore lacked the influential small-scales. Other solar cycle models circumvented this problem by utilising the mean field $\alpha-\omega$ dynamo formulation, where the expected rotation law was input and the interaction between magnetic fields and convection accounted for by two parameters, but the choice of parameters used had little physical justification. Our high-resolution simulations of rotationally constrained turbulence (obtained in part with SPTP support) reveal the presence of large-scale coherent structures which transport angular momentum and magnetic flux in a novel manner that cannot be simply parameterized or ignored. Continued progress in understanding the dynamics and magnetohydrodynamics of the solar interior must be guided by numerical simulations that can capture turbulent processes including a wide range of scales with some fidelity.

We propose two different types of computations, broadly aimed at understanding the operation of the solar dynamo. For a cyclic dynamo, it is probably essential to model the full spherical geometry of the solar interior, but such simulations cannot resolve the important small scales inherent in turbulence. Simulations of localized parts of the domain, carried out at high resolution, offer better insight into those small-scale effects. We propose an integrated set of problems to be studied by both approaches in a complementary manner. We will use our anelastic spherical harmonic ASH code for global simulations and our spectral finite-difference HPS and AMC codes for local calculations. All three codes were developed with partial SPTP support. We will address two interrelated problem areas:~ $(A)$ origin and maintenance of the differential rotation including the tachocline, and ~$(B)$ dynamo and magnetic flux transport processes near the base of the convection zone, including the formation and subsequent evolution of magnetic flux tubes and their relation to active regions. This work will be relevant to at least two current NASA mission projects, the Solar Oscillations Investigation -- Michelson Doppler Imager (SOI-MDI) experiment on SOHO and the Transition Region and Coronal Explorer (TRACE), which fall under the Campaign on Solar Variability of the SEC Roadmap, and the proposed future missions of Solar-B, Solar Polar Imager, Solar Probe, and STEREO.

# Results of current and previous projects

• Turbulent convection coupled with rotation

• Turbulent convection coupled with magnetic fields