Linear stability of boundary-layer flow over compliant walls. Effects of wall mean state

Abstract

This paper examines the linear stability of boundary-layer flow over compliant surfaces or coatings subject to significant flow loading. To take into account the interaction between the initial stress and deformation state of the wall (which is in static equilibrium with the mean flow) and the small perturbation, the classical theory of nonlinear elasticity is used, in which the properties of the compliant wall material are prescribed by a linear isotropic law between the second Piola-Kirchoff stress tensor and the Green strain tensor. Results obtained show that hydrostatic pressure loading can strongly influence the stability of flow over compliant surfaces, and should be taken into account when evaluating the performance of compliant coatings as transition-delaying or noise-reducing devices in underwater applications.