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Attenuation by uniform suction of compressible Görtler vortices induced by free stream vortical disturbances

Published online by Cambridge University Press:  15 September 2025

Ludovico Fossà Open the ORCID record for Ludovico Fossà [Opens in a new window]  and
Pierre Ricco Open the ORCID record for Pierre Ricco [Opens in a new window]
Ludovico Fossà*
Affiliation:
School of Mechanical, Aerospace and Civil Engineering, University of Sheffield, Sheffield S1 3JD, UK Complex Fluids and Flows Unit, Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha, Onna-son, Kunigami-gun, Okinawa-ken 904-0495, Japan
Pierre Ricco
Affiliation:
School of Mechanical, Aerospace and Civil Engineering, University of Sheffield, Sheffield S1 3JD, UK
*
Corresponding author: Ludovico Fossà, ludovico-fossa@oist.jp
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Abstract

The effect of uniform wall suction on compressible Görtler vortices excited by free stream vortical disturbances is studied via asymptotic and numerical methods. The flow is described by the boundary-region framework, written and solved herein for non-similar boundary layers. The suction, applied downstream of an impermeable region, reduces the amplitude of steady and unsteady Görtler vortices. The vortices are attenuated more when the boundary layer has reached the asymptotic-suction condition than when it is streamwise-dependent. The impact of suction weakens as the free stream Mach number increases. As the boundary layer becomes thinner, the exponential growth of the vortices is prevented because the disturbance spanwise pressure gradient and spanwise viscous diffusion are inhibited. The flow is described by the boundary-layer equations in this case, for which the wall-normal momentum equation is uninfluential at leading order and the curvature effects responsible for the inviscid pressure-centrifugal imbalance are therefore negligible. The influence of unsteadiness weakens as suction intensifies because, in the limit of a thin boundary layer, the boundary-region solution simplifies to a regular-perturbation series whose first terms are described by the steady boundary-layer equations. Suction broadens the stability regions and may favour the presence of oblique Tollmien–Schlichting waves at the expense of more energetic Görtler vortices for relatively high frequencies and moderate Mach numbers.

JFM classification

Boundary Layers: Boundary layer control Boundary Layers: Boundary layer receptivity Compressible Flows: Compressible boundary layers

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JFM Papers
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Journal of Fluid Mechanics , Volume 1019 , 25 September 2025 , A10
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© The Author(s), 2025. Published by Cambridge University Press

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References

Al-Malki, M., Hussain, Z., Garrett, S. & Calabretto, S. 2021 Effects of parietal suction and injection on the stability of the Blasius boundary-layer flow over a permeable, heated plate. Phys. Rev. Fluids 6, 113902.CrossRefGoogle Scholar
Anderson, J.D. 2016 Fundamentals of Aerodynamics. McGraw-Hill Education.Google Scholar
Anderson, J.D. 2019 Hypersonic and High-Temperature Gas Dynamics. AIAA.Google Scholar
Aref, H. & Balachandar, S. 2018 A First Course in Computational Fluid Dynamics. Cambridge University Press.Google Scholar
Beckwith, I.E. & Bertram, M.H. 1972 A survey of NASA Langley studies on high-speed transition and the quiet tunnel. Tech. Memo. NASA-TM-X-2566, NASA Langley Research Centre.Google Scholar
