Abstract
The flow transition has a critical impact on aerodynamic heating, drag, and vehicle operation because turbulent flows generate tremendously higher friction and heating to the vehicles than laminar ones.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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 No 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)
Fedorov, A.: Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43, 79–95 (2011). doi:10.1146/annurev-fluid-122109-160750
Zhong, X., Wang, X.: Direct numerical simulation on the receptivity, instability, and transition of hypersonic boundary layers. Ann. Rev. Fluid Mech. 44, 527–561 (2012). doi:10.1146/annurev-fluid-120710-101208
Theofilis, V.: Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerosp. Sci. 39(4), 249–315 (2003). doi:10.1016/S0376-0421(02)00030-1, http://www.sciencedirect.com/science/article/pii/S0376042102000301
Theofilis, V.: Global linear instability. Ann. Rev. Fluid Mech. 43, 319–352 (2011). doi:10.1146/annurev-fluid-122109-160705, http://www.annualreviews.org/doi/abs/10.1146/annurev-fluid-122109-160705
Reed, H.L., Saric, W.S., Arnal, D.: Linear stability theory applied to boundary layers. Annual Review of Fluid Mechanics 28, 389–428 (1996). doi:10.1146/annurev.fl.28.010196.002133. http://www.annualreviews.org/doi/abs/10.1146/annurev.fl.28.010196.002133
Fu, S., Wang, L.: Rans modeling of high-speed aerodynamic flow transition with consideration of stability theory. Prog. Aerosp Sci. 58, 36–59 (2013). doi:10.1016/j.paerosci.2012.08.004, http://www.sciencedirect.com/science/article/pii/S0376042112000851
Ma, Y., Zhong, X.: Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to free-stream sound. J. Fluid Mech. 488, 79–121 (2003). doi:10.1017/S0022112003004798, http://journals.cambridge.org/article_S0022112003004798
Ma, Y., Zhong, X.: Receptivity of a supersonic boundary layer over a flat plate. part 3. effects of different types of free-stream disturbances. J. Fluid Mech. 532, 63–109 (2005). doi:10.1017/S0022112005003836, http://journals.cambridge.org/article_S0022112005003836
Fedorov, A.V.: Receptivity of a high-speed boundary layer to acoustic disturbances. J. Fluid Mech. 491 101–129 (2003). doi:10.1017/S0022112003005263, http://journals.cambridge.org/article_S0022112003005263
Fedorov, A.V., Ryzhov, A.A., Soudakov, V.G., Utyuzhnikov, S.V.: Receptivity of a high-speed boundary layer to temperature spottiness. J. Fluid Mech. 722 533–553 (2013). doi:10.1017/jfm.2013.111, http://journals.cambridge.org/article_S0022112013001110
Tempelmann, D., Schrader, L.U., Hanifi, A., Brandt, L., Henningson, D.S.: Swept wing boundary-layer receptivity to localized surface roughness. J. Fluid Mech. 711, 516–544 (2012). doi:10.1017/jfm.2012.405, http://journals.cambridge.org/article_S0022112012004053
Fedorov, A.V.: Receptivity of a supersonic boundary layer to solid particulates. J. Fluid Mech. 737, 105–131 (2013). doi:10.1017/jfm.2013.564, http://journals.cambridge.org/article_S0022112013005648
Ruban, A.I., Bernots, T., Pryce, D.: Receptivity of the boundary layer to vibrations of the wing surface. J. Fluid Mech. 723 480–528 (2013). doi:10.1017/jfm.2013.119, http://journals.cambridge.org/article_S0022112013001195
Kovasznay, L.S.G.: Turbulence in supersonic flow. J. Aeronaut. Sci. 20(10), 657–674 (1953)
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
