Global instability in the onset of transonic-wing buffet

Global stability analysis is used to analyse the onset of transonic buffet on infinite swept and unswept wings. This high-Reynolds-number flow is governed by the unsteady Reynolds averaged Navier–Stokes equations. The analysis generalizes earlier studies focused on two-dimensional airfoils. For the unswept wing, results show spanwise-periodic stationary modes in addition to the earlier-observed oscillatory mode. The oscillatory mode is nominally two-dimensional with a spanwise wavelength greater than ten wing chords. The stationary modes of instability exist over two bands of spanwise wavelengths centred around an intermediate wavelength of one wing chord, and around a short wavelength of one tenth of a wing chord. The intermediate-wavelength modes have a flow structure characteristic of airfoil buffeting modes, concentrated at the shock and in the shear layer downstream of the shock. The short-wavelength modes are only concentrated in the shear layer downstream of the shock. These stationary modes can lead to spanwise-periodic flow structures for the unswept wing. For the swept wing, these stationary modes become unsteady travelling modes and contribute to the more complex buffeting-flow structures observed on swept wings as compared with unswept wings. The spanwise-wavelength bands of the travelling modes translate to different frequencies, resulting in a broad-banded unsteady response for the swept wing. For a swept wing, the frequencies associated with the intermediate-wavelength modes are approximately 10 times higher than the swept-wing generalization of the long-wavelength oscillatory mode, and approximately 6 times higher than the long-wavelength mode for the unswept wing. These instability characteristics are in good agreement with experimental observations.