The response of an incompressible, viscoelastic coating to pressure fluctuations in a turbulent boundary layer

Abstract

The response of the interface between a compliant surface and a turbulent boundary-layer flow is examined theoretically. This response is forced by transient, convected, interfacial pressure pulses that represent the footprints of turbulent flow structures in the boundary layer. Calculations are presented for coatings with a wide range of damping and densities equal to the density of the flow. For coatings with moderate damping, three regimes of response are found. When the flow speed U∞ is less than about 1.2 (non-dimensionalized by the shear wave speed of the coating), the response is stable and primarily localized under the pressure pulse. For flow speeds from 1.2 to as high as 2.8, depending on the damping, the response is also stable, but it includes a wave pattern behind the pressure pulses. For flow speeds above 2.8, the response is unstable and eventually forms a two-dimensional wavetrain moving in the flow direction. At the highest stable flow velocity, the amplitude of the surface displacements reaches 4.0% of the boundary-layer displacement thickness δ* and the energy transfer from the pressure pulse reaches 5.0 × 10−4 U∞2 (δ*)2. For high damping, the coating response is again stable when the flow speed is below 2.8. However, there is no wavelike response regime; the path that is traversed by the pressure pulse is covered by a scar that heals according to the viscous relaxation properties of the material. The amplitude of the response is at most 0.01δ*.