  The present paper is about a famous extension of the Prandtl equation, the
so-called Interactive Boundary Layer model (IBL). This model has been used
intensively in the numerics of steady boundary layer flows, and compares
favorably to the Prandtl one, especially past separation. We consider here the
unsteady version of the IBL, and study its linear well-posedness, namely the
linear stability of shear flow solutions to high frequencyperturbations. We
show that the IBL model exhibits strong unrealistic instabilities, that are in
particular distinct from the Tollmien-Schlichting waves. We also exhibit
similar instabilities for a Prescribed Displacement Thickness model (PDT),
which is one of the building blocks of numerical implementations of the IBL
model.
