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Complete breakdown of an unsteady interactive boundary layer (over a surface distortion or in a liquid layer)
Author(s) -
Brotherton-Ratcliffe R. V.,
Smith F. T.
Publication year - 1987
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300013322
Subject(s) - inviscid flow , boundary layer , instability , froude number , mathematics , mechanics , flow (mathematics) , boundary (topology) , blasius boundary layer , displacement (psychology) , distortion (music) , work (physics) , nonlinear system , layer (electronics) , boundary layer thickness , classical mechanics , mathematical analysis , geometry , physics , materials science , thermodynamics , amplifier , optoelectronics , cmos , composite material , psychology , quantum mechanics , psychotherapist
Summary It is shown first that internal or external boundary‐layer flow over obstacles or other surface distortions is susceptible to a novel kind of viscous‐inviscid instability, involving growth rates much larger than those of traditional Tollmien‐Schlichting and Gortler modes for instance. The same instabilities arise in liquid‐layer flow at sub‐critical Froude number, and they are associated with an interacting boundary‐layer problem where the normalized pressure is equal to the normalized displacement decrement. Second, certain limiting linear and nonlinear disturbances are studied to shed more light on the overall instability process and each form of disturbance leads to a finite‐time collapse, although different in each case. Thirdly, and in consequence, the work finds the significant feature that the whole interacting boundary layer can break down nonlinearly within a finite scaled time.