Beckwith, I.E., Harvey, W.D., Harris, J.E. & Holley, B.B. 1973 Control of supersonic wind-tunnel noise by laminarization of nozzle-wall boundary layer. Tech. Rep. NASA-TM-X-2879, NASA Langley Research Centre.Google Scholar
Bountin, D.A., Gromyko, Y.V., Maslov, A.A., Polivanov, P.A. & Sidorenko, A.A. 2016 Effect of the surface roughness of blunt cone forebody on the position of laminar-turbulent transition. Thermophys. Aeromech. 23 (5), 629–638.CrossRefGoogle Scholar
Cebeci, T. 2002 Convective Heat Transfer. Horizons Publications.10.1007/978-3-662-06406-1CrossRefGoogle Scholar
Ciolkosz, L.D. & Spina, E.F. 2006 An experimental study of Görtler vortices in compressible flow. In 42nd AIAA/ASME/SAE/ASEE Jt. Propuls. Conf., AIAA Paper, 2006-4512, AIAA.CrossRefGoogle Scholar
Dimond, B., Costantini, M. & Klein, C. 2022 Experimental analysis of the effect of suction and step height on boundary-layer transition. In IUTAM Laminar-Turbul. Transit. (ed. S. Sherwin, P. Schmid &X. Wu), pp. 171–180. Springer International Publishing.10.1007/978-3-030-67902-6_14CrossRefGoogle Scholar
Dimond, B., Costantini, M., Risius, S., Klein, C. & Rein, M. 2020 Experimental investigation of the delay of gap- and step-induced transition by means of suction. In New Results Numer. Exp. Fluid Mech, vol. XII, pp. 165–174, Springer International Publishing CrossRefGoogle Scholar
van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic Press.Google Scholar
El-Hady, N.M. & Verma, A.K. 1981 Growth of Görtler vortices in compressible boundary layers along curves surfaces. In 14th Fluid Plasma Dyn. Conf., AIAA Paper 1981-1278, AIAA.CrossRefGoogle Scholar
El-Hady, N.M. & Verma, A.K. 1984 Instability of compressible boundary layers along curved walls with suction or cooling. AIAA J. 22 (2), 206–213.10.2514/3.8369CrossRefGoogle Scholar
Es-Sahli, O., Sescu, A., Koshuriyan, M.Z.A., Hattori, Y. & Hirota, M. 2023 Lagrange multiplier-based optimal control technique for streak attenuation in high-speed boundary layers. AIAA J. 61 (1), 63–75.10.2514/1.J062255CrossRefGoogle Scholar
Finnis, M.V. & Brown, A. 1997 The linear growth of Görtler vortices. Intl J. Heat Fluid Flow 18 (4), 389–399.CrossRefGoogle Scholar
Flechner, S.G., Jacobs, P.F. & Whitcomb, R.T. 1976 A high subsonic speed wind tunnel investigation of winglets on a representative second-generation jet transport wing. Tech. Rep. NASA-TN-D-8264, NASA Langley Research Centre.Google Scholar
Floryan, J.M. 1997 Stability of wall-bounded shear layers in the presence of simulated distributed surface roughness. J. Fluid Mech. 335, 29–55.Google Scholar
Floryan, J.M. & Saric, W.S. 1979 Stability of Görtler vortices in boundary layers with suction. In 12th Fluid Plasma Dyn. Conf. AIAA Paper 1979-1497.10.2514/6.1979-1497CrossRefGoogle Scholar
Floryan, J.M. & Saric, W.S. 1983 Effects of suction on the Görtler instability of boundary layers. AIAA J. 21 (12), 1635–1639.10.2514/3.8304CrossRefGoogle Scholar
Fransson, J.H.M. & Alfredsson, P.H. 2003 On the disturbance growth in an asymptotic suction boundary layer. J. Fluid Mech. 482, 51–90.Google Scholar
Goldstein, M.E. 1983 The evolution of Tollmien–Schlichting waves near a leading edge. J. Fluid Mech. 127, 59–81.10.1017/S002211208300261XCrossRefGoogle Scholar
Görtler, H. 1957 On the calculation of steady laminar boundary layer flows with continuous suction. J. Math. Mech. 6 (3), 323–340.Google Scholar
Graziosi, P. & Brown, G.L. 2002 Experiments on stability and transition at Mach 3. J. Fluid Mech. 472, 83–124.CrossRefGoogle Scholar
