Koopman spectral analysis of separated flow over a finite-thickness flat plate with elliptical leading edge

Abstract

The separated flow over an airfoil is characterized by up to three distinct natural frequencies: those of the shear layer, separation bubble, and wake. Previous work has shown that open-loop forcing at sub- and super- harmonics of these frequencies can be especially effective in controlling the extent of the separation bubble. Unfortunately, an understanding of the mechanisms driving this behavior is far from complete. In this work, we investigate the interactions between the shear layer and wake using a combination of direct numerical simulations and spectral analysis. We simulate the forced and unforced flows over a finite-thickness flat plate using an immersed boundary method. Spectral analysis of the resulting dynamics is performed using the Koopman operator, a linear operator applicable even to nonlinear systems, as well as traditional signal processing techniques. Using these two approaches, we identify pertinent flow structures based on their frequency content and posit the nature of their interactions.