Role of energy transfers in the dynamo effect: application to the von Kármán flow

Jury

• Yannick PONTY, Directeur de recherche, CNRS, Laboratoire Lagrange Observatoire de la Côte d’Azur
• Nathanaël SCHAEFFER, Chargé de recherche, HDR, CNRS, Laboratoire ISTerre
• Sébastien GALTIER, Professeur à l’Universite Paris-Saclay, Laboratoire de Physique des Plasmas, Ecole polytechnique
• Francky LUDDENS, Maître de conférences à l’Université de Rouen Normandie, Laboratoire de Mathématiques Raphaël Salem

Abstract

In this thesis, the aim is to better understand the dynamo effect that takes place in conducting fluids by studying the various energy transfers in magnetohydrodynamics (MHDMagnétohydrodynamique). Motivated by the observation that dynamo is a conversion mechanism between magnetic and kinetic energy, we develop a new approach to unravel the dynamo mechanism based on local (in space, scale, and time) energy budgets 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.
In order to simulate the MHDMagnétohydrodynamique, we use the SFEMaNS code which is a hybrid method using both a finite element and spectral decomposition. We first present some developments in SFEMaNS: a better repartition of the unstructured mesh on the processors and a study on solving the Navier-Stokes equations using preconditioning matrix methods instead of the current prediction-correction method. Then, we explain how various post-processing tools have been implemented in order to compute, visualize, and study the energy transfers.
Finally, these tools are used to study the von Kármán Sodium setup, 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 kinetic energy both in the bulk and in the vicinity of the impellers, whereas for soft iron impellers, the dynamo effect comes from the impellers. We also discuss possible signatures of precursors to anomalous dissipation and fast dynamo, that could become relevant in the inviscid limit.