Effects of wall compliance on the hydrodynamic stability and transition delay of a wall-jet flow

Abstract

The purpose of the present work is to examine the possibility of transition delay in plane wall-jet flows using a compliant surface. Because the wall-jet first becomes unstable with respect to the inflectional type instability, the main focus of the study is concerned with the effect of a compliant wall on the ‘inviscid mode’ of the wall-jet. As a starting point, a simple model of an inviscid shear layer over a compliant surface is analyzed. Unlike the case of a shear layer over a rigid boundary, a surface induced instability may occur, in addition to the existing inviscid type instability. Nevertheless, a set of parameters is found for which the growth rate of both instability modes is completely suppressed. In addition, an exchange between the two modes is found. Similar effects are found in the wall-jet case. Accordingly, a set of optimal surface parameters for which the maximum growth rates of both modes are significantly less than the maximum growth rate of the ‘inviscid mode’ in the case of a rigid wall, is found. Because such sets of optimal parameters can be obtained for the entire range of Reynolds numbers where the ‘inviscid mode’ is the only existing unstable mode in the rigid boundary case, transition delay can be achieved.