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On the nonlinear growth of single three‐dimensional disturbances in boundary layers
Author(s) -
Smith F. T.,
Stewart P. A.,
Bowles R. G. A.
Publication year - 1994
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/s0025579300007178
Subject(s) - nonlinear system , mathematics , reynolds number , mechanics , amplitude , sideband , flutter , mathematical analysis , geometry , aerodynamics , physics , optics , quantum mechanics , microwave , turbulence
Summary Experiments indicate the importance of three‐dimensional action during transition, while high‐Reynolds‐number‐flow theory indicates a multi‐structured type of analysis. In line with this, the three‐dimensional nonlinear unsteady triple‐deck problem is addressed here, for slower transition. High‐amplitude/high‐frequency properties show enhanced disturbance growth occurring downstream for single nonlinear oblique waves inclined at angles greater than tan −1 √2 (≈54.7°) to the free stream, in certain interesting special cases. The three‐dimensional response there is very ‘spiky’ and possibly random, with sideband instabilities present. A second nonlinear stage, and then an Euler stage, are entered further downstream, although faster transition can go straight into these more nonlinear stages. More general cases are also considered. Sideband effects, sublayer bursting and secondary instabilities are discussed, along with the relation to experimental observations.