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Finite‐time break‐up can occur in any unsteady interacting boundary layer
Author(s) -
Smith F. T.
Publication year - 1988
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/s0025579300015254
Subject(s) - singularity , mathematics , discontinuity (linguistics) , boundary (topology) , bounded function , compressibility , boundary layer , flow (mathematics) , mathematical analysis , type (biology) , work (physics) , nonlinear system , mechanics , geometry , physics , geology , paleontology , quantum mechanics , thermodynamics
Summary This theoretical work shows formally that unsteady interactive boundary layers can break up within a finite time by encountering a nonlinear localized singularity. The theory is an extension of, and is guided to a large extent by, Brotherton‐Ratcliffe and Smith's (1987) work on a special case. Two major types of singularity are proposed, a “moderate” type yielding a singular pressure gradient and a “severe” type associated with a pressure discontinuity. Each type produces a singular response in the skin friction in the case of wall‐bounded flows. The present finite‐time singularity applies to any unsteady interactive flow, e.g. , incompressible or compressible boundary layers, internal flows, wakes, in two or three dimensions; and the singularity and its associated change in flow structure have numerous repercussions, which are discussed, physically and theoretically, concerning boundary‐layer transition in particular.