Caporn, Paul; (1998) Linear and nonlinear instability of shear driven liquid films. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The governing equations for a high Reynolds number flow in a boundary layer over a film coated wall are derived from the full two dimensional Navier Stokes equations of motion for a two fluid flow. Numerical studies of the properties of the base flow and its stability are described for the case of the flow over an isolated surface roughness on an otherwise fiat surface. Investigations of both short and long obstacles are undertaken in terms of the flow in a viscous-inviscid interaction region. An investigation of strongly non-linear vortex wave interaction in a laminar boundary layer with two pairs of oblique waves is carried out. For a particular choice of flow parameters a resonance is found linking the two pairs of waves, and the governing amplitude equation for the leading order disturbance is derived and investigated. Wave-amplitude equations are derived for the non-linear modulation of Tollmien-Schlichting (TS) type disturbances at high Reynolds numbers. An investigation of the instability of Reynolds-stress generated mean flow to short wavelength secondary disturbances is carried out. A regime with linear TS/capillary wave resonance is examined and the governing amplitude equation for non-linear wave interaction is derived. Two intermediary regimes are also studied. The linear instability of high Reynolds number boundary layer flow over a film-coated wall is studied both numerically and analytically for the practically important limit of high film viscosity. We examine the various instabilities present and relate them to the instability classifications of Benjamin (1963) and Landahl (1962). The work presented in Chapter 4 represents a joint investigation undertaken with Dr S.N. Timoshin and Dr R.I. Bowles and forms the basis of a paper to be published in Proceedings of the Royal Society.

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