This work is concerned with the laminar–turbulent transition in the boundary layer on an aircraft wing covered by a water film. We consider the initial stage of the transition process known as the receptivity of the boundary layer, namely, we study the generation of the interfacial instability waves by the unsteady free-stream acoustic noise interacting with a small roughness on the wing surface. For effective receptivity, the ‘forcing’ should obey the so-called ‘double-resonance’ principle. According to this principle, both the frequency and the wavenumber of the external perturbations should be in tune with the natural instability modes of the flow. Correspondingly, we choose the frequency of the acoustic wave to coincide with that of the interfacial instability wave. However, this makes the wavelength of the acoustic wave significantly larger than wavelength of the instability wave. Thus, the second resonance condition is not satisfied, which means that the acoustic wave alone cannot produce the instability waves in the boundary layer. Instead, the Stokes layer is created in the boundary layer just above the liquid film. As far as the film is concerned, it also experiences wave-like motion caused by the varying shear stress on the interface. The generation of the interfacial instability waves takes place when the Stokes layer encounters a wall roughness that is short enough for an appropriate scale conversion to take place. To describe the flow in the vicinity of the roughness, a suitably modified triple-deck theory is used.

In this paper we study the generation of Tollmien–Schlichting waves initiated by vibrations of a wall where the wall is coated with a thin liquid film in a transonic flow regime. Motion of fluids are described by the two-dimensional Navier–Stokes equations assuming the Reynolds number is large. To find asymptotic solutions of the transonic boundary layer, we conduct an inspection analysis on the affine transformations of the triple-deck model for a subsonic flow and the unsteady full potential equations, with the intention of obtaining the order quantity of the free-stream Mach number in the transonic flow. We construct a modified triple-deck model for the transonic flow by considering the scalings of the perturbations that lead to the viscous–inviscid interaction problem for the flow in a subsonic regime. In particular, we are interested in the region where the subsonic scalings become invalid as the flow approaches transonic regime. We assume the wall oscillates in the vertical direction to the oncoming flow and these vibrations are periodic in time. We outline the process where the flow in the boundary layer converts the wall vibration perturbations into the instability modes which are measured by the receptivity coefficient. The viscous–inviscid interaction problem describes the stability of the boundary layer on the lower branch of the neutral curve. We show that the governing equations for the air viscous sublayer and the film flow are quasi-steady. The equation describing the inviscid layer of the airflow is unsteady and its referred to as the unsteady Kàrmàn–Guderley equation. The influence of the film surface tension is expressed through normal shear stress condition at the interface. We present an analytic formula for the amplitude of the Tollmien–Schlichting waves that are formed in the boundary layer. We analysed our model with different values of surface tension, initial film thickness and Kàrmàn–Guderley parameter. Depending on the value of these parameters, the initial amplitude of the instability waves may grow or decay.