Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-20T15:55:25.560Z Has data issue: false hasContentIssue false
  • English
  • Français

On the spatial evolution of centrifugal instabilities within curved incompressible mixing layers

Published online by Cambridge University Press:  26 April 2006

S. R. Otto ,
T. L. Jackson  and
F. Q. Hu
S. R. Otto
Affiliation:
School of Mathematics and Statistics, The University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK
T. L. Jackson
Affiliation:
ICASE, Mail Stop 132 C, NASA Langley Research Center, Hampton, VA 23681-0001, USA
F. Q. Hu
Affiliation:
Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

It is known that certain configurations which possess curvature are prone to a class of instabilities which their ‘flat’ counterparts will not support. The main thrust of the study of these centrifugal instabilities has concentrated on curved solid boundaries and their effect on the fluid motion. In this article attention is shifted towards a fluid-fluid interface observed within a curved incompressible mixing layer. Experimental evidence is available to support the conjecture that this situation may be subject to centrifugal instabilities. The evolution of modes with wavelengths comparable with the layer's thickness is considered within moderately curved mixing layers. The high Taylor/Görtler number régime is also discussed which characterizes the ultimate fate of the modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 315 , 25 May 1996 , pp. 85 - 103
Copyright
© 1996 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

Castro, I. P. & Bradshaw, P. 1976 The turbulence structure of a highly curved mixing layer. J. Fluid Mech. 73, 265–304.Google Scholar
Choudhari, M., Hall, P. & Streett, C. L. 1994 On the spatial evolution of long-wavelength Görtler vortices governed by a viscous-inviscid interaction, Part 1: The linear case. Q. J. Mech. Appl. Maths 47, 207–229.Google Scholar
Denier, J. P., Hall, P. & Seddougui, S. 1991 On the receptivity problem for Görtler vortices: vortex motion induced by wall roughness. Phil. Trans. R. Soc. Lond. A 335, 51–85.Google Scholar
Drazin, P.G. & Reid, W.H. 1979 Hydrodynamic Instability. Cambridge University Press.
Görtler, H. 1940 On the three dimensional instability of laminar boundary layers on concave walls. NACA Tech. Mem. 1375.
Hall, P. 1982 Taylor-Görtler vortices in fully developed or boundary layer flows. J. Fluid Mech. 124, 475–494.Google Scholar
Hall, P. 1983 The linear development of Görtler vortices in growing boundary layers. J. Fluid Mech. 130, 41–58.Google Scholar
Hall, P. 1990 Görtler vortices in growing boundary layers: the leading edge receptivity problem, linear growth and the nonlinear breakdown stage. Mathematika 37, 151–189.Google Scholar
Hu, F. Q., Otto, S. R. & Jackson, T. L. 1994 On the stability of a curved mixing layer. In Proc. ICASE Workshop on Transition, Turbulence and Combustion, 1993 (ed. T. B. Gatski, M. Y. Hussaini & T. L. Jackson), pp. 107–116. Kluwer.
Karasso, P. S. & Mungal, M. G. 1990 An experimental study of curved mixing layers: flow visualization using volume rendering. Center for Turbulence, Annual Research Briefs, pp. 195–201.
Karasso, P. S. & Mungal, M. G. 1991 Mixing measurements of straight and curved shear layers. Center for Turbulence, Annual Research Briefs, pp. 343–348.
Leboeuf, R. L. 1991 Progress toward identification of streamwise vorticity meander in a plane mixing layer. Center for Turbulence, Annual Research Briefs, pp. 349–354.
Liou, W. W. 1994 Linear Instability of curved free shear layers. Phys. Fluids 6, 541–549.Google Scholar
Lock, R. C. 1951 The velocity distribution in the laminar boundary layer between parallel streams. Q. J. Mech. 4, 42–57.Google Scholar
Margolis, D. P. & Lumley, J. L. 1965 Curved turbulent mixing layer. Phys. Fluids 8, 1775–1784.Google Scholar
Michalke, A. 1964 On the inviscid instability of the hyperbolic-tangent velocity profile. J. Fluid Mech. 19, 543–556.Google Scholar
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521–544.Google Scholar
Otto, S. R. & Bassom, A. P. 1993 An algorithm for solving the viscous equations arising in the stability of three-dimensional centrifugal instabilities. ICASE Internal Rep. 38.
Otto, S. R. & Bassom, A. P. 1994 The effect of crossflow on Taylor vortices. Q. J. Mech. Appl. Maths 47, 323–339.Google Scholar
Otto, S. R. & Denier, J. P. 1996 The effect of pressure gradients and three-dimensional flows on Görtler vortices. J. Fluid Mech (submitted).Google Scholar
Plesniak, M. W., Mehta, R. D. & Johnston, J. P. 1994 Curved two-stream turbulent mixing layers: three-dimensional structure and streamwise evolution. J. Fluid Mech. 270, 1–50.Google Scholar
Taylor, G.I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289–343.Google Scholar
Wang, C. 1984 The effects of curvature on turbulent mixing layers. PhD thesis, California Institute of Technology.
Wyngaard, J. C., Tennekes, H., Lumley, J. L. & Margolis, D. P. 1968 Structure of turbulence in a curved mixing layer. Phys. Fluids 11, 1251–1253.Google Scholar