Linear stability of non-parallel boundary-layer flow over compliant walls subjected to fluid loading

Abstract

In this paper, the effects of wall's mean state (induced by fluid loading) on the linear stability of non-parallel boundary-layer flow over compliant surfaces is being studied. This study is concerned with the spatial evolution of such wavy disturbance taking into account the slow variation of the boundary-layer velocity profile in the streamwise direction. Purely non-parallel effects on the flow stability over compliant surfaces (without wall's mean state effects) has been studied by Chong, Yeo and Khoo. Classical nonlinear elastodynamic theory is used to account for the interaction between the mean stressed state of the compliant layer and propagating perturbations. A formulation based on the symmetric second Piola-Kirchoff stress tensor and the Green strain tensor is used here. A multiple-scale perturbation approach is adopted in which the perturbation quantities of the flow and the wall are expanded in powers of the small parameter.