Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-19T09:58:59.153Z Has data issue: false hasContentIssue false
  • English
  • Français

Streamwise vortices in heated boundary layers

Published online by Cambridge University Press:  26 April 2006

Philip Hall
Philip Hall
Affiliation:
Department of Mathematics, Manchester University, Manchester M13 9PL, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The nonlinear instability of the boundary layer on a heated flat plate placed in an oncoming flow is investigated. Such flows are unstable to stationary vortex instabilities and inviscid travelling wave disturbances governed by the Taylor-Goldstein equation. For small temperature differences the Taylor-Goldstein equation reduces to Rayleigh's equation. When the temperature difference between the wall and free stream is small the preferred mode of instability is a streamwise vortex. It is shown in this case that the vortex, assumed to be of small wavelength, restructures the underlying mean flow to produce a profile which can be massively unstable to inviscid travelling waves. The mean state is shown to be destabilized if the Prandtl number is less than unity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 252 , July 1993 , pp. 301 - 324
Copyright
© 1993 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chen, K. & Cheng, M. M. 1984 Thermal instability of forced boundary layers. Trans. ASME C: J. Heat Transfer 106, 284–289.Google Scholar
Denier, J. 1992 The Taylor vortex problem in the small wavelength limit. IMA J. Appl. Maths (to appear).Google Scholar
Hall, P. 1988 The nonlinear development of Görtler vortices in growing boundary layers. J. Fluid Mech. 193, 243–266.Google Scholar
Hall, P. & Horseman, N. J. 1991 The linear secondary instability of longitudinal vortex structures in boundary layers. J. Fluid Mech. 232, 357–375.Google Scholar
Hall, P. & Lakin, W. D. 1988 The fully nonlinear development of Görtler vortices in growing boundary layers. Proc. R. Soc. Lond. A 415, 421–444.Google Scholar
Hall, P. & Morris, H. 1992 On the instability of boundary layers on heat flat plates. J. Fluid Mech. 245, 367–400.Google Scholar
Hall, P. & Smith, F. T. 1991 On strongly nonlinear vortex/wave interaction in boundary layer transition. J. Fluid Mech. 227, 641–666.Google Scholar
Moutsoglou, A., Chen, T. S. & Cheng, K. C. 1981 Vortex instability of mixed convection flow over a horizontal flat plate. Trans. ASME C: J. Heat Transfer 103, 257–261.Google Scholar
Wu, R. S. & Cheng, K. C. 1976 Thermal instability of Blasius flow along horizontal plates. Int. J. Heat Mass Transfer 105, 907–913.Google Scholar