Griffith, A.A. & Meredith, F.W. 1936 The possible improvement in aircraft performance due to the use of boundary-layer suction. Tech. Rep. 2315 RAE E 3501, Aeronautical Research Council.Google Scholar
Gui, Y., Zhang, C., Li, X., Xu, D. & Wu, J. 2023 Hypersonic boundary-layer instability characterization and transition downstream of distributed roughness. Exp. Fluids 64 (10), 159.10.1007/s00348-023-03703-xCrossRefGoogle Scholar
Hader, C. & Fasel, H.F. 2021 Flow control using steady blowing and suction strips in a Mach 6 boundary layer on a flared cone. In AIAA Scitech 2021 Forum, AIAA Paper 2021-1206.Google Scholar
Hall, P. 1983 The linear development of Görtler vortices in growing boundary layers. J. Fluid Mech. 130, 41–58.10.1017/S0022112083000968CrossRefGoogle Scholar
Hoare, C.A.R. 1962 Quicksort. Comput. J. 5 (1), 10–16.10.1093/comjnl/5.1.10CrossRefGoogle Scholar
Hollender, C., Dwivedi, A. & Candler, G.V. 2019 Response of a Mach 6 cone-flare geometry to steady vortical disturbances: effect of steady suction. In AIAA Aviation of 2019 Forum, AIAA Paper 2019-3219.Google Scholar
Kay, J.M. 1953 Boundary-layer flow along a flat plate with uniform suction. ARC Tech. Rep. 2628, Cambridge University Engineering Laboratory.Google Scholar
Kobayashi, R. 1972 Note on the stability of a boundary layer on a concave wall with suction. J. Fluid Mech. 52 (2), 269–272.10.1017/S0022112072001405CrossRefGoogle Scholar
Kobayashi, R. 1974 Taylor–Görtler instability of a boundary layer with suction or blowing. AIAA J. 12 (3), 394–395.10.2514/3.49247CrossRefGoogle Scholar
Krishnan, K.S.G., Bertram, O. & Seibel, O. 2017 Review of hybrid laminar flow control systems. Prog. Aerosp. Sci. 93, 24–52.10.1016/j.paerosci.2017.05.005CrossRefGoogle Scholar
Kurian, T. & Fransson, J.H.M. 2011 Transient growth in the asymptotic suction boundary layer. Exp. Fluids 51 (3), 771–784.10.1007/s00348-011-1095-1CrossRefGoogle Scholar
Leib, S.J., Wundrow, D.W. & Goldstein, M.E. 1999 Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer. J. Fluid Mech. 380, 169–203.10.1017/S0022112098003504CrossRefGoogle Scholar
Leontiev, A.I. & Pavlyuchenko, A.M. 2008 Investigation of laminar-turbulent transition in supersonic boundary layers in an axisymmetric aerophysical flight complex and in a model in a wind tunnel in the presence of heat transfer and suction of air. High Temp. 46 (4), 542–565.CrossRefGoogle Scholar
Lew, H.G. & Fanucci, J.B. 1955 On the laminar compressible boundary layer over a flat plate with suction or injection. J. Aeronaut. Sci. 22 (9), 589–597.10.2514/8.3408CrossRefGoogle Scholar
Li, F., Choudhari, M.M., Paredes, P., Schneider, S.P. & Portoni, P. 2018 Görtler instability and its control via surface suction over an axisymmetric cone at Mach 6. In 2018 Fluid Dyn. Conf., AIAA Paper, 2018-3069, AIAA.Google Scholar
de Luca, L., Cardone, G., Aymer de la Chevalerie, D. & Fonteneau, A. 1993 Goertler instability of a hypersonic boundary layer. Exp. Fluids 16 (1), 10–16.10.1007/BF00188500CrossRefGoogle Scholar
Mangalam, S., Dagenhart, J. & Kalburgi, V. 1987 Influence of suction and curvature on the growth of Görtler vortices on an airfoil. In 25th AIAA Aerosp. Sci. Meet., AIAA Paper 1987-0481. AIAA.Google Scholar
Marensi, E. & Ricco, P. 2017 Growth and wall-transpiration control of nonlinear unsteady Görtler vortices forced by free-stream vortical disturbances. Phys. Fluids 29 (11), 114106.Google Scholar
Maslov, A.A., Shiplyuk, A.N., Sidorenko, A.A. & Arnal, D. 2001 Leading-edge receptivity of a hypersonic boundary layer on a flat plate. J. Fluid Mech. 426, 73–94.CrossRefGoogle Scholar
