The Linear Stability of Boundary-Layer Flow over Compliant Walls-The Effects of the Wall Mean State, Induced by Flow Loading

Abstract

This paper is concerned with the linear hydrodynamic stability of boundary-layer flow over a compliant wall subjected to steady-state stresses on its surface. Surface stress loading induces an equilibrium state of stress and strain in the compliant wall, termed the wall mean (basic) state. Flow stability is affected by the surface loading, as a result of an interaction between the propagating wall perturbation and the induced wall mean state. This perturbation-mean state interaction in the wall is accounted for in this paper by the application of a nonlinear elasticity theory, suitably linearized about the mean state, in which the compliant material is assumed to obey a linear isotropic (stress-strain) law between the second Piola-Kirchoff stress tensor and the Green strain tensor. Surface loading due to combine hydrostatic pressure and boundary-layer viscous shear is considered. It is found that hydrostatic pressure can strongly affect the stability of flow over compliant walls; with a stabilizing influence on the Tollmen-Schlichting instabilities and a destabilizing influence on the compliance-related instabilities. The underlying mechanics for both incompressible compliant layers are explained. The present study shows that the pressure of the operational environment should be taken into account when evaluating the performance of compliant coatings as transition-delaying or noise-reducing devices in underwater applications. © 1994 Academic Press. All rights reserved.