THE ABSOLUTE AND CONVECTIVE INSTABILITIES OF BOUNDARY-LAYER FLOWS OVER COMPLIANT WALLS

Abstract

The absolute instabilities of modified potential and boundary-layer flows over viscoelastic compliant walls have been studied numerically. The Chebyshev collocation method and companion matrix procedure are employed to produce a generalized linear eigenvalue problem, for which QZ algorithm may be applied directly to determine all the temporal eigenvalues. The occurrence of absolute instability is detected using a mapping technique based on an asymptotic spatio-temporal interpretation of wave evolution. Absolute instability is found to occur on compliant walls with low stiffness and high levels of material damping. It is produced by the coalescence of eigenmodes from different wave classes. The study shows that the instability of a uniform potential flow over a viscoelastic compliant wall is always absolute. Laminar and turbulent boundary-layer flows admit both convective and absolute instabilities. The onset velocity of convective instability in a turbulent flow approaches the onset value of absolute instability at high levels of wall damping, but this is not the case for a laminar flow. The absolute instabilities of spanwise-periodic three-dimensional waves are also investigated for the purpose of making a qualitative assessment of the relative importance of two-dimensional and three-dimensional disturbance modes.