Matsubara, M. & Alfredsson, P.H. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149–168.10.1017/S0022112000002810CrossRefGoogle Scholar
Messing, R. & Kloker, M.J. 2010 Investigation of suction for laminar flow control of three-dimensional boundary layers. J. Fluid Mech. 658, 117–147.10.1017/S0022112010001576CrossRefGoogle Scholar
Methel, J., Forte, M., Vermeersch, O. & Casalis, G. 2021 Experimental investigation on the effect of forward-facing steps and gaps combined with wall suction on boundary layer transition. Exp. Fluids 63 (1), 21.10.1007/s00348-021-03361-xCrossRefGoogle Scholar
Morduchow, M. 1963 General asymptotic solution of the laminar compressible boundary layer with heat transfer. AIAA J. 1 (8), 1949–1951.10.2514/3.1974CrossRefGoogle Scholar
Myose, R.Y. & Blackwelder, R.F. 1995 Control of streamwise vortices using selective suction. AIAA J. 33 (6), 1076–1080.10.2514/3.12667CrossRefGoogle Scholar
Negi, P.S., Mishra, M. & Skote, M. 2015 DNS of a single low-speed streak subject to spanwise wall oscillations. Flow Turbul. Combust. 94 (4), 795–816.10.1007/s10494-015-9599-zCrossRefGoogle Scholar
Panday, S. & Floryan, J.M. 2023 Accurate determination of stability characteristics of spatially modulated shear layers. J. Fluid Mech. 975, A50.10.1017/jfm.2023.877CrossRefGoogle Scholar
Polyanin, A.D. & Nazaikinskii, V.E. 2015 Handbook of Linear Partial Differential Equations for Engineers and Scientists. 2nd edn. CRC Press.10.1201/b19056CrossRefGoogle Scholar
Ricco, P. & Dilib, F. 2010 The influence of wall suction and blowing on boundary-layer laminar streaks generated by free-stream vortical disturbances. Phys. Fluids 22 (4), 044101.Google Scholar
Ricco, P., Shah, D. & Hicks, P.D. 2013 Compressible laminar streaks with wall suction. Phys. Fluids 25 (5), 054110.Google Scholar
Ricco, P. & Wu, X. 2007 Response of a compressible laminar boundary layer to free-stream vortical disturbances. J. Fluid Mech. 587, 97–138.10.1017/S0022112007007070CrossRefGoogle Scholar
Roberts, P.J.D. & Floryan, J.M. 2002 Instability of accelerated boundary layers induced by surface suction. AIAA J. 40 (5), 851–859.10.2514/2.1751CrossRefGoogle Scholar
Roberts, P.J.D. & Floryan, J.M. 2008 Instability of adverse-pressure-gradient boundary layers with suction. AIAA J. 46 (10), 2416–2423.10.2514/1.32624CrossRefGoogle Scholar
Roberts, P.J.D., Floryan, J.M., Casalis, G. & Arnal, D. 2001 Boundary layer instability induced by surface suction. Phys. Fluids 13 (9), 2543–2552.10.1063/1.1384868CrossRefGoogle Scholar
Running, C.L., Bemis, B.L., Hill, J.L., Borg, M.P., Redmond, J.J., Jantze, K. & Scalo, C. 2023 Attenuation of hypersonic second-mode boundary-layer instability with an ultrasonically absorptive silicon-carbide foam. Exp. Fluids 64 (4), 79.10.1007/s00348-023-03615-wCrossRefGoogle Scholar
Saric, W.S. 1985 Laminar flow control with suction: theory and experiment. AGARD Rep. 723, 2-1–2-13.Google Scholar
Schmidt, B.E., Bitter, N.P., Hornung, H.G. & Shepherd, J.E. 2016 Injection into supersonic boundary layers. AIAA J. 54 (1), 161–173.10.2514/1.J054123CrossRefGoogle Scholar
Schneider, S.P. 2008 a Development of hypersonic quiet tunnels. J. Spacecr. Rockets 45 (4), 641–664.10.2514/1.34489CrossRefGoogle Scholar
Schneider, S.P. 2008 b Effects of roughness on hypersonic boundary-layer transition. J. Spacecr. Rockets 45 (2), 193–209.CrossRefGoogle Scholar
Sescu, A., Alaziz, R. & Afsar, M. 2018 Control of Görtler vortices in high-speed boundary layers. In 2018 AIAA Aerosp. Sci. Meet., AIAA Paper 2018-1078.Google Scholar
Sescu, A., Alaziz, R. & Afsar, M. 2019 Effect of wall transpiration and heat transfer on Görtler vortices in high-speed flows. AIAA J. 57 (3), 1159–1171.10.2514/1.J057330CrossRefGoogle Scholar