Fedorov, A.V., Khokhlov, A.P.: Prehistory of instability in a hypersonic boundary layer. Theor. Comput. Fluid Dyn. 14(6), 359–375 (2001). doi:10.1007/s001620100038, http://dx.doi.org/10.1007/s001620100038
Federov, A., Tumin, A.: Initial-value problem for hypersonic boundary-layer flows. AIAA J. 41(3), 379–389 (2003)
Gushchin, V., Fedorov, A.: Excitation and development of unstable disturbances in a supersonic boundary layer. Fluid Dyn. 25(3), 344–352 (1990). doi:10.1007/BF01049814, http://dx.doi.org/10.1007/BF01049814
Lifshitz, Y., Degani, D., Tumin, A.: Study of discrete modes branching in high-speed boundary layers. AIAA J. 50(10), 2202–2210 (2012)
Görtler, H.: Über eine dreidimensionale instabilität laminarer grenzschichten an konkaven wänden. Ges. D. Wiss. Göttingen, Nachr 1(2) (1940) (Translated as On the three-dimensional instability of laminar boundary layers on concave walls. NACA TM 1375, 1954)
Herbert, T.: On the stability of the boundary layer along a concave wall. Archiwum mechaniki stosowanej 28(5–6), 1039–1055 (1976)
Hall, P.: Görtler vortices in growing boundary layers: the leading edge receptivity problem, linear growth and the nonlinear breakdown stage. Mathematika 37, 151–189 (1990). doi:10.1112/S0025579300012894
Floryan, J.: On the Görtler instability of boundary layers. Prog. Aerosp. Sci. 28(3), 235–271 (1991). doi:10.1016/0376-0421(91)90006-P
Saric, W.S.: Görtler vortices. Annu. Rev. Fluid Mech. 26(1), 379–409 (1994). doi:10.1146/annurev.fl.26.010194.002115
Bassom, A.P., Seddougui, S.O.: Receptivity mechanisms for Görtler vortex modes. Theor. Comput. Fluid Dyn. 7(5), 317–339 (1995). doi:10.1007/BF00312412
Denier, J.P., Hall, P., Seddougui, S.O.: On the receptivity problem for gortler vortices: Vortex motions induced by wall roughness. Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 335(1636), 51–85 (1991). doi:10.1098/rsta.1991.0036
Bassom, A.P., Hall, P.: The receptivity problem for O(1) wavelength gortler vortices. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 446 no. 1928, pp. 499–516 (1994). doi:10.1098/rspa.1994.0117
Luchini, P., Bottaro, A.: Görtler vortices: a backward-in-time approach to the receptivity problem. J. Fluid Mech. 363, 1–23 (1998). doi:10.1017/S0022112098008970
Schrader, L.u., Brandt, L., Zaki, T.A.: Receptivity, instability and breakdown of Görtler flow. J. Fluid Mech. 682, 362–396 (2011). doi:10.1017/jfm.2011.229
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
Hall, P.: Taylor- Görtler vortices in fully developed or boundary-layer flows: linear theory. J. Fluid Mech. 124, 475–494 (1982). doi:10.1017/S0022112082002596
Hall, P.: The linear development of Görtler vortices in growing boundary layers. J. Fluid Mech. 130, 41–58 (1983). doi:10.1017/S0022112083000968
Bottaro, A., Luchini, P.: Görtler vortices: Are they amenable to local eigenvalue analysis? Eur. J. Mech. B/Fluids 18(1), 47–65 (1999). doi:10.1016/S0997-7546(99)80005-3
Day, H.P., Herbert, T., Saric, W.S.: Comparing local and marching analysis of Görtler instability. AIAA J. 28(6), 1010–1015 (1990)
Goulpié, P., Klingmann, B.G.B., Bottaro, A.: Görtler vortices in boundary layers with streamwise pressure gradient: Linear theory. Phys. Fluids 8(2), 451–459 (1996). doi:10.1063/1.868799
Hall, P., Fu, Y.: On the Görtler vortex instability mechanism at hypersonic speeds. Theor. Comput. Fluid Dyn. 1(3), 125–134 (1989). doi:10.1007/BF00417916
Spall, R.E., Malik, M.R.: Goertler vortices in supersonic and hypersonic boundary layers. Phys. Fluids A: Fluid Dyn. 1(11), 1822–1835 (1989). doi:10.1063/1.857508
