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Genetic-algorithm-based control of a turbulent boundary layer

Published online by Cambridge University Press:  22 June 2026

Jianing Yu Open the ORCID record for Jianing Yu [Opens in a new window]  and
Yu Zhou
Jianing Yu
Affiliation:
School of Mechanical Engineering & Mechanics, Eastern Institute of Technology , Ningbo 315000, PR China Center for Turbulence Control, Harbin Institute of Technology, Shenzhen 315000, PR China
Yu Zhou*
Affiliation:
School of Mechanical Engineering & Mechanics, Eastern Institute of Technology , Ningbo 315000, PR China
*
Corresponding author: Yu Zhou, yuzhou@eitech.edu.cn
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Abstract

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This work aims to investigate experimentally the control of a turbulent boundary layer over a flat plate based on a genetic-algorithm (GA)-based control system. A novel actuator is developed in house, consisting of one array of 11 spanwise-aligned synthetic minijets through longitudinal miniature slits, each independently controlled in terms of its exit momentum coefficient Cμ, frequency fe and phase ϕ, while nine wall wires are placed downstream of the actuator to measure a variation in wall friction. A GA is employed for the unsupervised learning of near-optimal control strategies, i.e. the optimal ϕ of the synthetic jets, with fe and Cμ optimized first. The learning process unveils three typical control strategies that may attain substantial drag reduction (DR) in both actuation and downstream regions, i.e. conventional uniform forcing (CUF), GA-I and GA-II. The latter two are characterized by the triangle- and trapezoid-like distributions of ϕ, respectively, thus each producing a spanwise motion. The three strategies achieve spanwise-averaged local DR by 45 %, 52 % and 52 %, respectively. The downstream drag-reducing areas exhibit an appreciable difference between the three cases, with CUF recovering drag more rapidly than the other two. It has been found that the three cases are associated with different DR mechanisms and flow physics, which account for the distinct control performances.

JFM classification

Turbulent Flows: Turbulent boundary layers Flow Control: Drag reduction Mathematical Foundations: Machine learning

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JFM Papers
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Journal of Fluid Mechanics , Volume 1037 , 25 June 2026 , A34
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© The Author(s), 2026. Published by Cambridge University Press

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References

Abbassi, M.R., Baars, W.J., Hutchins, N. & Marusic, I. 2017 Skin-friction drag reduction in a high-Reynolds-number turbulent boundary layer via real-time control of large-scale structures. Intl J. Heat Fluid Flow 67, 30–41.CrossRefGoogle Scholar
Alamé, K. & Mahesh, K. 2019 Wall-bounded flow over a realistically rough superhydrophobic surface. J. Fluid Mech. 873, 977–1019.CrossRefGoogle Scholar
Antonia, R., Kim, J. & Browne, L. 1991 Some characteristics of small-scale turbulence in a turbulent duct flow. J. Fluid Mech. 233, 369–388.CrossRefGoogle Scholar
Antonia, R.A., Zhu, Y. & Sokolov, M. 1995 Effect of concentrated wall suction on a turbulent boundary layer. Phys. Fluids 7 (10), 2465–2474.CrossRefGoogle Scholar
Bai, H.L., Zhou, Y., Zhang, W.G. & Antonia, R.A. 2018 Streamwise vortices and velocity streaks in a locally drag-reduced turbulent boundary layer. Flow Turbul. Combust. 100 (2), 391–416.10.1007/s10494-017-9860-8CrossRefGoogle Scholar
