Abstract
As the steady state for secondary instabilities to set-in, the linear and nonlinear development of Görtler vortices are discussed in this section.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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
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
Li, F., Malik, M.R.: Fundamental and subharmonic secondary instabilities of Görtler vortices. J. Fluid Mech. 297, 77–100 (1995). doi:10.1017/S0022112095003016
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
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
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
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
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
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
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
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
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
Bottaro, A., Klingmann, B.: On the linear breakdown of Görtler vortices. Eur. J. Mech. B Fluids 15(3), 301–330 (1996)
Mack, L.M.: Linear stability theory and the problem of supersonic boundary-layer transition. AIAA J. 13(3), 278–289 (1975)
Mack, L.M.: Boundary-layer linear stability theory. AGARD Report 709, Special Course on Stability and Transition of Laminar Flows (1984)
Federov, A., Tumin, A.: High-speed boundary-layer instability: old terminology and a new framework. AIAA J. 49(8), 1647–1657 (2011)
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
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
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
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
Herbert, T.: Secondary instability of boundary layers. Ann. Rev. Fluid Mech. 20(1), 487–526 (1988). doi:10.1146/annurev.fl.20.010188.002415
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
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
Xu, G., Liu, G., Jiang, X.: The nonlinear instability of the supersonic crossflow vortex. In: 44th AIAA Fluid Dynamics Conference, AIAA-2014-2637 (2014)
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)
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)
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
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Ren, J. (2018). Secondary Instability. In: Secondary Instabilities of Görtler Vortices in High-Speed Boundary Layers. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-6832-4_4
Download citation
DOI: https://doi.org/10.1007/978-981-10-6832-4_4
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6831-7
Online ISBN: 978-981-10-6832-4
eBook Packages: EngineeringEngineering (R0)