Fu, Y., Hall, P.: Nonlinear development and secondary instability of large-amplitude Görtler vortices in hypersonic boundary-layers. Euro. J. Mech. B-Fluids 11(4), 465–510 (1992)
Fu, Y., Hall, P.: Effects of Görtler vortices, wall cooling and gas dissociation on the rayleigh instability in a hypersonic boundary layer. J. Fluid Mech. 247, 503–525 (1993). doi:10.1017/S0022112093000540
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
Luca, L., Cardone, G., Aymer de la Chevalerie, D., Fonteneau, A.: Goertler instability of a hypersonic boundary layer. Exp. Fluids 16(1), 10–16 (1993). doi:10.1007/BF00188500
de la Chevalerie, D., Fonteneau, A., Luca, L.D., Cardone, G.: Görtler-type vortices in hypersonic flows: the ramp problem. Exp. Therm. Fluid Sci. 15(2), 69–81 (1997). doi:10.1016/S0894-1777(97)00051-4
Schrijer, F.: Investigation of Görtler vortices in a hypersonic double compression ramp flow by means of infrared thermography. Quant. Infrared Thermogr. J. 7(2), 201–215 (2010). doi:10.3166/qirt.7.201-215
Chen, F.J., Wilkinson, S.P., Beckwith, I.E.: Görtler instability and hypersonic quiet nozzle design. J. Spacecr. Rocket. 30(2), 170–175 (1993)
Schneider, S.P.: Design of a mach-6 quiet-flow wind-tunnel nozzle using the e**n method for transition estimation. In: 36th AIAA Aerospace Sciences Meeting and Exhibit, AIAA- 1998-0547 (1998)
Schneider, S.P.: Development of hypersonic quiet tunnels. J. Spacecr. Rocket. 45(4), 641–664 (2008). doi:10.2514/1.34489
Volino, R.J., Simon, T.W.: Spectral measurements in transitional boundary layers on a concave wall under high and low free-stream turbulence conditions. J. Turbomach. 122, 450–457 (2000)
Boiko, A., Ivanov, A., Kachanov, Y., Mischenko, D.: Quasi-steady and unsteady goertler vortices on concave wall: experiment and theory. In: J. Palma., A. Lopes (eds.) Advances in Turbulence XI, Springer Proceedings Physics, vol. 117, pp. 173–175. Springer, Berlin (2007). doi:10.1007/978-3-540-72604-3_54, http://dx.doi.org/10.1007/978-3-540-72604-3_54
Boiko, A., Ivanov, A., Kachanov, Y., Mischenko, D.: Steady and unsteady Görtler boundary-layer instability on concave wall. Euro. J. Mech. B/Fluids 29(2), 61–83 (2010)
Landahl, M.T.: Wave breakdown and turbulence. SIAM J. Appl. Math. 28(4), 735–756 (1975). doi:10.1137/0128061, http://dx.doi.org/10.1137/0128061
Landahl, M.T.: A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243–251 (1980). doi:10.1017/S0022112080000122, http://journals.cambridge.org/article_S0022112080000122
Ellingsen, T., Palm, E.: Stability of linear flow. Phys. Fluids (1958-1988) 18(4), 487–488 (1975). doi:10.1063/1.861156
Hultgren, L.S., Gustavsson, L.H.: Algebraic growth of disturbances in a laminar boundary layer. Phys. Fluids (1958-1988) 24(6), 1000–1004 (1981). doi:10.1063/1.863490
Andersson, P., Berggren, M., Henningson, D.S.: Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11(1), 134–150 (1999). doi:10.1063/1.869908, http://scitation.aip.org/content/aip/journal/pof2/11/1/10.1063/1.869908
Luchini, P.: Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289–309 (2000). doi:10.1017/S0022112099007259, http://journals.cambridge.org/article_S0022112099007259
Leib, S.J., Wundrow, D.W., Goldstein, M.E.: Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer. J. Fluid Mech. 380, 169–203 (1999). doi:10.1017/S0022112098003504, http://journals.cambridge.org/article_S0022112098003504