Bai, H.L., Zhou, Y., Zhang, W.G., Xu, S.J., Wang, Y. & Antonia, R.A. 2014 Active control of a turbulent boundary layer based on local surface perturbation. J. Fluid Mech. 750, 316–354.10.1017/jfm.2014.261CrossRefGoogle Scholar
Benard, N., Pons-Prats, J., Periaux, J., Bugeda, G., Braud, P., Bonnet, J.P. & Moreau, E. 2016 Turbulent separated shear flow control by surface plasma actuator: experimental optimization by genetic algorithm approach. Exp. Fluids 57 (2), 22.10.1007/s00348-015-2107-3CrossRefGoogle Scholar
Blackwelder, R.F. & Haritonidis, J.H. 1983 Scaling of the bursting frequency in turbulent boundary layers. J. Fluid Mech. 132, 87–103.10.1017/S0022112083001494CrossRefGoogle Scholar
Blackwelder, R.F. & Kaplan, R.E. 1976 On the wall structure of the turbulent boundary layer. J. Fluid Mech. 76 (1), 89–112.10.1017/S0022112076003145CrossRefGoogle Scholar
Brandt, L. 2014 The lift-up effect: the linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. B 47, 80–96.CrossRefGoogle Scholar
Brunton, S.L. & Noack, B.R. 2015 Closed-loop turbulence control: progress and challenges. Appl. Mech. Rev. 67 (5), 050801.10.1115/1.4031175CrossRefGoogle Scholar
Canton, J., Örlü, R., Chin, C., Hutchins, N., Monty, J. & Schlatter, P. 2016 a On large-scale friction control in turbulent wall flow in low Reynolds number channels. Flow Turbul. Combust. 97 (3), 811–827.10.1007/s10494-016-9723-8CrossRefGoogle Scholar
Canton, J., Örlü, R., Chin, C. & Schlatter, P. 2016 b Reynolds number dependence of large-scale friction control in turbulent channel flow. Phys. Rev. Fluids 1 (8), 081501.10.1103/PhysRevFluids.1.081501CrossRefGoogle Scholar
Chang, G.H., Tang, S.L., Fan, D.W. & Zhou, Y. 2025 AI-based active flow control for drag reduction of a maglev train model. In Proceedings of 6th International Conference in Numerical and Experimental Aerodynamics of Road Vehicles and Trains (Aerovehicles 6), July 1–3, 2025, pp. 59–62. University of Birmingham.Google Scholar
Checco, A., Ocko, B.M., Rahman, A., Black, C.T., Tasinkevych, M., Giacomello, A. & Dietrich, S. 2014 Collapse and reversibility of the superhydrophobic state on nanotextured surfaces. Phys. Rev. Lett. 112 (21), 216101.10.1103/PhysRevLett.112.216101CrossRefGoogle Scholar
Cheng, X.Q., Qiao, Z.X., Zhang, X., Quadrio, M. & Zhou, Y. 2021 a Skin-friction reduction using periodic blowing through streamwise slits. J. Fluid Mech. 920, A50.10.1017/jfm.2021.439CrossRefGoogle Scholar
Cheng, X.Q., Wong, C.W., Hussain, F., Schröder, W. & Zhou, Y. 2021 b Flat plate drag reduction using plasma-generated streamwise vortices. J. Fluid Mech. 918, A24.10.1017/jfm.2021.311CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–539.10.1017/S0022112093002575CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75–110.10.1017/S0022112094000431CrossRefGoogle Scholar
Choi, K.-S. 1989 Near-wall structure of a turbulent boundary layer with riblets. J. Fluid Mech. 208, 417–458.CrossRefGoogle Scholar
Choi, K.-S. & Clayton, B.R. 2001 The mechanism of turbulent drag reduction with wall oscillation. Intl J. Heat Fluid Flow 22 (1), 1–9.CrossRefGoogle Scholar
Choi, K.-S., Yang, X., Clayton, B., Glover, E., Atlar, M., Semenov, B. & Kulik, V. 1997 Turbulent drag reduction using compliant surfaces. Proc. R. Soc. Lond. A 453 (1965), 2229–2240.10.1098/rspa.1997.0119CrossRefGoogle Scholar
Corke, T.C. & Thomas, F.O. 2018 Active and passive turbulent boundary-layer drag reduction. AIAA J. 56 (10), 3835–3847.CrossRefGoogle Scholar
Cox, T.F. & Cox, M.A.A. 2000 Multidimensional scaling. In Monographs On Statistics and Applied Probability, vol. 88. Chapman and Hall.Google Scholar
