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The investigation of magnetic phenomena on the Sun is confronted with the problem of turbulently moving electrically conducting media in rotating objects. One way of attacking this complicated problem, which was at first successful, was the development of mean-field magnetohydrodynamics, where the cooperative action of the small-scale turbulence was taken into account by certain average effects. The...
We use the latest models of turbulence to compute a new expression for the turbulent convective flux, Fc. The new values of Fc are up to ten times larger than those given by the mixing length theory, MLT. Astrophysical considerations indicate that the new model fares better with observational data than the MLT.
We show that, representing the descending fluid in a convection zone by a porous medium, the differential rotation of the (rising) fluid is very close to that in an axisymmetric model of the convection zone with anisotropic viscosity
In addition to the well-known granulation and supergranulation of the solar convection zone (the “SCZ”), the presence of so-called “giant cells” has been postulated. These are supposed span the entire thickness of the SCZ and to stretch from pole to pole in a sequence of elongated cells like a “cartridge belt” or a bunch of “bananas” strung uniformly round the Sun. Conclusive evidence for the existence...
Thermal convection in the Sun and cool stars is often modeled with the assumption of an effective Prandtl number ≃ 1. Such a parameterization results in masking of the presence of internal shear layers which, for small a, might control the large scale dynamics. In this paper we discuss the relevance of such layers in turbulent convection. Implications for heat transport — i.e. for the Nusselt number...
In order to understand what happens in the Sun when convection overshoots into the radiation zone an idealized model of penetrative convection with rotation is studied. Here we highlight two properties of the model which occur with parameters relevant to the Sun. Firstly rotation allows motions to persist far beneath the convection zone, and secondly the profile of helicity with depth is dominated...
Problems associated with topological pumping in the lower overshoot layer suggest a strongly turbulent and strongly differentially rotating upper radiative zone as the seat of the dynamo and as flux reservoir.
A new method for the calculation of kinetic coefficients is presented. This method allows us to obtain the distribution of scalar and vector fields (such as the temperature, the admixture particle number density and the magnetic field) in turbulent cosmic media with any value of S = uoτro/R0. The explicit expression for the “turbulent” diffusivity DT is...
A direct numerical simulation at resolution 2403 is used to obtain a statistically stationary three-dimensional homogeneous and isotropic turbulent field at a Reynolds number around 1000 (Rλ ≈ 150). The energy spectrum displays an inertial subrange extending over more than one decade. In the physical space, the strongest vorticity is organized in very elongated thin tubes. The typical length...
The generation of magnetic field by a conducting, compressible fluid inside a spherical shell is studied by direct numerical simulations. A pseudo-spectral method is used in order to resolve accurately all the scales present in the problem. The range of parameters considered is the following: a unit Prandtl number, Rayleigh numbers up to 100 times critical, Taylor number 625, an aspect ratio of 2,...
We investigate convective overshoot in a layer of electrically conducting fluid. The radiative conductivity is assumed to be larger in the lower part of the layer which makes it stable to convective motions, yet penetrative convection from the upper layer can occur. The numerical resolution is 633 gridpoints. We observe a dynamo effect for magnetic Reynolds numbers around one thousand when a magnetic...
A magnetic tube is introduced into turbulent compressible penetrative convection. After being strongly advected, most of the magnetic flux is stored in the overshoot region. With rotation there are meridional travelling waves.
The condition for homogeneous radiative stellar models to be marginally stable to convection at the centre is investigated for the family of models where the opacity κ and energy generation ɛ are given by power laws in temperature and density κ = K0 ρα T−β, ɛ = ɛ0 ρ Tη. The Naur-Osterbrock (1953) condition 6η > 6 + 10β - 15α is a necessary but not sufficient condition. A better estimate is obtained...
Three-dimensional hydrodynamic simulations are carried out in a rectangular box. The angle between gravity and rotation axis is kept as an external parameter in order to study the latitude-dependence of convection. Special attention is given to the horizontal Reynolds stress and the Λ-effect (Rüdiger, 1989). The results of the simulations are compared with observations and theory and a good agreement...
A local potential approach to nonlinear dynamo models which allows the use of variational techniques to investigate the problem of stability is introduced. The method applies at least to quasi-kinematic dynamo models, i. e. to models which include the back-reaction of the magnetic field on the fluid motion in a simplified way. A special application leads to a previously investigated one-dimensional...
Recent observations seem to have detected large scale nonaxisymmetric structures on active giant stars. These structures are plausibly associated with underlying, dynamo generated, nonaxisymmetric magnetic fields. Such developments have motivated the development of a computer code to solve the nonlinear mean field dynamo equation in spherical geometry with no imposed geometrical symmetries. The nonlinearity...
We develop a theory of the sunspot cycle predicated on the assumption that the observed bands of activity are packets of dynamo waves. An approximate equation is proposed to describe the dynamics of these packets, using standard ideas from bifurcation theory. We show that in a certain limit the system can be described in terms of a slowlyevolving solitary wave, and that periodic behavior, like that...
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