The dynamics of the interstellar medium is dominated by events like supernovae explosions that can be modelled as irrotational flows. The first part is dedicated to the analysis of some characteristics of these flows, in particular how they influence the typical turbulent magnetic diffusivity of a medium, and it is shown that the diffusivity is generally enhanced, except for some specific cases such 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 the instability 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 structures longer 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 the imposed-field and the test-field methods. After that, it is analyzed how dynamos are affected by advection of magnetic fields and material away from the domain in which they operate. It is demonstrated that the presence of an outflow, like stellar or galactic winds in real astrophysical cases, alleviates the so-called catastrophic quenching, that is the damping of a dynamo in highly conductive media, thus allowing the dynamo process to work better.