Daniello, R.J., Waterhouse, N.E. & Rothstein, J.P. 2009 Drag reduction in turbulent flows over superhydrophobic surfaces. Phys. Fluids 21 (8), 085103.10.1063/1.3207885CrossRefGoogle Scholar
Debien, A., von Krbek, K.A.F.F., Mazellier, N., Duriez, T., Cordier, L., Noack, B.R., Abel, M.W. & Kourta, A. 2016 Closed-loop separation control over a sharp edge ramp using genetic programming. Exp. Fluids 57 (3), 40.10.1007/s00348-016-2126-8CrossRefGoogle Scholar
Delaunay, B. 1934 Sur la sphère vide. A la mémoire de Georges Voronoï. Cl. Sci. Math. Nat. 6, 793–800.Google Scholar
Deng, B.Q. & Xu, C.X. 2012 Influence of active control on STG-based generation of streamwise vortices in near-wall turbulence. J. Fluid Mech. 710, 234–259.10.1017/jfm.2012.361CrossRefGoogle Scholar
Di Cicca, G.M., Iuso, G., Spazzini, P.G. & Onorato, M. 2002 Particle image velocimetry investigation of a turbulent boundary layer manipulated by spanwise wall oscillations. J. Fluid Mech. 467, 41–56.CrossRefGoogle Scholar
Du, Y. & Karniadakis, G.E. 2000 Suppressing wall turbulence by means of a transverse travelling wave. Science 288, 1230–1234.CrossRefGoogle Scholar
Duong, A.H., Corke, T.C. & Thomas, F.O. 2021 Characteristics of drag-reduced turbulent boundary layers with pulsed-direct-current plasma actuation. J. Fluid Mech. 915, A113.10.1017/jfm.2021.167CrossRefGoogle Scholar
Duriez, T., Brunton, S.L. & Noack, B.R. 2017 Machine Learning Control: Taming Nonlinear Dynamics and Turbulence, Fluid Mechanics and its Applications, vol. 116. Springer-Verlag.10.1007/978-3-319-40624-4CrossRefGoogle Scholar
Endo, T., Kasagi, N. & Suzuki, Y. 2000 Feedback control of wall turbulence with wall deformation. Intl J. Heat Fluid Flow 21 (5), 568–575.10.1016/S0142-727X(00)00046-1CrossRefGoogle Scholar
Fan, D., Zhang, B., Zhou, Y. & Noack, B.R. 2020 a Optimization and sensitivity analysis of active drag reduction of a square-back Ahmed body using machine learning control. Phys. Fluids 32 (12), 125117.10.1063/5.0033156CrossRefGoogle Scholar
Fan, D., Zhou, Y. & Noack, B.R. 2020 b Fast triple-parameter extremum seeking exemplified for jet control. Exp. Fluids 61 (7), 152.10.1007/s00348-020-02953-3CrossRefGoogle Scholar
Fukagata, K., Kern, S., Chatelain, P., Koumoutsakos, P. & Kasagi, N. 2008 Evolutionary optimization of an anisotropic compliant surface for turbulent friction drag reduction. J. Turbul. 9, N35.CrossRefGoogle Scholar
Gautier, N., Aider, J.L., Duriez, T., Noack, B.R., Segond, M. & Abel, M. 2015 Closed-loop separation control using machine learning. J. Fluid Mech. 770, 442–457.10.1017/jfm.2015.95CrossRefGoogle Scholar
Goldberg, D.E. 1989 Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Pub. Co.Google Scholar
Hamilton, J.M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.10.1017/S0022112095000978CrossRefGoogle Scholar
Hussain, A.F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303–356.10.1017/S0022112086001192CrossRefGoogle Scholar
Hutchins, N. & Choi, K.-S. 2002 Accurate measurements of local skin friction coefficient using hot-wire anemometry. Prog. Aerosp. Sci. 38, 421–446.CrossRefGoogle Scholar
Itoh, M., Tamano, S., Yokota, K. & Taniguchi, S. 2006 Drag reduction in a turbulent boundary layer on a flexible sheet undergoing a spanwise traveling wave motion. J. Turbul. 7 (27), N27.10.1080/14685240600647064CrossRefGoogle Scholar
Iuso, G., Di Cicca, G.M., Onorato, M., Spazzini, P.G. & Malvano, R. 2003 Velocity streak structure modifications induced by flow manipulation. Phys. Fluids 15 (9), 2602–2612.10.1063/1.1597680CrossRefGoogle Scholar
