Perry Johnson, Mechanical Engineering
Finite-time Lyapunov exponents (FTLE) offer a rich description of Lagrangian particle trajectories in fluid flows through exploring the exponential rate of divergence for neighboring trajectories. In turbulence flows, which are approximately statistically isotropic at the small-scales relevant to FTLE, the fact that they converge for long time to a non-zero Lyapunov exponents is a leading indicator of chaotic behavior for the particle trajectories. Recently, the notion of Lagrangian Coherent Structures (LCS) has gained attention as a tool for qualitative visualization of flow structures important for mixing processes. LCS visualize repelling and attracting manifolds marked by local ridges in the field of maximal and minimal FTLE, respectively. For small enough particles, FTLE can describe particle deformation, which is useful in the study of droplet deformation as well as polymer additives in turbulent flows. In this work, we demonstrate the use of the Johns Hopkins Turbulence Databases (JHTDB) to explore FTLE in homogeneous isotropic turbulence (HIT). In addition to visualizing LCS for small-scale turbulence at $Re_\lambda$ = 433, we apply the statistical theory of large deviations to characterize the long-time behavior of the probability density function (PDF) for the FTLE. Further, we generalize the large deviations formalism to explore joint-statistics of the FTLE. Finally, we assess the effect of particle rotation by computing FTLE using only the strain-rate. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude and the most likely ratio of FTLEs changes from 4:1:-5 to 8:3:-11, highlighting the role of rotation in de-correlating the fluid deformations along particle paths.