A general theory for two- and three-dimensional wall-mode instabilities in boundary layers over isotropic and anisotropic compliant walls

An asymptotic theory is developed and applied to two- and three-dimensional disturbances developing in boundary layers over isotropic and anisotropic compliant walls. The theory utilizes the multideck structure of a two- dimensional boundary layer to derive asymptotic approximations at a high Reynolds number for the perturbation wall pressure and viscous stresses. The disturbances can be treated as either temporally or spatially growing. For isotropic compliant walls the theory confirms that the phase shift in the disturbance velocity across the critical layer plays a dominant role in destabilization of the class B traveling-wave flutter by making irreversible energy transfer possible due to the work done by the fluctuating wall pressure. For anisotropic walls an important mechanism for irreversible energy transfer is the work done by the shear stress fluctuations, which almost invariably have a stabilizing effect on the traveling-wave flutter. (S.A.V.)