Iuso, G., Onorato, M., Spazzini, P.G. & Di Cicca, G.M. 2002 Wall turbulence manipulation by large-scale streamwise vortices. J. Fluid Mech. 473, 23–58.10.1017/S0022112002002574CrossRefGoogle Scholar
Jacobson, S.A. & Reynolds, W.C. 1998 Active control of streamwise vortices and streaks in boundary layers. J. Fluid Mech. 360, 179–211.10.1017/S0022112097008562CrossRefGoogle Scholar
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.10.1017/S0022112096003965CrossRefGoogle Scholar
Johansson, A.V., Alfredsson, P.H. & Kim, J. 1991 Evolution and dynamics of shear-layer structures in near-wall turbulence. J. Fluid Mech. 224, 579–599.CrossRefGoogle Scholar
Jung, W.J., Mangiavacchi, N. & Akhavan, R. 1992 Suppression of turbulence in wall-bounded flows by high-frequency spanwise oscillations. Phys. Fluids A 4 (8), 1605–1607.10.1063/1.858381CrossRefGoogle Scholar
Kametani, Y. & Fukagata, K. 2011 Direct numerical simulation of spatially developing turbulent boundary layers with uniform blowing or suction. J. Fluid Mech. 681, 154–172.10.1017/jfm.2011.219CrossRefGoogle Scholar
Kang, S. & Choi, H. 2000 Active wall motions for skin-friction drag reduction. Phys. Fluids 12 (12), 3301–3304.10.1063/1.1320833CrossRefGoogle Scholar
Kim, H.T., Kline, S.J. & Reynolds, W.C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50 (1), 133–160.10.1017/S0022112071002490CrossRefGoogle Scholar
Kim, J. 1983 On the structure of wall-bounded turbulent flows. Phys. Fluids 26 (8), 2088–2097.10.1063/1.864413CrossRefGoogle Scholar
Kim, J., Kim, K. & Sung, H.J. 2003 Wall pressure fluctuations in a turbulent boundary layer after blowing or suction. AIAA J. 41 (9), 1697–1704.10.2514/2.7315CrossRefGoogle Scholar
Kim, K. & Sung, H.J. 2006 Effects of unsteady blowing through a spanwise slot on a turbulent boundary layer. J. Fluid Mech. 557, 423–450.10.1017/S0022112006009906CrossRefGoogle Scholar
Kline, S.J., Reynolds, W.C., Schraub, F.A. & Runstadler, P.W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30 (4), 741–773.10.1017/S0022112067001740CrossRefGoogle Scholar
Kravchenko, A.G., Choi, H. & Moin, P. 1993 On the relation of near-wall streamwise vortices to wall skin friction in turbulent boundary layers. Phys. Fluids A 5 (12), 3307–3309.CrossRefGoogle Scholar
Lai, P., Wang, R., Zhang, W. & Xu, H. 2021 Parameter optimization of open-loop control of a circular cylinder by simplified reinforcement learning. Phys. Fluids 33, 107110.10.1063/5.0068454CrossRefGoogle Scholar
Lee, T., Fisher, M. & Schwarz, W. 1993 Investigation of the stable interaction of a passive compliant surface with a turbulent boundary layer. J. Fluid Mech. 257, 373–401.10.1017/S002211209300312XCrossRefGoogle Scholar
Li, H., Yu, J., Chen, Z. & Ren, K. 2023 Numerical research on drag-reduction characteristics of a body of revolution based on periodic forcing. Ocean Engng 280, 114909.10.1016/j.oceaneng.2023.114909CrossRefGoogle Scholar
Li, R.Y., Noack, B.R., Cordier, L., Borée, J. & Harambat, F. 2017 Drag reduction of a car model by linear genetic programming control. Exp. Fluids 58, 1–20.10.1007/s00348-017-2382-2CrossRefGoogle Scholar
Li, W., Roggenkamp, D., Hecken, T., Jessen, W., Klaas, M. & Schröder, W. 2018 Parametric investigation of friction drag reduction in turbulent flow over a flexible wall undergoing spanwise transversal traveling waves. Exp. Fluids 59 (6), 105.10.1007/s00348-018-2559-3CrossRefGoogle Scholar
Li, Y., Cui, W., Jia, Q., Li, Q., Yang, Z., Morzyński, M. & Noack, B.R. 2022 Explorative gradient method for active drag reduction of the fluidic pinball and slanted Ahmed body. J. Fluid Mech. 932, A7.10.1017/jfm.2021.974CrossRefGoogle Scholar
