We study convective overshooting by means of local 3D convection calculations. Using a mixing length model of the solar convection zone (CZ) as a guide, we determine the Coriolis number (Co), which is the inverse of the Rossby number, to be of the order of ten or larger at the base of the solar CZ. Therefore we perform convection calculations in the range Co = 0. . .10 and interpret the value of Co realised in the calculation to represent a depth in the solar CZ. In order to study the dependence on rotation, we compute the mixing length parameters αT and αu relating the temperature and velocity fluctuations, respectively, to the mean thermal stratification. We find that the mixing length parameters for the rapid rotation case, corresponding to the base of the solar CZ, are 3-5 times smaller than in the nonrotating case. Introducing such depth-dependent α into a solar structure model employing a non-local mixing length formalism results in overshooting which is approximately proportional to α at the base of the CZ. Although overshooting is reduced due to the reduced α, a discrepancy with helioseismology remains due to the steep transition to the radiative temperature gradient.

In comparison to the mixing length models the transition at the base of the CZ is much gentler in the 3D models. It was suggested recently (Rempel 2004) that this discrepancy is due to the significantly larger (up to seven orders of magnitude) input energy flux in the 3D models in comparison to the Sun and solar models, and that the 3D calculations should be able to approach the mixing length regime if the input energy flux is decreased by a moderate amount. We present results from local convection calculations which support this conjecture.

A random superposition of waves in a rotating, stratified, electrically conducting fluid leads to dynamo action in the sense that it yields a mean electric field having a component parallel to the mean magnetic field (‘α-effect’). Using Fourier analysis methods, we derive an explicit expression for the mean electric field. The α-effect has tensor form. We obtain a finite α-tensor even in a case of vanishing mean helicity. The result is discussed in the context of the solar turbulent dynamo.

The focus of Commission 12 is on the solar interior, on global phenomena of the quiet Sun, and on the Sun’s radiative outputs, both spectral and total. These are the topics treated below in our discussion of Scientific Highlights. The many topics having to do with solar activity at photospheric to coronal levels, are dealt with in the report by Commission 10, while the report of Commission 49 describes research on the solar wind and interplanetary medium.

Convection consists of rising hot and descending cool parcels of gas. In order to assess the effect of such an in homogeneity on acoustic waves a simple model has been proposed by Zhugzhda and Stix (1994). The model consists of a sequence of alternating vertical layers with temperatures T1 and T2 and upward and downward velocities V1 and V2. At the interfaces between the layers the horizontal component of the velocity and the pressure are continuous. This model allows to determine the phase velocity of a vertically propagating acoustic wave. The main result is that, with increasing frequency, this phase velocity approaches the sound speed of the cooler layers. The reason of such a behavior is that the horizontal structure of the wave is oscillatory in the cool layers, but exponential (evanescent) in the hot layers, so that there is a certain amount of wave trapping in the cool layers. An analogous effect of trapping in a horizontal layer has been described by Kahn (1961) for the temperature minimum of the solar atmosphere.

Traditionally the theory of the solar dynamo has been divided into two parts. The first, more difficult part, is the derivation of equations governing the mean magnetic field; the second, easier, is the solution of this equation, and the interpretation of the result in terms of observed solar magnetism. This report follows the traditional division.

The differential equations describing stellar oscillations are transformed into an algebraic eigenvalue problem. Frequencies of adiabatic oscillations are obtained as the eigenvalues of a banded real symmetric matrix. We employ the Cowling-approximation, i.e. neglect the Eulerian perturbation of the gravitational potential, and, in order to preserve selfadjointness, require that the Eulerian pressure perturbation vanishes at the outer boundary. For a solar model, comparison of first results with results obtained from a Henyey method shows that the matrix method is convenient, accurate, and fast.

The purpose of theoretical work is twofold: we want to understand physical mechanisms — and we want to predict numbers which can be compared with observations. In the field of solar and stellar magnetism much of the work still belongs to the first category.

We extend to the lower main sequence stars the analysis of convection interacting with rotation in a compressible spherical shell, already applied to the solar case (Belvedere and Paterno, 1977; Belvedere et al. 1979a). We assume that the coupling constant ε between convection and rotation, does not depend on the spectral type. Therefore we take ε determined from the observed differential rotation of the Sun, and compute differential rotation and magnetic cycles for stars ranging from F5 to MO, namely for those stars which are supposed to possess surface convection zones (Belvedere et al. 1979b, c, d). The results show that the strength of differential rotation decreases from a maximum at F5 down to a minimum at G5 and then increases towards later spectral types. The computations of the magnetic cycles based on the αω-dynamo theory show that dynamo instability decreases from F5 to G5, and then increases towards the later spectral types reaching a maximum at MO. The period of the magnetic cycles increases from a few years at F5 to about 100 years at MO. Also the extension of the surface magnetic activity increases substantially towards the later spectral types. The results are discussed in the framework of Wilson’s (1978) observations.

In this paper solutions of the mean field induction equation in a spherical geometry are discussed. In particular, the 22-year solar magnetic cycle is considered to be governed by an axisymmetric, periodic solution which is antisymmetric with respect to the equatorial plane. This solution essentially describes flux tubes travelling as waves from mid-latitudes towards the equator. In a layer of infinite extent the period of such dynamo waves solely depends on the strength of the two induction effects, differential rotation and α-effect (cyclonic turbulence). In a spherical shell, however, mean flux must be destroyed by turbulent diffusion, so the latter process might actually control the time scale of the solar cycle.

A special discussion is devoted to the question of whether the angular velocity increases with increasing depth, as the dynamo waves seem to require, or whether it decreases, as many theoretical models concerned with the Sun's differential rotation predict. Finally, theories for the sector structure of the large scale photospheric field are reviewed. These describe magnetic sectors as a consequence of the sectoral pattern in the underlying large scale convection, as non-axisymmetric solutions of the mean field induction equation, or as hydromagnetic waves, modified by rotational effects.