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Weakly nonlinear stability of viscous vortices in three-dimensional boundary layers

journal contribution
posted on 2023-05-18, 18:34 authored by Andrew BassomAndrew Bassom, Otto, SR
Recently it has been demonstrated that three-dimensionality can play an important role in dictating the stability of any Görtler vortices which a particular boundary layer may support. According to a linearized theory, vortices within a high Görtler number flow can take one of two possible forms within a two-dimensional flow supplemented by a small crossflow of size O(Re12 G35), where Re is the Reynolds number of the flow and G the Görtler number. Bassom & Hall (1991) showed that these forms are characterized by O(1)-wavenumber inviscid disturbances and larger O(G15)-wave-number modes which are trapped within a thin layer adjacent to the bounding surface. Here we concentrate on the latter, essentially viscous, vortices. These modes are unstable in the absence of crossflow but the imposition of small crossflow has a stabilizing effect. Bassom & Hall (1991) demonstrated the existence of neutrally stable vortices for certain crossflow/wavenumber combinations and here we describe the weakly nonlinear stability properties of these disturbances. It is shown conclusively that the effect of crossflow is to stabilize the nonlinear modes and the calculations herein allow stable finite-amplitude vortices to be found. Predictions are made concerning the likelihood of observing some of these viscous modes within a practical setting and asymptotic work permits discussion of the stability properties of modes with wavenumbers that are small relative to the implied O(G15) scaling.

History

Publication title

Journal of Fluid Mechanics

Volume

249

Pagination

597-618

ISSN

0022-1120

Department/School

School of Natural Sciences

Publisher

Cambridge Univ Press

Place of publication

40 West 20Th St, New York, USA, Ny, 10011-4211

Rights statement

Copyright 1993 Cambridge University Press

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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