Measurements of 10Be concentration in the Dye 3 ice core show that magnetic cycles persisted throughout the Maunder Minimum, although the Sun's overall activity was drastically reduced and sunspots...

We present the results of a series of numerical experiments that investigate the transport of magnetic —elds by turbulent penetrative compressible convection. We —nd that magnetic —ux is preferentially transported downward out of a turbulent convecting region and stored in a stably strati—ed region below. This pumping mechanism is believed to be a crucial component for the operation of a large-scale solar interface dynamo since it may be responsible for the transport of —ux from the solar convection zone to the stable overshoot region. The high-resolution three-dimensional simulations show that effi- cient pumping occurs as a result of the action of strong coherent down—owing plumes. The properties of the transport are evaluated as a function of magnetic —eld strength, rotation rate, supercriticality, stiÜness of the interface, and con—guration. The turbulent pumping of magnetic —ux is remarkably robust and more efficient than its laminar counterpart. The turbulent convection naturally ampli—es magnetic energy from any existing mean —eld. The transport of —ux from the convection zone removes the source for this local ampli—cation there, and thus the peak magnetic energy also comes to reside in the stable region. This is important for an eÜective interface dynamo. Subject headings: convectionMHDSun: interiorSun: magnetic —elds

We present direct statistical simulation of jet formation on a $\beta$ plane, solving for the statistics of a fluid flow via an expansion in cumulants. Here we compare an expansion truncated at second order (CE2) to statistics accumulated by direct numerical simulations. We show that, for jets near equilibrium, CE2 is capable of reproducing the jet structure (although some differences remain in the second cumulant). However, as the degree of departure from equilibrium is increased (as measured by the zonostrophy parameter), the jets meander more and CE2 becomes less accurate. We discuss a possible remedy by inclusion of higher cumulants.

In this paper, we introduce the concept of direct statistical simulation for astrophysical flows. This technique may be appropriate for problems in astrophysical fluids where the instantaneous dynamics of the flows are of secondary importance to their statistical properties. We give examples of such problems including mixing and transport in planets, stars, and disks. The method is described for a general set of evolution equations, before we consider the specific case of a spectral method optimized for problems on a spherical surface. The method is illustrated for the simplest non-trivial example of hydrodynamics and magnetohydrodynamics on a rotating spherical surface. We then discuss possible extensions of the method both in terms of computational methods and the range of astrophysical problems that are of interest.

Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. We present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through nonlocal spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta plane and show that it is accurate even for a small number of large-scale modes. As GQL is formally linear in the small zonal scales, it allows for the closure of the system and can be utilized in direct statistical simulation schemes that have proved an attractive alternative to direct numerical simulation for many geophysical and astrophysical problems.