Sims, J.L. 1964 Tables for supersonic flow around right circular cones at zero angle of attack. Tech. Rep. NASA-SP-3004, NASA Marshall Space Flight Center, NASA Special Publication.Google Scholar
Stewartson, K. 1964 The Theory of Laminar Boundary Layers in Compressible Fluids. Clarendon Press.10.1063/1.3051661CrossRefGoogle Scholar
Swearingen, J.D. & Blackwelder, R.F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255–290.10.1017/S0022112087002337CrossRefGoogle Scholar
Tandiono, T., Winoto, S.H. & Shah, D.A. 2008 On the linear and nonlinear development of Görtler vortices. Phys. Fluids 20 (9), 094103.10.1063/1.2980349CrossRefGoogle Scholar
Tani, I. 1962 Production of longitudinal vortices in the boundary layer along a concave wall. J. Geophys. Res. 67 (8), 3075–3080.10.1029/JZ067i008p03075CrossRefGoogle Scholar
Traub, H., Kube, J., Jose, S., Prasannakumar, A. & Hühne, C. 2024 Structural and aerodynamic characteristics of micro-perforated porous sheets for laminar flow control. In ASME. 2024 Aerosp. Struct. Struct. Dyn. Mater. Conf., Proc. ASME. 2024 SSDM2024-121620, pp. V001T03A020.Google Scholar
Viaro, S. & Ricco, P. 2019 a Compressible unsteady Görtler vortices subject to free-stream vortical disturbances. J. Fluid Mech. 867, 250–299.CrossRefGoogle Scholar
Viaro, S. & Ricco, P. 2019 b Neutral stability curves of compressible Görtler flow generated by low-frequency free-stream vortical disturbances. J. Fluid Mech. 876, 1146–1157.10.1017/jfm.2019.590CrossRefGoogle Scholar
Wang, Q., Wang, Z. & Zhao, Y. 2018 Visualization of Görtler vortices in supersonic concave boundary layer. J. Vis. 21 (1), 57–62.10.1007/s12650-017-0443-5CrossRefGoogle Scholar
Wedin, H., Cherubini, S. & Bottaro, A. 2015 Effect of plate permeability on nonlinear stability of the asymptotic suction boundary layer. Phys. Rev. E 92, 013022.Google ScholarPubMed
Wu, X., Zhao, D. & Luo, J. 2011 Excitation of steady and unsteady Görtler vortices by free-stream vortical disturbances. J. Fluid Mech. 682, 66–100.10.1017/jfm.2011.224CrossRefGoogle Scholar
Wundrow, D.W. & Goldstein, M.E. 2001 Effect on a laminar boundary layer of small-amplitude streamwise vorticity in the upstream flow. J. Fluid Mech. 426, 229–262.10.1017/S0022112000002354CrossRefGoogle Scholar
Xu, D., Liu, J. & Wu, X. 2020 Görtler vortices and streaks in boundary layer subject to pressure gradient: excitation by free stream vortical disturbances, nonlinear evolution and secondary instability. J. Fluid Mech. 900, A15.10.1017/jfm.2020.438CrossRefGoogle Scholar
Xu, D., Ricco, P. & Duan, L. 2024 Görtler instability and transition in compressible flows. AIAA J. 62 (2), 489–517.10.2514/1.J062866CrossRefGoogle Scholar
Xu, D., Zhang, Y. & Wu, X. 2017 Nonlinear evolution and secondary instability of steady and unsteady Görtler vortices induced by free-stream vortical disturbances. J. Fluid Mech. 829, 681–730.10.1017/jfm.2017.572CrossRefGoogle Scholar
Yang, G. & Weigand, B. 2018 Investigation of the Klinkenberg effect in a micro/nanoporous medium by direct simulation Monte Carlo method. Phys. Rev. Fluids 3, 044201.10.1103/PhysRevFluids.3.044201CrossRefGoogle Scholar
Yoshioka, S., Fransson, J.H.M. & Alfredsson, P.H. 2004 Free stream turbulence induced disturbances in boundary layers with wall suction. Phys. Fluids 16 (10), 3530–3539.10.1063/1.1775222CrossRefGoogle Scholar
Young, A.D. 1948 Note on the velocity and temperature distributions attained with suction on a flat plate of infinite extent in compressible flow. Q. J. Mech. Appl. Maths 1 (1), 70–75.10.1093/qjmam/1.1.70CrossRefGoogle Scholar