Hostname: page-component-5d59c44645-l48q4 Total loading time: 0 Render date: 2024-02-27T07:15:44.970Z Has data issue: false hasContentIssue false

Friction-Drag Reduction by Transverse Wall Motion – A Review

Published online by Cambridge University Press:  25 August 2020

Michael A. Leschziner*
Imperial College London
*Corresponding author (M. A. Leschziner,
Get access


The quest for drag reduction is driven by environmental concerns, in general, and the need to reduce fuel consumption in transport applications, in particular. Turbulent friction is especially important in civil aviation, accounting for over 50% of the total drag in cruise. In this context, spatially and/or temporally varying in-plane wall motion, while undoubtedly difficult to implement in practice, has attracted major interest, because of the large drag-reduction margins it yields. It is also a forcing method that is of fundamental interest, as it provokes intriguing interactions between the spanwise Stokes layer induced by the wall motion and the near-wall turbulence-regeneration mechanisms. This article provides a relatively brief, ‘entry-level’, review of research in this area, principally over the past two decades. While far from being exhaustive, the review conveys a reasonably detailed picture of some major physical issues as well as of the outcome of the most important computational and experimental studies. Particular emphasis is placed on the question of how results obtained in idealised laboratory conditions and by simulation at relatively low Reynolds-number values pertain to high values typical of high-speed transport.

Research Article
Copyright © 2020 The Society of Theoretical and Applied Mechanics

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)



