The absolute instability of boundary-layer flow over viscoelastic walls

Abstract

The linear stability of boundary-layer flow over a viscoelastic-layer wall is considered. A companion matrix technique is used to formulate the stability problem as a linear matrix eigenvalue problem for complex frequency and all the eigenvalues may be determined without any initial guess values. The eigenvalues are compared with those obtained with an accurate shooting method. The instability character of the boundary-layer flow is further investigated with the purpose of finding the conditions under which the instability of the flow could become absolute. The mapping technique of Kupfer et al. (1987) is used to identify the occurrence of absolute instability eigenvalues. Absolute instabilities are discovered for cases of soft damped wall over certain ranges of Reynolds number. The effects of wall material stiffness, damping coefficient, thickness of layer, and Reynolds number on the occurrence of absolute instability are examined and presented.