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On the nonlinear growth of single three-dimensional disturbances in boundary layers

Smith, FT; (1994) On the nonlinear growth of single three-dimensional disturbances in boundary layers. Mathematika , 41 (1) 1 - 39. 10.1112/S0025579300007178. Green open access

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Abstract

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.

Type: Article
Title: On the nonlinear growth of single three-dimensional disturbances in boundary layers
Open access status: An open access version is available from UCL Discovery
DOI: 10.1112/S0025579300007178
Publisher version: http://dx.doi.org/10.1112/S0025579300007178
Language: English
Additional information: © 1994 Cambridge University Press
Keywords: Incompressible viscous fluids, Boundary-layer separation
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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/82788
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