Agostini, L. and Leschziner, M. A., “On the influence of outer large-scale structures on near-wall turbulence in channel flow,” Physics of Fluids, 26(7), 075107 (2014).CrossRefGoogle Scholar
Agostini, L. and Leschziner, M.A., “On the validity of the quasi-steady-turbulence hypothesis in representing the effects of large scales on small scales in boundary layers,” Physics of Fluids, 28(4), 045102 (2016).Google Scholar
Agostini, L. and Leschziner, M.A., “The impact of footprints of large-scale outer structures on the nearwall layer in the presence of drag-reducing spanwise wall motion,” Flow Turbulence and Combustion, 100(4), pp. 10371061 (2018).CrossRefGoogle Scholar
Agostini, L. and Leschziner, M.A., “The connection between the spectrum of turbulent scales and the skinfriction statistics in channel flow at Re τ=1000,” Journal of Fluid Mechanics, 871, pp. 2251 (2019).CrossRefGoogle Scholar
Agostini, L., Leschziner, M.A. and Gaitonde, D., “Skewness-induced asymmetric modulation of small-scale turbulence by large-scale structures,” Physics of Fluids, 28(1), 015110 (2016).CrossRefGoogle Scholar
Agostini, L., Touber, E. and Leschziner, M. A., “Spanwise oscillatory wall motion in channel flow: drag-reduction mechanisms inferred from DNS-predicted phase-wise property variations at, Reτ=1000,” Journal of Fluid Mechanics, 743, pp. 606635 (2014).CrossRefGoogle Scholar
Agostini, L., Touber, E. and Leschziner, M. A., “The turbulence vorticity as a window to the physics of friction-drag reduction by oscillatory wall motion,” International Journal of Heat and Fluid Flow, 51, pp. 315 (2015).CrossRefGoogle Scholar
Auteri, F., Baron, A., Belan, M., Campanardi, G. and Quadrio, M., “Experimental assessment of drag reduction by traveling waves in a turbulent pipe flow,” Physics of Fluids, 22(11), 115103 (2010).CrossRefGoogle Scholar
Baron, A. and Quadrio, M., “Turbulent drag reduction by spanwise wall oscillations,” Applied Scientific Research, 55(4), pp. 311326 (1995).CrossRefGoogle Scholar
Baars, W. J., Hutchins, N. and Marusic, I., “Spectral stochastic estimation of high-Reynolds-number wall-bounded turbulence for a refined inner-outer interaction model,” Physical Review Fluids, 1(5), 054406 (2016).CrossRefGoogle Scholar
Baars, W. J. and Marusic, I., “Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 1. Energy spectra,” Journal of Fluid Mechanics, 882, A25-1 (2020).CrossRefGoogle Scholar
Bechert, D. W., Bruse, M., Hage, W., Van der Hoeven, J. G. T. and Hoppe, G., “Experiments on drag-reducing surfaces and their optimization with an adjustable geometry,” Journal of Fluid Mechanics, 338, pp. 5987 (1997).CrossRefGoogle Scholar
Bird, J., Santer, M. and Morrison, J. F., “Compliant kagome lattice structures for generating in-plane waveforms,” International Journal of Solids and Structures, 141, pp. 86101 (2018).CrossRefGoogle Scholar
Bird, J., Santer, M. and Morrison, J. F., “Experimental control of turbulent boundary layers with in-plane travelling waves,” Flow Turbulence and Combustion, 100(4), pp. 10151035 (2018).CrossRefGoogle ScholarPubMed
Blesbois, O., Chernyshenko, S. I., Touber, E. and Leschziner, M. A., “Pattern prediction by linear analysis of turbulent flow with drag reduction by wall oscillation,” Journal of Fluid Mechanics, 724, pp. 607641 (2013).CrossRefGoogle Scholar
Bradshaw, P. and Pontikos, N. S., “Measurements in the turbulent boundary-layer on an infinite swept wing,” Journal of Fluid Mechanics, 159, pp. 105130 (1985).CrossRefGoogle Scholar
Bernardini, M. and Pirozzoli, S., “Inner/outer layer interactions in turbulent boundary layers: a refined measure for the large-scale amplitude modulation mechanism,” Physics of Fluids, 23(6), 061701 (2011).CrossRefGoogle Scholar
Choi, K.-S., “Near-wall structure of turbulent boundary layer with spanwise-wall oscillation,” Physics of Fluids, 14(7), pp. 25302542 (2002).CrossRefGoogle Scholar
Choi, K.-S. and Graham, M., “Drag reduction of turbulent pipe flows by circular-wall oscillation,” Physics of Fluids, 10(1), pp. 79 (1998).CrossRefGoogle Scholar
Dean, R. B., “Reynolds-number dependence of skin friction and other bulk flow variables in 2-dimensional rectangular duct flow,” Journal of Fluids Engineering - Transactions of the ASME, 100(2), pp. 215223 (1978).CrossRefGoogle Scholar
Du, Y. Q., Symeonidis, V. and Karniadakis, G. E., “Drag reduction in wall-bounded turbulence via a transverse travelling wave,” Journal of Fluid Mechanics, 457, pp. 134 (2002).CrossRefGoogle Scholar
