Lagrangian and Eulerian signatures of inertio-elastic instabilities and turbulence in polymer jets*

We report on the spatiotemporal evolution of flow structures in a jet of dilute polymer solution entering a quiescent bath of Newtonian fluid. High-speed digital Schlieren imaging and laser Doppler velocimetry are used to study the Lagrangian and Eulerian signatures of the onset of inertio-elastic instabilities and the subsequent transition to a turbulent flow state. Applying Dynamic Mode Decomposition to the Schlieren images reveals the dominant inertio-elastic instability modes and their dependence on elasticity number and polymer extensibility. The advective growth of these inertio-elastic modes results in the jet transitioning to a state of elasto-inertial turbulence (EIT). Velocity measurements at fixed Eulerian locations along the center line of the jet show that EIT is characterized by a dramatic decrease in turbulence intensity with a distinctly different power-law spectrum as compared to a turbulent Newtonian jet.