Elastic Turbulence: Lagrangian Approach

A new approach to study velocity and acceleration in elastic turbulence in a Lagrangian presentation, i.e. performing velocity measurements at locations moving with the flow along the 3D Lagrangian trajectories, was developed. Such approach applied recently in hydrodynamic turbulence provides both new information about properties of turbulent flow and new opportunities to test recent theoretical predictions about physical phenomena in the Lagrangian picture. So we expect that this approach to a random flow will further elucidate the nature of elastic turbulence, which is one of the examples of a spatially smooth and random in time flow with the spatial velocity field correlated on a vessel size. So, a widely used so-called “Taylor frozen turbulence hypothesis”, which suggests to analyze  the velocity time series taken at a fixed point as a spatial cut through the turbulent field for comparison with theory, does not work well in a smooth, random flow, as we showed some time ago. Thus it is in particular instructive and critical to study this flow in the 3D Lagrangian presentation. We realized this program by using a recently developed digital holographic microscopy, which allows simultaneously characterizing and tracking individual colloidal particles.  By reducing a resolution of the developed technique down to about 0.5 μm, we were able to follow 3D particles position more than 50 μm in the axial direction.