INSTABILITIES IN A HIGH-REYNOLDS-NUMBER BOUNDARY-LAYER ON A FILM-COATED SURFACE

A high-Reynolds-number asymptotic theory is developed for linear insta bility waves in a two-dimensional incompressible boundary layer on a f lat surface coated with a thin film of a different fluid. The focus in this study is on the influence of the film flow on the lower-branch T ollmien-Schlighting waves, and also on the effect of boundary-layer/po tential flow interaction on interfacial instabilities. Accordingly, th e film thickness is assumed to be comparable to the thickness of a vis cous sublayer in a three-tier asymptotic structure of lower-branch Tol lmien-Schlichting disturbances. A fully nonlinear viscous/inviscid int eraction formulation is derived, and computational and analytical solu tions for small disturbances are obtained for both Tollmien-Schlichtin g and interfacial instabilities for a range of density and viscosity r atios of the fluids, and for various values of the surface tension coe fficient and the Froude number. It is shown that the interfacial insta bility contains the fastest growing modes and an upper-branch neutral point within the chosen flow regime if the film viscosity is greater t han the viscosity of the ambient fluid. For a less viscous film the th eory predicts a lower neutral branch of shorter-scale interfacial wave s. The film flow is found to have a strong effect on the Tollmien-Schl ichting instability, the most dramatic outcome being a powerful destab ilization of the flow due to a linear resonance between growing Tollmi en-Schlichting and decaying capillary modes. Increased film viscosity also destabilizes Tollmien-Schlichting disturbances, with the maximum growth rate shifted towards shorter waves. Qualitative and quantitativ e comparisons are made with experimental observations by Ludwieg & Hor nung (1989).