From irrotational flows to turbulent dynamos

Abstract: Many of the celestial bodies we know are found to be magnetized:the Earth, many of the planets so far discovered, the Sun and other stars,the interstellar space, the Milky Way and other galaxies.The reason for that is still to be fully understood, and this work is meant to be a step in that direction.The dynamics of the interstellar medium is dominated by events likesupernovae explosions that can be modelled as irrotational flows.The first part of this thesis is dedicated to the analysis of some characteristics of these flows, in particular how they influencethe typical turbulent magnetic diffusivity of a medium, and it is shownthat the diffusivity is generally enhanced, except for some specific casessuch as steady potential flows, where it can be lowered.Moreover, it is examined how such flows can develop vorticity when they occur in environments affected by rotation or shear,or that are not barotropic.Secondly, we examine helical flows, that are of basic importance for the phenomenon of the amplification of magnetic fields, namely the dynamo.Magnetic helicity can arise from the occurrence of an instability: here we focus on theinstability of purely toroidal magnetic fields, also known as Tayler instability.It is possible to give a topological interpretation of magnetic helicity.Using this point of view, and being aware that magnetic helicity is a conserved quantity in non-resistive flows,it is illustrated how helical systems preserve magnetic structureslonger than non-helical ones.The final part of the thesis deals directly with dynamos.It is shown how to evaluate dynamo transport coefficients with two of the most commonly used techniques, namely theimposed-field and the test-field methods.After that, it is analyzed how dynamos are affected by advectionof magnetic fields and material away from the domain in which theyoperate.It is demonstrated that the presence of an outflow, likestellar or galactic winds in real astrophysical cases,alleviates the so-calledcatastrophic quenching, that is the damping of a dynamoin highly conductive media, thus allowing the dynamo process to work better.