Linking Lagrangian Acoustic Wave Dynamics via Finite-Time Lyapunov Exponent Fields

摘要

A fundamental assessment of the Finite-Time Lyapunov Exponent (FTLE) approach is carried out to demonstrate a connection between Lagrangian and acoustic waves. The dilatational operator, commonly used to represent acoustic fields in linear regions, is an integral component of the FTLE algorithm and is exposed with the analysis of planar propagating waves. Troughs and peaks in the dilatation contours of single-frequency acoustic (i.e. monopole and quadrupole) fields are captured by the backward- and forward-integrated FTLE coefficients, respectively. A complete reconstruction of the dilatation field is possible by conducting the Lagrangian integration over a single time step at each instance in time. Increasing integration time results in significant differences in amplitude and phase of the FTLE fields, relative to the dilatation. In single-frequency flow fields, an integration time corresponding exactly to the period of oscillation is also shown to result in a near-zero FTLE field. These results confirm the significance of Lagrangian waves resolved in prior analyses of subsonic jet near-fields.