Analyses de simulations magnétohydrodynamiques du cycle solaire

A large set of global magnetohydrodynamical numerical simulations of the solar convection zone are undertaken in order to understand numerous aspects of the solar dynamo. Motivations behind the research presented here lies with the observation of solar phenomenons, namely the existence of a secondary, short period, solar cycle, the differential rotation in the convection zone, and the pole to equator temperature difference. The thesis is separated in 5 sections : a research paper in which the first phenomenon, appearing in an MHD simulation of the solar convection zone, is investigated, a chapter displaying four typical simulations generated from a benchmarking process between two codes, and a second research paper where the relationship between the differential rotation and the latitudinal gradient is explored in the simulations described in the previous chapter. Additionnally, an introduction to the basics of solar physics, and a conclusion in which ideas to projects related to those presented here are discussed, complete the thesis. The first research paper analyze a global MHD simulation of the solar convection generating regular large-scale magnetic cycles for which a secondary cycle with a short periodicity is detected and characterized. With the help of kinematic mean-field αΩ2 solar dynamo models using the turbulent electromotive force extracted from the global model, we discover that this secondary cycle originates from the joint complexity of this force with the differential rotation, rather than dynamical interactions with the inductive flows. A deeper analysis of the simulation generated from the global model reveals a short cycle signature in the temperature field, consistent with helioseismic signatures. These results support the existence of a secondary dynamo process operating in the upper half of the convection zone. The following chapter focus on the elaboration and analysis of four simulations designed in the context of a large benchmarking exercise between ASH and EULAG models. The simulations are identical one to another, except for the presence or absence of a stable layer underlying the convectively unstable one, and the inclusion (or not) of magnetism. An empirical description of the physical characteristics is given. Surprisingly, the addition of a stable layer has an impact as large as, or even greater than, magnetism on the quasi-equilibrium established within the convection zone. Energy flux through the interface is certainly playing a role in these dynamics. The addition of a stable layer on a simulation containing magnetism triggers transitions in the dynamo regime, these not being explained to this day. The second research paper analyzes the impact of a latitudinal temperature gradient beneath the interface on the differential rotation, this gradient establishing itself naturally in the simulations with a stable layer introduced in the preceding chapter. This gradient breaks the Taylor-Proudman constraint, this being explained by the thermal wind balance equation. The natural establishment of the gradient comes from the rotationally-induced latitudinal dependence of convective energy transport and the low thermal diffusivity characteristics in EULAG simulations. These enable the building up and maintenance of a solar-like differential rotation profile a subset of simulations.

Keyphrases: Dynamo, Sun, Magnetohydrodynamics, Numerical simulations, Solar cycle