The linear stability of flows in curved compliant channels is examined. The walls bounding the fluid are modelled as thin cylindrical shells supported by a rigid outer frame through arrays of springs and dampers; this is often referred to as Kramer-type coating. Sufficiently soft compliant walls have an influence on the large-scale streamwise vortices produced in the channel by the centrifugal force, although the effect is limited to modes of large enough spanwise wavelengths. For even longer wavelengths, a spanwise-periodic surface-based wave precedes the onset of the streamwise vortex instability. Longitudinal or oblique travelling-wave flutter modes may appear and dominate the transition scenario, for sufficiently compliant walls, depending on the receptivity conditions.

The stability of the laminar flow in the narrow gap between infinitely long concentric cylinders, the inner of which rotates, is examined for the case of compliant bounding walls, modelled as thin cylindrical shells supported by rigid frames through arrays of springs and dampers. Sufficiently soft walls have a destabilizing influence on the axisymmetric Taylor vortices produced by the centrifugal force, although the effect is limited to modes with large axial wavelengths. Due to the walls flexibility, hydroelastic modes are generated. Complex modal exchanges are observed, as function of the wall properties and the Reynolds number. For axisymmetric modes an asymptotic analysis is conducted in the limit of small axial wavenumber, to show the correspondence between such exchanges and singularities in the analytical solutions. While the axisymmetric modes dominate the spectrum when the walls are rigid or very mildly compliant, a critical non-zero azimuthal wavenumber exists for which the hydroelastic modes become more unstable. Shorter azimuthal waves are favoured by increasing spring stiffness.