The Turbulent Energy Cascade in Dilute Polymer Solutions

This thesis reports experimental measurements of turbulent flow in water and dilute solutions of high molecular weight polyacrylamide. We use three-dimensional Particle Tracking Velocimetry to measure the trajectories of tracer particles and infer their velocity and acceleration. Turbulence is generated in a von Karman swirling flow whose properties are calibrated in pure water to form a baseline for comparison. We report measurements of Eulerian and Lagrangian structure functions, Lagrangian acceleration correlations, as well as multiparticle pair dispersion rates at a Taylor-microscale Reynolds number of 420 and Weissenberg number 2.8 over polymer concentrations ranging from 1 to 20 parts per million by weight. In all cases, we find a suppression of small-scale fluctuations consistent with the predictions of an existing model based on a modification of the energy flux through the turbulent energy cascade. However our data also point to the existence of a critical concentration between 5 and 10 p.p.m. separating the effects we observe into two categories. We propose a conjecture for the origin of this concentration based on a dynamic version of the overlap concentration.;A core assumption behind the model we test is based on the geometry of polymer extension in turbulent flow. As a first step towards understanding the deformation of small fluid elements in three-dimensional turbulence, we present an experimental investigation of the shape dynamics of Lagrangian clusters in a chaotic two-dimensional flow. We computed the statistics of ensembles of virtual Lagrangian points evolving from various initial shapes. Our results are systematically compared with their counterpart in a diffusion model to emphasize the non-trivial shape deformation caused by chaotic flow. We focus in particular on the role played by stagnation points in the initial deformation of material volumes, and discuss the implications of these findings for polymer solutions.