Cross-frequency amplification of perturbations in a laminar separation bubble using resolvent analysis

Abstract

A large-eddy simulation (LES) of a laminar separation bubble (LSB) induced by an adverse pressure gradient over a flat plate is performed at an inflow displacement-thickness-based Reynolds number of 410 and a free-stream Mach number of 0.25. With a mean peak reverse flow of 21.4%, the bubble sustains self-excited vortex shedding through a local region of absolute instability, in the absence of any external forcing. Spectral proper orthogonal decomposition (SPOD) applied to the LES data identifies three dominant coherent structures within the LSB: two-dimensional and oblique Kelvin--Helmholtz (KH) waves in the separated shear layer at the vortex-shedding frequency, and stationary spanwise-periodic streaks near reattachment at near-zero frequency. Classical resolvent analysis of the mean flow identifies strong convective amplification of the KH waves over a range of spanwise wavenumbers, but predicts only weak amplification in the low-frequency, streak-forming region, where the leading gain is orders of magnitude smaller and no dominant rank-one mechanism is present. This discrepancy with the SPOD energy indicates that the streaks are not sustained by same-frequency linear amplification, but are instead energized by the intrinsic forcing, which the classical framework treats as an unexplained input. Harmonic resolvent analysis of the time-periodic base flow reveals the underlying mechanism: the base-flow unsteadiness couples the oblique KH wave at the shedding frequency to the stationary streak through cross-frequency amplification, yielding a gain far larger than that of the direct same-frequency amplification. This cross-frequency route provides a likely explanation for how the stationary streaks observed near reattachment are energized.