Study of the transfer between helicity components in vortex ring configurations

The present master’s thesis has the aim to implement and study vortex ring configurations with the objective to characterise the evolution of their helicity content, constituting a relatively controversial dynamic quantity. That work has been carried out within the continuity of previous master’s theses tackling vortex rings evolutions, led within the Thermodynamics and Fluid Mechanics (TFL) pole of UCLouvain. First, the framework of the present work is delineated. Dynamic quantities of interest are presented and defined, and helicity is introduced as a combination of three storage modes. The study of the possible transfer from one mode to another is then undertaken. The final objective is indeed to identify the relative stability of each mode, the exchanges between them and the potential ability for helicity to be conserved. The three main chapters of the document thus tackle the investigation of the three constituting storage modes. Then, a chapter is dedicated to the gathering of the obtained results as a manner to describe the interactions between the helicity contents and compare them. Finally, the point of view of the knot theory is embraced, as a tool to further analyse and describe the topologies adopted by the various initiated structures, as well as the contribution of the topology in the protection of the helicity from viscosity. The appendices describe the implementation of the main tools developed as a part of the present investigation.