Secondary instabilities of shear layers

  • 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)


When a linear instability mode reaches a large-enough amplitude, it enters the region of its essentially nonlinear, but still deterministic development. Usually the disturbance amplitude saturates in this region, which resembles the formation of a new quasi-steady state that opens in some cases the door for mechanisms of secondary instabilities discussed below.


Boundary Layer Shear Layer Wave Packet Streamwise Vortex Turbulent Transition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Alfredsson PH, Bakchinov AA, Kozlov VV, Matsubara M (1996) Laminar–turbulent transition at a high level of a free stream turbulence. In: Duck and Hall(1996), pp 423–436 Google Scholar
  2. Boiko AV, Kozlov VV, Syzrantsev VV, Scherbakov VA (1997) A study of the influence of internal structure of a streamwise vortex on the development of traveling disturbances inside it. Thermophys Aeromech 4(4):343–354 MathSciNetGoogle Scholar
  3. Bottaro A, Klingmann BGB (1996) On the linear breakdown of Görtler vortices. Eur J Mech B/Fluids 15(3):301–330 zbMATHGoogle Scholar
  4. Brandt L, Cossu C, Chomaz JM, Huerre P, Henningson DS (2003) On the convectively unstable nature of optimal streaks in boundary layers. J Fluid Mech 485:221–242 MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. Corke TC, Mangano RA (1989) Resonant growth of three-dimensional modes in transitioning boundary layers. J Fluid Mech 209:93–150 ADSCrossRefGoogle Scholar
  6. Crouch JD, Herbert T (1993) Nonlinear evolution of secondary instabilities in boundary-layer transition. Theoret Comput Fluid Dyn 4:151–175 ADSzbMATHCrossRefGoogle Scholar
  7. Duck PW, Hall P (eds) (1996) Nonlinear Instability and Transition in Three-Dimensional Boundary Layers, Fluid Mechanics and its Application, Kluwer, Dordrecht Google Scholar
  8. Gaster M (1979) The propagation of linear wave packet in laminar boundary layers — asymptotic theory for non-conservative wave systems. AIAA Paper 79–1492 Google Scholar
  9. Herbert T (1988) Secondary instability of boundary layers. Ann Rev Fluid Mech 20:487–526 ADSCrossRefGoogle Scholar
  10. Kohama Y, Onodera T, Egami Y (1996) Design and control of crossflow instability field. In: Duck and Hall(1996), pp 147–156 Google Scholar
  11. Landahl ML (1972) Wave mechanism of breakdown. J Fluid Mech 56:775–802 ADSzbMATHCrossRefGoogle Scholar
  12. Li F, Malik MR (1995) Fundamental and subharmonic secondary instabilities of Görtler vortices. J Fluid Mech 297:77–100 MathSciNetADSzbMATHCrossRefGoogle Scholar
  13. Poll DIA (1979) Transition in the infinite swept attachment line boundary layer. Aeronaut Quart 30:607–629 Google Scholar
  14. Poll DIA (1985) Some observations on the transition process on the windward face of a long yawed cylinder. J Fluid Mech 150:329–356 ADSCrossRefGoogle Scholar
  15. Saric WS, Kozlov VV, Levchenko VY (1984) Forced and unforced subharmonic resonance in boundary-layer transition. AIAA Paper 84–0007 Google Scholar
  16. Zelman MB, Maslennikova II (1993) Tollmien–Schlichting-wave resonant mechanism for subharmonic-type transition. J Fluid Mech 252:449–478 MathSciNetADSzbMATHCrossRefGoogle Scholar

