Recent theoretical findings show that the curvature of streamsurfaces naturally warping in the crossflow direction of a three-dimensional boundary layer can maintain centrifugal forces, provoking unsteady short-scaled vortices. The wave/vortex eigenmode coupling takes place in the linear stage of disturbance evolution and results in streamwise absolute instability. The two-dimensional flow past a curved cylindrical surface under consideration here provides an example where centrifugal forces are associated with the fixed curvature of a solid wall bending in the direction of the main stream. The spiral-type Görtler vortices develop in proximity to the surface and their interaction with the Tollmien–Schlichting eigenmodes creates a mechanism driving disturbances both downstream and upstream of a perturbing agency. The vortex eigenmodes arising from centrifugal forces are balanced out by the normal-to-wall pressure gradient. Some higher-order terms need to be kept in its expansion to achieve the modal coupling. As a consequence, a side band appears in the spectra of eigen-frequencies and wavenumbers featuring the classical triple-deck scheme. The extended composite asymptotic model proves to be self-consistent, with the Cauchy problem well-posed in the limit of large Reynolds numbers. It follows from the extended model that the boundary layer on a concave surface, much like the one with crossflow, suffers absolute instability in the streamwise direction. This unusual property may lead to earlier transition or, conversely, be exploited to artificially excite the nonlinear vortex structures with delayed transition.