Instabilities of plane flows over curvilinear surfaces

  • Andrey V. BoikoEmail author
  • Alexander V. Dovgal
  • Genrih R. Grek
  • Victor V. Kozlov
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 98)


In this chapter, we consider the linear stability of some flows over a curvilinear wall, which have close relations to the plane shear layers considered in previous chapters: the Couette flow between concentric rotating cylinders, the flow in a curved channel, and the self-similar boundary layer over a curved wall.


Boundary Layer Stationary Vortex Hydrodynamic Instability Taylor Number Curve Channel 
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  1. Bippes H (1972) Experimentelle Untersuchung des laminar-turbulenten Umschlags an einer parallel angeströmten konkaven Wand. In: Sitzungberichte der Heidelberger Akademie der Wissenschaften Mathematischnaturwissenschaftliche Klasse 3, Springer, Berlin, pp 103–180, translated as NASA TM 72243, 1978. Google Scholar
  2. Boiko AV, Ivanov AV, Kachanov YS, Mischenko DA (2010) Steady and unsteady Görtler boundary-layer instability on concave wall. Eur J Mech B/Fluids 29(2):61–83 zbMATHCrossRefGoogle Scholar
  3. Clauser M, Clauser F (1937) The effect of curvature on the transition from laminar to turbulent boundary layer. TN 613, NACA Google Scholar
  4. Dean WR (1928) Fluid motion in a curved channel. Proc R Soc Lond A 121:402–420 ADSzbMATHCrossRefGoogle Scholar
  5. Floryan JM, Saric WS (1982) Stability of Görtler vortices in boundary layers. AIAA J 20(3):316–324 MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. Floryan JM, Saric WS (1984) Wavelength selection and growth of Görtler vortices. AIAA J 22(11):1529–1538 ADSzbMATHCrossRefGoogle Scholar
  7. Görtler H (1941) Instabilität laminaren Grenzschichten an konkaven Wänden gegenüber gewissen dreidimensionalen Störungen. Z Angew Math Mech 21:250–252 MathSciNetCrossRefGoogle Scholar
  8. Gregory N, Walker WS (1956) The effect on transition of isolated surface excrescences in the boundary-layer. R&M 2779, ARC Google Scholar
  9. Hall P (1982) Taylor–Görtler vortices in fully developed or boundary-layer flows: Linear theory. J Fluid Mech 124:475–494 ADSzbMATHCrossRefGoogle Scholar
  10. Hall P (1983) The linear development of Görtler vortices in growing boundary layers. J Fluid Mech 130:41–58 MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. Ito A (1987) Visualization of boundary layer transition along a concave wall. In: Proc. 4th Int. Symp. Flow Visualization, Hemisphere, Washington, pp 339–344 Google Scholar
  12. Liepmann HW (1943) Investigations on laminar boundary layer stability and transition on curved boundaries. Wartime Report W-107, NACA Google Scholar
  13. Lord Rayleigh (1916) On the dynamics of revolving fluids. Scientific papers 6:447–453 MathSciNetGoogle Scholar
  14. Schultz MP, Volino RJ (2003) Effects of concave curvature on boundary layer transition under high free-stream turbulence conditions. ASME J Fluids Eng 125:18–27 CrossRefGoogle Scholar
  15. Synge JL (1933) The stability of heterogeneous fluids. Trans R Soc, Canada 27(3):1–18 Google Scholar
  16. Tani I (1962) Production of longitudinal vortices in the boundary-layer along a curved wall. J Geophys Res 67:3075–3080 ADSCrossRefGoogle Scholar
  17. Tani I, Sakagami J (1962) Boundary-layer instability at subsonic speeds. In: Proc. Int. Council Aerosp. Sci. 3rd Congress, Spartan, Washington D.C., pp 391–403 Google Scholar
  18. Taylor GI (1923) Stability of a viscous liquid contained between two rotating cylinders. Proc R Soc Lond A 223:289–343 ADSzbMATHGoogle Scholar

Further Reading

  1. Bassom AP, Hall P (1991) Concerning the interaction of non-stationary crossflow vortices in a three-dimensional boundary layer. Q J Mech Appl Math 44:147–172 MathSciNetzbMATHCrossRefGoogle Scholar
  2. Bottaro A, Luchini P (1999) Görtler vortices: Are they amenable to local eigenvalue analysis? Eur J Mech B/Fluids 18(1):47–65 MathSciNetzbMATHCrossRefGoogle Scholar
  3. Cebeci T (1999) An engineering approach to the calculation of aerodynmic flows. Springer–Verlag, Berlin Google Scholar
  4. Chomaz JM, Perrier M (1991) Nature of the Görtler instability in a forced experiment. In: The Geometry of Turbulence, Plenum, New York, pp 23–32 Google Scholar
  5. Denier JP, Hall P, Seddougui SO (1991) On the receptivity problem for Görtler vortices: Vortex motions induced by roughness. Philos Trans R Soc Lond A 335:51–85 MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. Drazin PG, Reid WH (1981) Hydrodynamic stability. Cambridge University Press, Cambridge zbMATHGoogle Scholar
  7. Floryan JM (1991) On the Görtler instability of boundary layers. J Aerosp Sci 28:235–271 zbMATHCrossRefGoogle Scholar
  8. Gaponenko VR, Ivanov AV, Kachanov YS, Crouch JD (2002) Swept-wing boundary-layer receptivity to surface non-uniformities. J Fluid Mech 461:93–126 MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. Hall P (1988) The nonlinear development of Görtler vortices in growing boundary layers. J Fluid Mech 193:243–266 MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. 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 MathSciNetzbMATHCrossRefGoogle Scholar
  11. Hämmerlin G (1955) Über das Eigenwertproblem der dreidimensionalen Instabilität laminarer Grenzschichten an konkaven Wänden. J Rat Mech Anal 4(2):279–321 zbMATHGoogle Scholar
  12. von Kàrmán T (1934) Some aspects of the turbulence problem. In: Proc. 4th Int. Congr. Appl. Mech., Cambridge University Press, Cambridge, England, pp 54–91 Google Scholar
  13. Luchini P, Bottaro A (1998) Görtler vortices: A backward in time approach to the receptivity problem. J Fluid Mech 363:1–23 MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. Murphy JS (1965) Extensions of the Falkner–Skan similar solutions to flows with surface curvature. AIAA J 3(11):2043–2049 CrossRefGoogle Scholar
  15. Saric WS (1994) Görtler vortices. Ann Rev Fluid Mech 26:379–409 MathSciNetADSCrossRefGoogle Scholar
  16. Smith AMO (1955) On the growth of Taylor–Görtler vortices along highly concave walls. Quart Appl Math 13:223 Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Andrey V. Boiko
    • 1
    Email author
  • Alexander V. Dovgal
    • 1
  • Genrih R. Grek
    • 1
  • Victor V. Kozlov
    • 1
  1. 1.Inst. Theoretical & Applied MechanicsRussian Academy of SciencesNovosibirskRussia

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