Relation Between the Finite-Time Lyapunov Exponent and Acoustic Wave

Abstract

The relation between different time scales of the finite-time Lyapunov exponent (FTLE) and the acoustic wave is studied. Gonzalez et al.’s proposition (“Finite-Time Lyapunov Exponent-Based Analysis for Compressible Flows,” Chaos, Vol. 26, No. 8, 2016, Paper 083112), stating that the joint FTLE is equal to dilatation that measures the aeroacoustic waves, is extended. A rigorous mathematical proof is provided for the two-dimensional problem. An analytical sound field induced by a dipole source and a numerical simulated flowfield of an open cavity are used to verify the relation between the FTLE and dilatation. Based on a heuristic analysis and a numerical visualization, it was also found that the long time FTLE has similar patterns to the schlieren and can reveal both the near-field flow structures and the far-field acoustic waves. The work shows that the FTLE can be useful in studying acoustics.