The effect of compliant walls on three-dimensional primary and secondary instabilities in boundary layer transition

he use of passive devices to obtain drag and noise reductions or transition delays in boundary layers is highly desirable. One such device that shows promise for hydrodynamic applications is the compliant coating. In previous two-dimensional studies with a mechanical model representing the compliant wall, coatings were found that provided significant transition delays. The present study extends the mechanical model to allow for three-dimensional waves. Previous studies were concerned with the initial linear stage of transition. In this study we also look at the effect of compliant walls on three-dimensional secondary instabilities.;For the initial stage of this analysis, two- and three-dimensional primary instabilities propagate over compliant coatings. Results over the compliant walls are compared with the rigid wall case. Three-dimensional instabilities are found to dominate transition over the compliant walls considered. However, transition delays are still obtained compared with transition delay predictions for rigid walls. Other modes of instability--Travelling-Wave Flutter and Static-Divergence--that arise as a result of the wall compliance are shown to remain marginally stable for oblique waves.;In the second stage of this study, the effect of compliant walls on secondary instabilities in boundary layer transition is determined. A theory developed by Herbert to represent secondary instabilities for two-dimensional primary instabilities is extended to allow for three-dimensional waves. The effect of the variation in primary amplitude, spanwise wavenumber, and Reynolds number on the secondary instabilities are examined. Similar to the rigid wall results, the sub-harmonic mode of secondary instability dominates low amplitude disturbances for compliant walls. Both isotropic and non-isotropic compliant walls lead to reduced secondary growth rates compared with the rigid wall results. For fixed properties, the growth rates for oblique waves decrease for the rigid and compliant walls. Two- and three-dimensional...