Lagrangian approach for modal analysis of fluid flows

Common modal decomposition techniques for flowfield analysis, data-driven modeling and flow control, such as proper orthogonal (POD) dynamic mode (DMD) are usually performed in an Eulerian (fixed) frame of reference with snapshots from measurements or evolution equations. The description poses some difficulties, however, when the domain mesh deforms time as, example, fluid-structure interactions. For cases, we first formulate a Lagrangian analysis (LMA) ansatz by posteriori transforming fields into maps through orientation measure-preserving diffeomorphism. development is then verified variants POD DMD using direct numerical simulations (DNS) two canonical configurations at Mach 0.5, lid-driven cavity past cylinder, representing internal external flows, respectively, pre- post-bifurcation Reynolds numbers. LMA demonstrated several situations encompassing unsteady without boundary deformation well non-uniform base flows that steady but not frames. We show application to nonuniform yields insights stability dynamics. naturally leads coherent structures connections finite-time Lyapunov exponents (FTLE). examine mathematical link between FTLE considering double-gyre pattern. Dynamically important features sense recovered performing forward backward (adjoint) procedures.