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On the starting process of strongly nonlinear vortex/Rayleigh-wave interactions

BROWN, PG; BROWN, SN; SMITH, FT; TIMOSHIN, SN; (1993) On the starting process of strongly nonlinear vortex/Rayleigh-wave interactions. MATHEMATIKA , 40 (1) 7 - 29. 10.1112/S0025579300013693. Green open access

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Abstract

An oncoming two-dimensional laminar boundary layer that develops an unstable inflection point and becomes three-dimensional is described by the Hall-Smith (1991) vortex/wave interaction equations. These equations are now examined in the neighbourhood of the position where the critical surface starts to form. A consistent structure is established in which an inviscid core flow is matched to a viscous buffer-layer solution where the appropriate jump condition on the transverse shear stress is satisfied. The final result is a bifurcation equation for the (constant) amplitude of the wave pressure. A representative classical velocity profile is considered to illustrate solutions of this equation for a range of values of the wave-numbers.

Type: Article
Title: On the starting process of strongly nonlinear vortex/Rayleigh-wave interactions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1112/S0025579300013693
Publisher version: http://dx.doi.org/10.1112/S0025579300013693
Language: English
Additional information: © 1993 Cambridge University Press
Keywords: BOUNDARY-LAYER-TRANSITION, TOLLMIEN-SCHLICHTING WAVES, LONGITUDINAL VORTICES, CHANNEL FLOWS
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/70257
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