Tracking dynamo mechanisms from local energy transfers: Application to the von Kármán sodium dynamo

Motivated by the observation that dynamo is a conversion mechanism between kinetic and magnetic energy, we develop a new approach to unravel dynamo mechanism based on local (in space, scale, and time) energy budget describing dissipation and scale-by-scale energy transfers. Our approach is based upon a new filtering approach that can be used effectively for any type of meshes, including unstructured ones. The corresponding formalism is very general and applies to any geometry or boundary conditions. We further discuss the interpretation of these energy transfers in the context of fast dynamo and anomalous dissipation. We apply it to the results from direct numerical simulations of the von Kármán Sodium setup (referred to as VKS) using a finite element code, showing dynamo action for two types of impellers (steel or soft iron) in the magnetic field growth and saturation phases. Although the two types of dynamo hardly differ from the mean-field theory point of view (the velocity fields are the same in both cases), the locality of our formalism allows us to trace the origin of the differences between these two types of dynamo: for steel impellers, the dynamo is due to the transfer of velocity energy both in the bulk and in the vicinity of the impellers, whereas for soft iron impellers, the dynamo effect mainly comes from the rotation of the blades. We finally discuss possible signatures of precursors to anomalous dissipation and fast dynamo, which could become relevant in the inviscid limit.