Frameworks for investigation of nonlinear dynamics: Experimental study of the turbulent jet

Abstract

Analysis methods that have been developed in the field of nonlinear dynamics have provided valuable insights into the physics of turbulent flows, although their application to open flows is less well explored. The nonlinear dynamics of a turbulent jet with a low-to-moderate Reynolds number is investigated by using the single-trajectory framework and ensemble framework. We have used Lyapunov exponents to calculate the spectra of scaling indices of the attractor. First, we evaluated the frameworks on two theoretical models, one with a stationary attractor (Lorenz-63) and the other with time-varying characteristics (Lorenz-84). Theoretical studies showed that in dynamical systems with a stable attractor, both frameworks estimated the same largest Lyapunov exponent. The ensemble framework enables us to resolve the unsteady characteristics of a time-varying strange attractor. Second, we applied both frameworks to time-resolved planar velocity fields in a turbulent jet at local Reynolds numbers (Reδ) of 3000 and 5000. Time-resolved particle image velocimetry was utilized to measure streamwise and transverse velocity components. Results support the presence of a low-dimensional attractor in the reconstructed phase space with a chaotic characteristic. Despite considerable changes in the dynamics for the higher Reynolds number case, the system’s fractal dimension did not change significantly. We have used Lagrangian Coherent Structures (LCSs) to study the relationship between changes in the Lyapunov exponent with flow topological features. Results suggest that holes in the stable LCSs provide a path for the entrainment of the coflow, which is shown to be one of the main contributors to high Lyapunov exponents.