DYNSEED

The considerable diversity of long-lived magnetic fields observed in the Universe raises fundamental questions regarding their origin. Although it is now widely accepted that such fields are sustained by a dynamo instability in the electrically conducting fluid layers of astrophysical bodies, in most cases the very nature of the flow motions powering the dynamo is essentially unknown. To exhibit a flow capable of amplifying and maintaining a magnetic field is a challenging task: indeed several anti-dynamo theorems forbid the emergence of a dynamo instability out of an infinitesimal magnetic seed field in « too simple » flows (in the sense that they present too many symmetries, either for the fluid motions to sustain a dynamo, or for a magnetic field to be sustained by dynamo action). However, these anti-dynamo theorems do not necessarily extend to the stability of a magnetohydrodynamic (MHD) flow with respect to finite-amplitude dynamo seeds, which on the other hand can now be investigated with mathematical tools stemming from nonlinear variational optimisation. The Direct-Adjoint Looping (DAL) method relies on successive forward and backward time-integration of the system governing equations and their adjoint to optimise fully nonlinear, time-dependent problems. This optimal control method has proved in the last few years to be a powerful ingredient to study the subcritical transition to hydrodynamic turbulence. The present research plan aims at developing the numerical tools required to apply the nonlinear DAL method for the first time to full, unsteady MHD flows. This approach will allow to study minimal dynamo seeds (or in other words, the amplitude and spatial structure of the smallest magnetic legacies that can trigger a subcritical dynamo) in simple swirling flows relevant to stellar systems. Furthermore, nonlinear optimal control will be used as a physical diagnostic to gain novel understanding of the mechanisms that are most favorable to self-sustained dynamo action in astrophysical flows.