Further Reading

  1. Berlin S, Wiegel M, Henningson DS (1999) Numerical and experimental investigations of oblique boundary layer transition. J Fluid Mech 393:23–57 ADSzbMATHCrossRefGoogle Scholar
  2. Betchov R (1960) On the mechanism of turbulent transition. Phys Fluids 3(6):1026–1027 ADSCrossRefGoogle Scholar
  3. Bippes H (1990) Instability features appearing on swept wing configurations. In: Arnal D, Michel R (eds) Laminar–Turbulent Transition, Springer–Verlag, Berlin, IUTAM Symposium, pp 419–430 Google Scholar
  4. Boiko AV, Kozlov VV, Syzrantsev VV, Scherbakov VA (1995) Experimental investigation of high-frequency secondary disturbances in a swept wing boundary layer. J Appl Mech Tehn Phys 36(3):385–393 ADSCrossRefGoogle Scholar
  5. Boiko AV, Kozlov VV, Syzrantsev VV, Scherbakov VA (1995) Experimental study of the transition to turbulence at a single stationary disturbance in the boundary layer on an oblique airfoil. J Appl Mech Tehn Phys 36(1):67–77 ADSCrossRefGoogle Scholar
  6. Borodulin VI, Kachanov YS (1994) Experimental study of nonlinear stages of a boundary layer breakdown. In: Lin SP, Phillips WRC, Valentine DT (eds) Nonlinear Instability of Nonparallel Flows, Springer–Verlag, Berlin, IUTAM Symposium, pp 69–80 Google Scholar
  7. Dryganets SV, Kachanov YS, Levchenko VY, Ramazanov MP (1990) Resonance flow randomization in the K-regime of boundary-layer transition. J Appl Mech Tehn Phys 31(2):239–249 ADSCrossRefGoogle Scholar
  8. Fischer TM, Dallmann U (1991) Primary and secondary stability analysis of a three-dimensional boundary-layer flow. Phys Fluids A 3(10):2378–2391 ADSzbMATHCrossRefGoogle Scholar
  9. Floryan JM (1991) On the Görtler instability of boundary layers. J Aerosp Sci 28:235–271 zbMATHCrossRefGoogle Scholar
  10. Gaster M (1979) The propagation of linear wave packet in laminar boundary layers — asymptotic theory for non-conservative wave systems. AIAA Paper 79–1492 Google Scholar
  11. Guo Y, Finlay WH (1994) Wavenumber selection and irregularity of spatially developing nonlinear Dean and Görtler vortices. J Fluid Mech 264:1–40 ADSzbMATHCrossRefGoogle Scholar
  12. Henningson DS (1995) Bypass transition and linear growth mechanisms. In: Benzi R (ed) Advances in turbulence, Kluwer, Dordrecht, pp 190–204 Google Scholar
  13. Klebanoff PS, Tidstrom KD, Sargent LM (1962) The three-dimensional nature of boundary-layer instability. J Fluid Mech 12:1–34 ADSzbMATHCrossRefGoogle Scholar
  14. Koch W, Bertolotti FP, Stolte A, Hein S (2000) Nonlinear equilibrium solutions in a three-dimensional boundary layer and their secondary instability. J Fluid Mech 406:131–174 MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. Lerche T (1997) Experimentelle Untersuchung nichtlinearer Strukturbildung im Transitionsprozess einer instabilen dreidimensionalen Grenzschicht. No. 310 in Reihe 7: Strömungstechnik, VDI Verlag GmbH, Düsseldorf Google Scholar
  16. Nayfeh AH (1987) Nonlinear stability of boundary layers. AIAA Paper 87–0044 Google Scholar
  17. Nishioka M, Asai M, Iida S (1980) An experimental investigation of the secondary instability. In: Eppler R, Fasel H (eds) Laminar–Turbulent Transition, Springer–Verlag, Berlin, IUTAM Symposium, pp 37–46 Google Scholar
  18. Nitschke-Kowsky P, Bippes H (1988) Instability and transition of a three-dimensional boundary layer on a swept flat plate. Phys Fluids 31(4):786–795 ADSCrossRefGoogle Scholar
  19. Swearingen JD, Blackwelder RF (1987) The growth and breakdown of streamwise vortices in the presence of a wall. J Fluid Mech 182:255–290 ADSCrossRefGoogle Scholar
  20. Wu X, Stewart PA, Cowley SJ (2008) On the catalytic effect of resonant interactions in boundary layer transition. In: Bock HG, Hoog F, Friedman A, Gupta A, Neunzert H, Pulleyblank WR, Rusten T, Santosa F, Tornberg AK, Capasso V, Mattheij R, Neunzert H, Scherzer O, Bonilla LL, Moscoso M, Platero G, Vega JM (eds) Progress in Industrial Mathematics at ECMI 2006, Mathematics in Industry, vol 12, Springer, pp 146–156. CrossRefGoogle 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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