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
Morkovin, M.: On roughness induced transition: Facts, views, and speculations. In: Hussaini M., Voigt R. (eds.) Instability and Transition, ICASE/NASA LaRC Series, pp. 281–295. Springer US (1990). doi:10.1007/978-1-4612-3430-2_318, doi:10.1007/978-1-4612-3430-2_34
Joslin, R.D., Grosch, C.E.: Growth characteristics downstream of a shallow bump: Computation and experiment. Phys. Fluids 7(12), 3042–3047 (1995). doi:10.1063/1.868680, http://scitation.aip.org/content/aip/journal/pof2/7/12/10.1063/1.868680
Tumin, A., Reshotko, E.: Receptivity of a boundary-layer flow to a three-dimensional hump at finite reynolds numbers. Phys. Fluids. 17(9) (2005). doi:10.1063/1.2033907
Hanifi, A., Schmid, P.J., Henningson, D.S.: Transient growth in compressible boundary layer flow. Phys. Fluids 8(3), 826–837 (1996). doi:10.1063/1.868864, http://scitation.aip.org/content/aip/journal/pof2/8/3/10.1063/1.868864
Tumin, A., Reshotko, E.: Spatial theory of optimal disturbances in boundary layers. Phys. Fluids 13(7), 2097–2104 (2001)
Tumin, A., Reshotko, E.: Optimal disturbances in compressible boundary layers. AIAA J. 41(12), 2357–2363 (2003)
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
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
Sabry, A.S., Liu, J.T.C.: Longitudinal vorticity elements in boundary layers: nonlinear development from initial görtler vortices as a prototype problem. J. Fluid Mech. 231, 615–663 (1991). doi:10.1017/S0022112091003543
Hall, P., Horseman, N.J.: The linear inviscid secondary instability of longitudinal vortex structures in boundary layers. J. Fluid Mech. 232, 357–375 (1991). doi:10.1017/S0022112091003725
Yu, X., Liu, J.T.C.: The secondary instability in Goertler flow. Phys. Fluids A: Fluid Dyn. 3(8), 1845–1847 (1991). doi:10.1063/1.857913
Yu, X., Liu, J.T.C.: On the mechanism of sinuous and varicose modes in three-dimensional viscous secondary instability of nonlinear Görtler rolls. Phys. Fluids 6(2), 736–750 (1994). doi:10.1063/1.868312
Liu, W., Domaradzki, J.A.: Direct numerical simulation of transition to turbulence in Görtler flow. J. Fluid Mech. 246, 267–299 (1993). doi:10.1017/S0022112093000126
Park, D.S., Huerre, P.: Primary and secondary instabilities of the asymptotic suction boundary layer on a curved plate. J. Fluid Mech. 283, 249–272 (1995). doi:10.1017/S0022112095002308
Li, F., Malik, M.R.: Fundamental and subharmonic secondary instabilities of Görtler vortices. J. Fluid Mech. 297, 77–100 (1995). doi:10.1017/S0022112095003016
Bottaro, A., Kingmann, B.: On the linear breakdown of Görtler vortices. Euro. J. Mech. B Fluids 15(3), 301–330 (1996)
Tandiono, Winoto, S.H., Shah, D.A.: On the linear and nonlinear development of Görtler vortices. Phys. Fluids 20(9), 094,103 (2008). doi:10.1063/1.2980349
Tandiono, Winoto, S.H., Shah, D.A.: Wall shear stress in Görtler vortex boundary layer flow. Phys. Fluids 21(8), 084106 (2009). doi:10.1063/1.3205428
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
Asai, M., Minagawa, M., Nishioka, M.: The instability and breakdown of a near-wall low-speed streak. J. Fluid Mech. 455, 289–314 (2002). doi:10.1017/S0022112001007431
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
Whang, C., Zhong, X.: Secondary Görtler instability in hypersonic boundary layers. In:39th Aerospace Sciences Meeting Exhibit (2001). AIAA-2001-0273
