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The effect of wall cooling on compressible Görtler vortices

Elliott, John W.; Bassom, Andrew P.


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Dr John Elliott
Lecturer in Mathematics/ Admissions officer

Andrew P. Bassom


It is known that in adiabatic boundary layer flow over a curved surface the detailed structure of the spanwise periodic Gortler vortex instability varies markedly over the range of spanwise wavelength. At short wavelengths the modes tend to be concentrated in a well-defined thin zone located within the boundary layer. As the vortex wavenumber diminishes so the region of vortex activity is first driven to the bounding wall but subsequently expands to cover the entire boundary layer at which stage the modes take on a principally inviscid form. At yet longer wavelengths the vortices are given by the solution of an interactive multi-deck structure which has some similarities with that for Tollmien-Schlichting waves. In this work we investigate how the application of wall cooling affects the above scenario. It is shown how cooling both restricts the range of mode types and gives rise to two new structures. The first, for moderate cooling and which relates to longer wavelengths, is interactive in nature. Here the viscous-inviscid interaction between an essentially inviscid Gortler problem, albeit for an effective basic flow which in its general form has a non-standard near-wall structure, and a viscous sublayer is provided by novel boundary conditions. Shorter wavelength vortices are largely unaffected by wall cooling unless this is quite severe. However when this degree of cooling is applied, the vortices take on a fully viscous form and are confined to a thin region next to the bounding wall wherein the basic flow assumes an analytic form. Numerical solutions are obtained and we provide evidence as to how the two new structures are related both to each other and to the previously known uncooled results.


Elliott, J. W., & Bassom, A. P. (2000). The effect of wall cooling on compressible Görtler vortices. European Journal of Mechanics - B/Fluids, 19(1), 37-68.

Journal Article Type Article
Acceptance Date Jul 29, 1999
Online Publication Date Feb 7, 2000
Publication Date 2000-01
Print ISSN 0997-7546
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 19
Issue 1
Pages 37-68
Keywords Stability of Fluid Flow
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