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Secondary Instability

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Part of the Springer Theses book series (Springer Theses)

Abstract

As the steady state for secondary instabilities to set-in, the linear and nonlinear development of Görtler vortices are discussed in this section.

References

  1. 1.
    Swearingen, J.D., Blackwelder, R.F.: The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255–290 (1987). doi: 10.1017/S0022112087002337
  2. 2.
    Mitsudharmadi, H., Winoto, S.H., Shah, D.A.: Secondary instability in forced wavelength görtler vortices. Phys. Fluids 17(7), 074104 (2005). doi: 10.1063/1.1941367, http://scitation.aip.org/content/aip/journal/pof2/17/7/10.1063/1.1941367
  3. 3.
    Li, F., Malik, M.R.: Fundamental and subharmonic secondary instabilities of Görtler vortices. J. Fluid Mech. 297, 77–100 (1995). doi: 10.1017/S0022112095003016
  4. 4.
    Ren, J., Fu, S.: Study of the discrete spectrum in a Mach 4.5 Görtler flow. Flow Turbul. Combust. 94(2), 339–357 (2015). doi: 10.1007/s10494-014-9575-z
  5. 5.
    Wu, X., Zhao, D., Luo, J.: Excitation of steady and unsteady Görtler vortices by free-stream vortical disturbances. J. Fluid Mech. 682, 66–100 (2011). doi: 10.1017/jfm.2011.224 CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Dando, A.H., Seddougui, S.O.: The compressible Görtler problem in two-dimensional boundary layers. IMA J. Appl. Math. 51(1), 27–67 (1993). doi: 10.1093/imamat/51.1.27
  7. 7.
    Ren, J., Fu, S.: Competition of the multiple Görtler modes in hypersonic boundary layer flows. Sci. China Phys. Mech. Astron. 57(6), 1178–1193 (2014). doi: 10.1007/s11433-014-5454-9
  8. 8.
    Lee, K., Liu, J.T.C.: On the growth of mushroomlike structures in nonlinear spatially developing Goertler vortex flow. Phys. Fluids A Fluid Dyn. 4(1), 95–103 (1992). doi: 10.1063/1.858506
  9. 9.
    Girgis, I.G., Liu, J.T.C.: Nonlinear mechanics of wavy instability of steady longitudinal vortices and its effect on skin friction rise in boundary layer flow. Phys. Fluids 18(2), 024,102 (2006). doi: 10.1063/1.2158430
  10. 10.
    Ricco, P., Wu, X.: Response of a compressible laminar boundary layer to free-stream vortical disturbances. J. Fluid Mech. 587, 97–138 (2007). doi: 10.1017/S0022112007007070, http://journals.cambridge.org/article_S0022112007007070
  11. 11.
    Li, F., Choudhari, M., Chang, C.L., Wu, M., Greene, P.: Development and breakdown of Görtler vortices in high speed boundary layers. In: 50th Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (2010), AIAA-2010-0705. doi: 10.2514/6.2010-705
  12. 12.
    Andersson, P., Brandt, L., Bottaro, A., Henningson, D.S.: On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60 (2001). doi: 10.1017/S0022112000002421, http://journals.cambridge.org/article_S0022112000002421
  13. 13.
    Bottaro, A., Klingmann, B.: On the linear breakdown of Görtler vortices. Eur. J. Mech. B Fluids 15(3), 301–330 (1996)Google Scholar
  14. 14.
    Mack, L.M.: Linear stability theory and the problem of supersonic boundary-layer transition. AIAA J. 13(3), 278–289 (1975)CrossRefGoogle Scholar
  15. 15.
    Mack, L.M.: Boundary-layer linear stability theory. AGARD Report 709, Special Course on Stability and Transition of Laminar Flows (1984)Google Scholar
  16. 16.
    Federov, A., Tumin, A.: High-speed boundary-layer instability: old terminology and a new framework. AIAA J. 49(8), 1647–1657 (2011)CrossRefGoogle Scholar
  17. 17.
    Ma, Y., Zhong, X.: Receptivity of a supersonic boundary layer over a flat plate. part 1. wave structures and interactions. J. Fluid Mech. 488, 31–78 (2003). doi: 10.1017/S0022112003004786, http://journals.cambridge.org/article_S0022112003004786
  18. 18.
    Ren, J., Fu, S.: Floquet analysis of fundamental, subharmonic and detuned secondary instabilities of Görtler vortices. Sci. China Phys. Mech. Astron. 57(3), 555–561 (2014). doi: 10.1007/s11433-014-5396-2
  19. 19.
    De Tullio, N., Paredes, P., Sandham, N.D., Theofilis, V.: Laminar-turbulent transition induced by a discrete roughness element in a supersonic boundary layer. J. Fluid Mech. 735, 613–646 (2013). doi: 10.1017/jfm.2013.520
  20. 20.
    Ricco, P., Luo, J., Wu, X.: Evolution and instability of unsteady nonlinear streaks generated by free-stream vortical disturbances. J. Fluid Mech. 677, 1–38 (2011). doi: 10.1017/jfm.2011.41, http://journals.cambridge.org/article_S0022112011000413
  21. 21.
    Herbert, T.: Secondary instability of boundary layers. Ann. Rev. Fluid Mech. 20(1), 487–526 (1988). doi: 10.1146/annurev.fl.20.010188.002415
  22. 22.
    Wassermann, P., Kloker, M.: Transition mechanisms in a three-dimensional boundary-layer flow with pressure-gradient changeover. J. Fluid Mech. 530, 265–293 (2005). doi: 10.1017/S0022112005003708, http://journals.cambridge.org/article_S0022112005003708
  23. 23.
    Bonfigli, G., Kloker, M.: Secondary instability of crossflow vortices: validation of the stability theory by direct numerical simulation. J. Fluid Mech. 583, 229–272 (2007). doi: 10.1017/S0022112007006179, http://journals.cambridge.org/article_S0022112007006179
  24. 24.
    Xu, G., Liu, G., Jiang, X.: The nonlinear instability of the supersonic crossflow vortex. In: 44th AIAA Fluid Dynamics Conference, AIAA-2014-2637 (2014)Google Scholar
  25. 25.
    Choudhari, M., Li, F., Chang, C.L., Edwards, J., Kegerise, M., King, R.: Laminar-turbulent transition behind discrete roughness elements in a high-speed boundary layer. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA-2010-1575 (2010)Google Scholar
  26. 26.
    Choudhari, M., Li, F., Chang, C.L., Norris, A., Edwards, J.: Wake instabilities behind discrete roughness elements in high speed boundary layers. In: 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA-2013-0081 (2013)Google Scholar
  27. 27.
    Groskopf, G., Kloker, M., Marxen, O.: Bi-global crossplane stability analysis of high-speed boundary-layer flows with discrete roughness. In: Schlatter, P., Henningson, D.S. (eds.) Seventh IUTAM Symposium on Laminar-Turbulent Transition, IUTAM Bookseries, vol. 18, pp. 171–176. Springer, Netherlands (2010). doi: 10.1007/978-90-481-3723-7_26
  28. 28.
    Kegerise, M.A., King, R.A., Owens, L.R., Choudhari, M.M., Norris, A.T., Li, F., Chang, C.L.: An experimental and numerical study of roughness-induced instabilities in a mach 3.5 boundary layer. In: RTO AVT-200 RSM-030 Specialists’ Meeting on Hypersonic Laminar-Turbulent Transition, NF1676L-14423 (2012)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Tsinghua UniversityBeijingChina

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