Lou, Y., Sun, S. & Nocedal, J. 2025 Design guidelines for noise-tolerant optimization with applications in robust design. SIAM J. Sci. Comput. 47 (3), A1335–A1357.10.1137/24M1632279CrossRefGoogle Scholar
Lu, L., Li, D., Gao, Z., Cao, Z., Bai, Y. & Zheng, J. 2020 Characteristics of array of distributed synthetic jets and effect on turbulent boundary layer. Acta Mechanica Sin. 36 (6), 1171–1190.10.1007/s10409-020-01001-xCrossRefGoogle Scholar
Martell, M.B., Perot, J.B. & Rothstein, J.P. 2009 Direct numerical simulations of turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 620, 31–41.10.1017/S0022112008004916CrossRefGoogle Scholar
Meyers, A., Duong, A., Corke, T.C. & Thomas, F.O. 2025 Characterizing turbulent boundary layer response and recovery to buffer region spanwise blowing. J. Fluid Mech. 1016, A26.10.1017/jfm.2025.10288CrossRefGoogle Scholar
Minelli, G., Dong, T., Noack, B.R. & Krajnović, S. 2020 Upstream actuation for bluff-body wake control driven by a genetically inspired optimization. J. Fluid Mech. 893, A1.10.1017/jfm.2020.220CrossRefGoogle Scholar
Mito, Y. & Kasagi, N. 1998 DNS study of turbulence modification with streamwise-uniform sinusoidal wall-oscillation. Intl J. Heat Fluid Flow 19 (5), 470–481.10.1016/S0142-727X(98)10025-5CrossRefGoogle Scholar
Nabae, Y., Kawai, K. & Fukagata, K. 2020 Prediction of drag reduction effect by streamwise traveling wave-like wall deformation in turbulent channel flow at practically high Reynolds numbers. Intl J. Heat Fluid Flow 82, 108550.10.1016/j.ijheatfluidflow.2020.108550CrossRefGoogle Scholar
Nakanishi, R., Mamori, H. & Fukagata, K. 2012 Relaminarization of turbulent channel flow using traveling wave-like wall deformation. Intl J. Heat Fluid Flow 35, 152–159.10.1016/j.ijheatfluidflow.2012.01.007CrossRefGoogle Scholar
Orlandi, P. & Jiménez, J. 1994 On the generation of turbulent wall friction. Phys. Fluids 6 (2), 634–641.10.1063/1.868303CrossRefGoogle Scholar
Paris, R., Beneddine, S. & Dandois, J. 2021 Robust flow control and optimal sensor placement using deep reinforcement learning. J. Fluid Mech. 913, A25.CrossRefGoogle Scholar
Park, J. & Choi, H. 1999 Effects of uniform blowing or suction from a spanwise slot on a turbulent boundary layer flow. Phys. Fluids 11 (10), 3095–3105.10.1063/1.870167CrossRefGoogle Scholar
Pirozzoli, S. & Smits, A.J. 2023 Outer-layer universality of the mean velocity profile in turbulent wall-bounded flows. Phys. Rev. Fluids 8 (6), 064607.10.1103/PhysRevFluids.8.064607CrossRefGoogle Scholar
Qayoum, A., Gupta, V., Panigrahi, P.K. & Muralidhar, K. 2010 Perturbation of a laminar boundary layer by a synthetic jet for heat transfer enhancement. Intl J. Heat Mass Transfer 53 (23–24), 5035–5057.10.1016/j.ijheatmasstransfer.2010.07.061CrossRefGoogle Scholar
Qiao, Z.X., Minelli, G., Noack, B.R., Krajnović, S. & Chernoray, V. 2021 Multi-frequency aerodynamic control of a yawed bluff body optimized with a genetic algorithm. J. Wind Engng Ind. Aerodyn. 212, 104600.10.1016/j.jweia.2021.104600CrossRefGoogle Scholar
Qiao, Z.X., Wu, Z. & Zhou, Y. 2018 Turbulent boundary layer manipulation under a proportional-derivative closed-loop scheme. Phys. Fluids 30, 115101.10.1063/1.5047537CrossRefGoogle Scholar
Qiao, Z.X., Xu, S.J. & Zhou, Y. 2019 On the measurement of wall-normal velocity derivative in a turbulent boundary layer. Flow Turbul. Combust. 103 (2), 369–387.10.1007/s10494-019-00031-1CrossRefGoogle Scholar
Qiao, Z.X., Zhou, Y. & Wu, Z. 2017 Turbulent boundary layer under the control of different schemes. Proc. Math. Phys. Sci. 473, 20170038.Google ScholarPubMed
Quadrio, M. 2011 Drag reduction in turbulent boundary layers by in-plane wall motion. Phil. Trans. A Math. Phys. Engng Sci. 369, 1428–1442.Google ScholarPubMed
