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Taylor-Görtler instabilities of Tollmien-Schlichting waves and other flows governed by the interactive boundary-layer equations

  • Philip Hall (a1) and James Bennett (a1)

Abstract

The Taylor-Görtler vortex instability equations are formulated for steady and unsteady interacting boundary-layer flows. The effective Görtler number is shown to be a function of the wall shape in the boundary layer and the possibility of both steady and unsteady Taylor-Görtler modes exists. As an example the steady flow in a symmetrically constricted channel is considered and it is shown that unstable Görtler vortices exist before the boundary layers at the wall develop the Goldstein singularity discussed by Smith & Daniels (1981). As an example of an unsteady spatially varying basic state we also consider the instability of high-frequency large-amplitude two- and three-dimensional Tollmien-Schlichting waves in a curved channel. It is shown that they are unstable in the first ‘Stokes-layer stage’ of the hierarchy of nonlinear states discussed by Smith & Burggraf (1985). This instability of Tollmien-Schlichting waves in an internal flow can occur in the presence of either convex or concave curvature. Some discussion of this instability in external flows is given.

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Taylor-Görtler instabilities of Tollmien-Schlichting waves and other flows governed by the interactive boundary-layer equations

  • Philip Hall (a1) and James Bennett (a1)

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