Turbulent flows at low Reynolds number

Supervisors: Anke Lindner (PMMH) and Sandra Lerouge (MSC)

In inertia-driven Newtonian fluids, the transition from laminar to turbulent flow in curved geometries is a well-established cascade of bifurcations, beginning with primary instabilities and leading to complex secondary flow structures. Analogously, over the past two decades, the study of viscoelastic fluids has revealed a distinct chaotic state known as elastic turbulence (ET), which is driven purely by fluid elasticity at negligible inertia. This phenomenon has been observed in various systems, from dilute polymer solutions to semi-dilute wormlike micelles. In this thesis, we present a comprehensive experimental study of the transition to and the statistical properties of elastic turbulence in two canonical viscoelastic flow systems. For micellar solutions in Taylor-Couette flow, we identify two distinct transition pathways to ET by varying the geometric curvature, leading to the construction of a universal state diagram. A statistical analysis of this turbulent  state reveals a multi-scaling energy cascade with intermittency. For dilute polymer solutions in von Kármán swirling flow, we fundamentally revise the base flow picture, showing it to be a competition between an inertia-driven central vortex and an elasticity-driven peripheral vortex. This two-vortex structure dictates a complex sequence of bifurcations leading to ET. We further characterize the statistical properties of this turbulent state, discovering the existence of elastic subrange and the strong intermittency. This work provides a unified framework for understanding the intricate interplay between fluid elasticity, geometry, and flow structure, paving the way for a deeper theoretical understanding of non-Newtonian turbulence.