Quadrio, M. & Luchini, P. 2003 Integral space–time scales in turbulent wall flows. Phys. Fluids 15 (8), 2219–2227.CrossRefGoogle Scholar
Quadrio, M. & Ricco, P. 2004 Critical assessment of turbulent drag reduction through spanwise wall oscillations. J. Fluid Mech. 521, 251–271.CrossRefGoogle Scholar
Quadrio, M., Ricco, P. & Viotti, C. 2009 Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction. J. Fluid Mech. 627, 161–178.10.1017/S0022112009006077CrossRefGoogle Scholar
Rabault, J., Kuchta, M., Jensen, A., Réglade, U. & Cerardi, N. 2019 Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. J. Fluid Mech. 865, 281–302.10.1017/jfm.2019.62CrossRefGoogle Scholar
Rastegari, A. & Akhavan, R. 2018 The common mechanism of turbulent skin-friction drag reduction with superhydrophobic longitudinal microgrooves and riblets. J. Fluid Mech. 838, 68–104.10.1017/jfm.2017.865CrossRefGoogle Scholar
Rathnasingham, R. & Breuer, K.S. 2003 Active control of turbulent boundary layers. J. Fluid Mech. 495, 209–233.10.1017/S0022112003006177CrossRefGoogle Scholar
Robinson, S. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601–639.10.1146/annurev.fl.23.010191.003125CrossRefGoogle Scholar
Robinson, S.K. 1990 A review of vortex structures and associated coherent motions in turbulent boundary layers. In Structure of Turbulence and Drag Reduction: IUTAM Symposium, July 25–28, Zurich, pp. 23–50. Springer.10.1007/978-3-642-50971-1_2CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 1998 A large-scale control strategy for drag reduction in turbulent boundary layers. Phys. Fluids 10 (5), 1049–1051.10.1063/1.869789CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.10.1017/S002211200100667XCrossRefGoogle Scholar
Skote, M. 2011 Turbulent boundary layer flow subject to streamwise oscillation of spanwise wall-velocity. Phys. Fluids 23, 081703.10.1063/1.3626028CrossRefGoogle Scholar
Smith, C. 1984 A Synthesized Model of the Near-Wall Behavior in Turbulent Boundary Layers. In Proceedings of the 8th Symposium on Turbulence,pp. 299–325. University Missouri-Rolla.Google Scholar
Spalart, P.R. 1988 Direct simulation of a turbulent boundary layer up to Rθ = 1410. J. Fluid Mech. 187, 61–98.10.1017/S0022112088000345CrossRefGoogle Scholar
Spinosa, E. & Zhong, S. 2017 Reduction of Skin Friction Drag in a Turbulent Boundary Layer Using Circular Synthetic Jets. In 55th AIAA Aerospace Sciences Meeting, 9–13 January 2017, Grapevine, Texas.10.2514/6.2017-0324CrossRefGoogle Scholar
Stroh, A., Hasegawa, Y., Schlatter, P. & Frohnapfel, B. 2016 Global effect of local skin friction drag reduction in spatially developing turbulent boundary layer. J. Fluid Mech. 805, 303–321.10.1017/jfm.2016.545CrossRefGoogle Scholar
Tang, H., Rabault, J., Kuhnle, A., Wang, Y. & Wang, T. 2020 Robust active flow control over a range of Reynolds numbers using an artificial neural network trained through deep reinforcement learning. Phys. Fluids 32 (5), 053605.10.1063/5.0006492CrossRefGoogle Scholar
Tardu, S.F. 2001 Active control of near-wall turbulence by local oscillating blowing. J. Fluid Mech. 439, 217–253.10.1017/S0022112001004542CrossRefGoogle Scholar
Thomas, F.O., Corke, T.C., Duong, A., Midya, S. & Yates, K. 2019 Turbulent drag reduction using pulsed-DC plasma actuation. J. Phys. D: Appl. Phys. 52 (43), 434001.CrossRefGoogle Scholar
Tomiyama, N. & Fukagata, K. 2013 Direct numerical simulation of drag reduction in a turbulent channel flow using spanwise traveling wave-like wall deformation. Phys. Fluids 25 (10), 105115.10.1063/1.4826887CrossRefGoogle Scholar
