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Instabilities in a high-Reynolds-number boundary layer on a film-coated surface

Timoshin, SN; (1997) Instabilities in a high-Reynolds-number boundary layer on a film-coated surface. J FLUID MECH , 353 163 - 195. 10.1017/S0022112097007337. Green open access

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Abstract

A high-Reynolds-number asymptotic theory is developed for linear instability waves in a two-dimensional incompressible boundary layer on a flat 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 Tollmien-Schlighting waves, and also on the effect of boundary-layer/potential flow interaction on interfacial instabilities. Accordingly, the film thickness is assumed to be comparable to the thickness of a viscous sublayer in a three-tier asymptotic structure of lower-branch Tollmien-Schlichting disturbances. A fully nonlinear viscous/inviscid interaction formulation is derived, and computational and analytical solutions for small disturbances are obtained for both Tollmien-Schlichting and interfacial instabilities for a range of density and viscosity ratios of the fluids, and for various values of the surface tension coefficient and the Froude number. It is shown that the interfacial instability contains the fastest growing modes and an upper-branch neutral point within the chosen flow regime if the film viscosity is greater than the viscosity of the ambient fluid. For a less viscous film the theory predicts a lower neutral branch of shorter-scale interfacial waves. The film flow is found to have a strong effect on the Tollmien-Schlichting instability, the most dramatic outcome being a powerful destabilization of the flow due to a linear resonance between growing Tollmien-Schlichting and decaying capillary modes. Increased film viscosity also destabilizes Tollmien-Schlichting disturbances, with the maximum growth rate shifted towards shorter waves. Qualitative and quantitative comparisons are made with experimental observations by Ludwieg & Hornung (1989).

Type: Article
Title: Instabilities in a high-Reynolds-number boundary layer on a film-coated surface
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S0022112097007337
Publisher version: http://dx.doi.org/10.1017/S0022112097007337
Language: English
Additional information: © 1997 Cambridge University Press
Keywords: SHEAR-FLOW INSTABILITY, GAS-LIQUID FLOWS, 2 VISCOUS FLUIDS, FLAT-PLATE, HYDRAULIC JUMPS, ROLL WAVES, BREAK-UP, INTERFACE, STABILITY, WATER
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/70249
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