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Singular modes in Rayleigh instability of three-dimensional streamwise-vortex flows

Timoshin, SN; Smith, FT; (1997) Singular modes in Rayleigh instability of three-dimensional streamwise-vortex flows. J FLUID MECH , 333 139 - 160. 10.1017/S0022112096004181. Green open access

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Abstract

The upper-branch neutral modes of inviscid instability in a boundary-layer flow with significant longitudinal vortices present are shown to possess typically a logarithmically singular, non-inflectional, critical layer. This contrasts with previous linear and nonlinear suggestions implemented in vortex-wave interaction and secondary instability theories, which are re-examined. The analysis here is based first on perturbation techniques applied to a Rayleigh unstable planar motion supplemented by a vortex centred around the inflection level, followed by the extension to more general cases. Flows with order one and larger spanwise scales are considered. Multiple solutions, their limit properties and parametric continuations are illustrated with concrete examples.

Type: Article
Title: Singular modes in Rayleigh instability of three-dimensional streamwise-vortex flows
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S0022112096004181
Publisher version: http://dx.doi.org/10.1017/S0022112096004181
Language: English
Additional information: © 1997 Cambridge University Press
Keywords: INVISCID SECONDARY INSTABILITY, BOUNDARY-LAYERS, NONLINEAR DEVELOPMENT, WAVE INTERACTIONS, VORTICES, DISTURBANCES, TRANSITION
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/82779
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