
University of Helsinki, Helsinki 2006 Local numerical modelling of magnetoconvection and turbulence  implications for meanfield theoriesPetri KäpyläDoctoral dissertation, October 2006. During the last decades meanfield models, in which largescale magnetic fields and differential rotation arise due to the interaction of rotation and smallscale turbulence, have been enormously successful in reproducing many of the observed features of the Sun. In the meantime, new observational techniques, most prominently helioseismology, have yielded invaluable information about the interior of the Sun. This new information, however, imposes strict conditions on meanfield models. Moreover, most of the present meanfield models depend on knowledge of the smallscale turbulent effects that give rise to the largescale phenomena. In many meanfield models these effects are prescribed in ad hoc fashion due to the lack of this knowledge. With large enough computers it would be possible to solve the MHD equations numerically under stellar conditions. However, the problem is too large by several orders of magnitude for the present day and any foreseeable computers. In our view, a combination of meanfield modelling and local 3D calculations is a more fruitful approach. The largescale structures are well described by global meanfield models, provided that the smallscale turbulent effects are adequately parameterized. The latter can be achieved by performing local calculations which allow a much higher spatial resolution than what can be achieved in direct global calculations. In the present dissertation three aspects of meanfield theories and models of stars are studied. Firstly, the basic assumptions of different meanfield theories are tested with calculations of isotropic turbulence and hydrodynamic, as well as magnetohydrodynamic, convection. Secondly, even if the meanfield theory is unable to give the required transport coefficients from first principles, it is in some cases possible to compute these coefficients from 3D numerical models in a parameter range that can be considered to describe the main physical effects in an adequately realistic manner. In the present study, the Reynolds stresses and turbulent heat transport, responsible for the generation of differential rotation, were determined along the mixing length relations describing convection in stellar structure models. Furthermore, the alphaeffect and magnetic pumping due to turbulent convection in the rapid rotation regime were studied. The third area of the present study is to apply the local results in meanfield models, which task we start to undertake by applying the results concerning the alphaeffect and turbulent pumping in meanfield models describing the solar dynamo. The title page of the publication
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