Utturkar, Y., Arik, M., Seeley, C.E. & Gursoy, M. 2008 An experimental and computational heat transfer study of pulsating jets. J. Heat Transfer 130, 062201.10.1115/1.2891158CrossRefGoogle Scholar
Walsh, M.J. 1983 Riblets as a viscous drag reduction technique. AIAA J. 21 (4), 485–486.10.2514/3.60126CrossRefGoogle Scholar
Wei, X. & Zhou, Y. 2024 Scaling of drag reduction in a turbulent boundary layer based on plasma-generated streamwise vortices. In Proceedings of 13th International Symposium on Turbulence and Shear Flow Phenomena, 25–38 Jun 2024, Montreal, Canada. Paper no. 389.Google Scholar
Wei, X. & Zhou, Y. 2025 Scaling of flat plate drag reduction using plasma-generated streamwise vortices. J. Fluid Mech. 1007, R5.10.1017/jfm.2025.116CrossRefGoogle Scholar
Wong, C.W., Zhou, Y., Li, Y. & Li, Y. 2015 Active drag reduction in a turbulent boundary layer based on plasma-actuator-generated streamwise vortices. In Proceeding of the 9th International Symposium on Turbulence and Shear Flow Phenomena, June 30 – July 3 2015, The University of Melbourne, Australia. Paper no. 209.Google Scholar
Wu, Z., Wong, C.W. & Zhou, Y. 2018 Dual-input/Single-output extremum-seeking system for jet control. AIAA J. 56 (4), 1463–1471.10.2514/1.J056675CrossRefGoogle Scholar
Xi, L., Quadrio, M. & Zhou, Y. 2024 Direct numerical simulation of skin-friction reduction using steady and periodic blowing through streamwise slits. In Fluid-Structure-Sound Interactions and Control, pp. 85–90.10.1007/978-981-97-6211-8_12CrossRefGoogle Scholar
Yao, J., Chen, X. & Hussain, F. 2018 Drag control in wall-bounded turbulent flows via spanwise opposed wall-jet forcing. J. Fluid Mech. 852, 678–709.10.1017/jfm.2018.553CrossRefGoogle Scholar
Yao, J., Chen, X., Thomas, F. & Hussain, F. 2017 Large-scale control strategy for drag reduction in turbulent channel flows. Phys. Rev. Fluids 2 (6), 062601.10.1103/PhysRevFluids.2.062601CrossRefGoogle Scholar
Ye, Z., Jiang, Y., Zhang, Y., Zou, J. & Zheng, Y. 2019 Effects of synthetic jet array on turbulent boundary layer. Intl J. Heat Technol. 37 (3), 893–898.10.18280/ijht.370327CrossRefGoogle Scholar
Yu, J., Fan, D., Noack, B.R. & Zhou, Y. 2022 Genetic-algorithm-based artificial intelligence control of a turbulent boundary layer. Acta Mechanica Sin. 37 (12), 1739–1747.10.1007/s10409-021-01145-4CrossRefGoogle Scholar
Yu, J., Mi, J. & Zhou, Y. 2025 Interactions between adjacent synthetic-jet-generated vortices of high Strouhal number. Phys. Fluids 37 (9), 097112.10.1063/5.0283271CrossRefGoogle Scholar
Zhang, B., Fan, D. & Zhou, Y. 2023 Artificial intelligence control of a low-drag Ahmed body using distributed jet arrays. J. Fluid Mech. 963, A3.10.1017/jfm.2023.291CrossRefGoogle Scholar
Zhang, K., Luo, J., Wei, X. & Zhou, Y. 2023 Skin Friction Reduction in a Turbulent Boundary Layer with Miniature Vortex Generators, Busan. In 6th Symposium on Fluid-Structure-Sound Interactions and Control, August 26–30, 2023, Busan, Korea, pp. 39–45. Springer.10.1007/978-981-97-6211-8_5CrossRefGoogle Scholar
Zhang, X., Wei, X.H., Wang, H.F. & Zhou, Y. 2024 Skin Friction Reduction in a High Reynolds Number Turbulent Boundary Layer Using Spanwise Blowing Microjets. In Fluid-Structure-Sound Interactions and Control. FSSIC 2023. Springer.Google Scholar
Zhou, Y., Fan, D., Zhang, B., Li, R. & Noack, B.R. 2020 Artificial intelligence control of a turbulent jet. J. Fluid Mech. 897, A27.10.1017/jfm.2020.392CrossRefGoogle Scholar
Zigunov, F., Sellappan, P. & Alvi, F. 2021 Beyond actuator line arrays in active flow control studies: lessons from a genetic algorithm approach. Phys. Rev. Fluids 6 (8), 083903.10.1103/PhysRevFluids.6.083903CrossRefGoogle Scholar