Stability Analysis of the Flow over a Swept Forward-Facing Step using PIV Base Flowsin a Non-Orthogonal Coordinate System

Understanding the flow of a crossflow-vortex-dominated boundary layer over a forward-facing step excrescence is necessary in order to mitigate an early transition scenario on the wings and tail of commercial aircraft. By performing BiGlobal stability analysis on the flowfield measured with high-resolution, stereographic Particle Image Velocimetry (PIV), previous work has shown that a family of unstable disturbances exists in the direct downstream vicinity of a supercritical, forward-facing step. The goal of the present paper is to improve the previously used stability approach on two fronts: 1) the stability problem is formulated in a non-orthogonal coordinate system and 2) the contribution of the out-of-plane base-flow derivatives is accounted for locally. The resulting eigen solutions feature significantly stronger growth rates and eigenfunctions that are localized above regions of reverse flow. The changes in the problem formulation furthermore establish a significant improvement in the comparison of the stability solutions with the results from the Spectral Proper Orthogonal Decomposition (SPOD) of a time-resolved measurement of the perturbation content. A large destabilizing effect by the out-of-plane base-flow derivatives is determined to be justified, despite the assumption that these derivatives are small, because the effect can be reconstructed upon using an eigenvalue-correction formula that assumes the responsible terms are infinitesimally small. The unstable perturbation mechanisms are demonstrated to have a convective nature by assessing the relation between the frequency and the out-of-plane wavenumber, which indicates that their group speed does not approach zero. The last 2 facts, that 1) the perturbations are convective and 2) that the out-of-plane base-flow-derivative terms are small, remove any qualitative suspicions that the perturbation problem is not conducive to parabolization. This opens the path to analyzing this problem with a plane-marching approach.