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). doi: 10.2514/6.2010-705. AIAA-2010-0705
Choi, K.S.: Fluid dynamics: The rough with the smooth. Nature 440(8), 754 (2006). doi:10.1038/440754a
Cossu, C., Brandt, L., Bagheri, S., Henningson, D.S.: Secondary threshold amplitudes for sinuous streak breakdown. Phys. Fluids 23(7), 074103 (2011). doi:10.1063/1.3614480
Cossu, C., Brandt, L.: Stabilization of tollmien-schlichting waves by finite amplitude optimal streaks in the blasius boundary layer. Phys. Fluids 14(8), L57–L60 (2002). doi:10.1063/1.1493791
Cossu, C., Brandt, L.: On tollmien-schlichting-like waves in streaky boundary layers. Euro. J. Mech. B/Fluids 23(6), 815–833 (2004). doi:10.1016/j.euromechflu.2004.05.001
Bagheri, S., Hanifi, A.: The stabilizing effect of streaks on tollmien-schlichting and oblique waves: A parametric study. Phys. Fluids 19(7), 078103 (2007). doi:10.1063/1.2746047
Fransson, J.H.M., Brandt, L., Talamelli, A., Cossu, C.: Experimental and theoretical investigation of the nonmodal growth of steady streaks in a flat plate boundary layer. Phys. Fluids 16(10), 3627–3638 (2004). doi:10.1063/1.1773493
Fransson, J.H.M., Brandt, L., Talamelli, A., Cossu, C.: Experimental study of the stabilization of tollmien-schlichting waves by finite amplitude streaks. Phys. Fluids 17(5), 054110 (2005). doi:10.1063/1.1897377
Fransson, J.H.M., Talamelli, A., Brandt, L., Cossu, C.: Delaying transition to turbulence by a passive mechanism. Phys. Rev. Lett. 96, 064501 (2006). doi:10.1103/PhysRevLett.96.064501
Fransson, J.H.M., Talamelli, A.: On the generation of steady streamwise streaks in flat-plate boundary layers. J. Fluid Mech. 698, 211–234 (2012). doi:10.1017/jfm.2012.80
Shahinfar, S., Sattarzadeh, S.S., Fransson, J.H.M., Talamelli, A.: Revival of classical vortex generators now for transition delay. Phys. Rev. Lett. 109, 074501 (2012). doi:10.1103/PhysRevLett.109.074501
Shahinfar, S., Fransson, J.H.M., Sattarzadeh, S.S., Talamelli, A.: Scaling of streamwise boundary layer streaks and their ability to reduce skin-friction drag. J. Fluid Mech. 733, 1–32 (2013). doi:10.1017/jfm.2013.431
Sattarzadeh, S.S., Fransson, J.H.: On the scaling of streamwise streaks and their efficiency to attenuate tollmien-schlichting waves. Exp. Fluids 56(3), 58 (2015). doi:10.1007/s00348-015-1930-x
Siconolfi, L., Camarri, S., Fransson, J.H.M.: Boundary layer stabilization using free-stream vortices. J.Fluid Mech. 764, R2 (2015). doi:10.1017/jfm.2014.731
Shahinfar, S., Sattarzadeh, S.S., Fransson, J.H.M.: Passive boundary layer control of oblique disturbances by finite-amplitude streaks. J. Fluid Mech. 749, 1–36 (2014). doi:10.1017/jfm.2014.211
Saric, W.S., Carillo, R.B., Reibert, M.S.: Leading-edge roughness as a transition control mechanism. In: AIAA Paper 98-0781 (1998)
Saric, W.S., Reed, H.L.: Supersonic laminar flow control on swept wings using distributed roughness. In: AIAA paper 2002-0147 (2002)
Hosseini, S.M., Tempelmann, D., Hanifi, A., Henningson, D.S.: Stabilization of a swept-wing boundary layer by distributed roughness elements. J. Fluid Mech. 718, R1 (2013). doi:10.1017/jfm.2013.33
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). Introduction. 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_1
Download citation
DOI: https://doi.org/10.1007/978-981-10-6832-4_1
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6831-7
Online ISBN: 978-981-10-6832-4
eBook Packages: EngineeringEngineering (R0)