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.
The interaction of flow with compliant surfaces is a highly complex phenomenon. In the linear limit of very small disturbances, laminar boundary layers over compliant surfaces are susceptible to a wide variety of instabilities. There is first of all the Tolimien-Schlichting Instabilities (TSI), which is a direct derivative of similar instabilities found in boundary layers on rigid surfaces. On a rigid surface, it is well known that the TSI are the precursors of boundary-layer transition to turbulence. There are also numerous other compliance or wall-related instability modes, known collectively as Compliance-induced Flow Instabilities (CIFO. Among the CIFI, the important instabilities are the Travelling-wave Flutter (TWF) and Static Divergence (SD). TWF may exist when the lowest free surface-wave speed of the compliant wall is less than the free-stream speed of the flow, while SD tends to be important in very soft wall, with a significant degree of material damping; Yeo (1990). On a compliant wall, any of these instabilities can be, a cause of transition to turbulence.