Duong, A., Mydia, S., Corke, T. C., Hussain, F. and Thomas, F. O., “Turbulent boundary layer drag reduction using pulsed-dc plasma actuation,” in Proceeding of 11th Int. Symposium on Turbulence and Shear Flow (TSFP11), Southampton (2019).Google Scholar
Fukagata, K., Iwamoto, K. and Kasagi, N., “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Physics of Fluids, 14(11), pp. L73L76 (2002).CrossRefGoogle Scholar
Gatti, D. and Quadrio, M., “Performance losses of drag-reducing spanwise forcing at moderate values of the Reynolds number,” Physics of Fluids, 25(12), 125109 (2013).CrossRefGoogle Scholar
Gatti, D. and Quadrio, M., “Reynolds-number dependence of turbulent skin-friction drag reduction induced by spanwise forcing,” Journal of Fluid Mechanics, 802, pp. 553582 (2016).CrossRefGoogle Scholar
Gatti, D., Guttler, A., Frohnapfel, B. and Tropea, C., “Experimental assessment of spanwise-oscillating dielectric electroactive surfaces for turbulent drag reduction in an air channel flow,” Experiments in Fluids, 56(5), 110 (2015).CrossRefGoogle Scholar
Ghebali, S., Chernyshenko, S. I. and Leschziner, M. A., “Can large-scale oblique undulations on a solid wall reduce the turbulent drag?,” Physics of Fluids, 29(10), 105102 (2017).CrossRefGoogle Scholar
Howard, R. J. A. and Sandham, N. D., “Simulation and modelling of a skewed turbulent channel flow,” Flow Turbulence and Combustion, 65(1), pp. 83109 (2000).CrossRefGoogle Scholar
Hurst, E., Yang, Q. and Chung, Y. M., “The effect of Reynolds number on turbulent drag reduction by streamwise travelling waves,” Journal of Fluid Mechanics, 759, pp. 2855 (2014).CrossRefGoogle Scholar
Jung, W. J., Mangiavacchi, N. and Akhavan, R., “Suppression of turbulence in wall-bounded flows by high-frequency spanwise oscillations,” Physics of Fluids A - Fluid Dynamics, 4(8), pp. 16051607 (1992).CrossRefGoogle Scholar
Laadhari, F., “Reynolds number effect on the dissipation function in wall-bounded flows,” Physics of Fluids, 19(3), 038101 (2007).CrossRefGoogle Scholar
Laadhari, F., Skandaji, L. and Morel, R., “Turbulence reduction in a boundary-layer by a local spanwise oscillating surface,” Physics of Fluids, 6(10), pp. 32183220 (1994).CrossRefGoogle Scholar
Lardeau, S. and Leschziner, M. A., “The streamwise drag-reduction response of a boundary layer subjected to a sudden imposition of transverse oscillatory wall motion,” Physics of Fluids, 25(7), 075109 (2013).CrossRefGoogle Scholar
Lee, M. and Moser, R. D., “Direct numerical simulation of turbulent channel flow up to Re τ=5300,” Journal of Fluid Mechanics, 774, pp. 395415 (2015).CrossRefGoogle Scholar
Lozano-Duran, A. and Jimenez, J., “Effect of the computational domain on direct simulations of turbulent channels up to Re τ=4200,” Physics of Fluids, 26(1), 011702 (2014).CrossRefGoogle Scholar
Luchini, P., “Reducing the turbulent skin friction,” in Computational methods in applied sciences, J.A. Dèsidèri, et al., Editors, Wiley: Paris. pp. 466470. (1996).Google Scholar
Marusic, I., Mathis, R. and Hutchins, N., “High Reynolds number effects in wall turbulence,” International Journal of Heat and Fluid Flow, 31(3), pp. 418428 (2010).CrossRefGoogle Scholar
Mathis, R., Hutchins, N. and Marusic, I., “A predictive inner-outer model for streamwise turbulence statistics in wall-bounded flows,” Journal of Fluid Mechanics, 681, pp. 537566 (2011).CrossRefGoogle Scholar
Moin, P., Shih, T. H., Driver, D. and Mansour, N. N., “Direct numerical simulation of a 3-dimensional turbulent boundary layer,” Physics of Fluids A - Fluid Dynamics, 2(10), pp. 18461853 (1990).CrossRefGoogle Scholar
Nugroho, B., Hutchins, N. and Monty, J. P., “Large-scale spanwise periodicity in a turbulent boundary layer induced by highly ordered and directional surface roughness,” International Journal of Heat and Fluid Flow, 41, pp. 90102 (2013).CrossRefGoogle Scholar
Pang, J. G. and Choi, K. S., “Turbulent drag reduction by Lorentz force oscillation,” Physics of Fluids, 16(5), pp. L35L38 (2004).CrossRefGoogle Scholar
Pirozzoli, S. and Bernardini, M., “Probing high- Reynolds-number effects in numerical boundary layers,” Physics of Fluids, 25(2), 021704 (2013).CrossRefGoogle Scholar
Quadrio, M. and Ricco, P., “Critical assessment of turbulent drag reduction through spanwise wall oscillations,” Journal of Fluid Mechanics, 521, pp. 251271 (2004).CrossRefGoogle Scholar
Quadrio, M. and Ricco, P., “The laminar generalized Stokes layer and turbulent drag reduction,” Journal of Fluid Mechanics, 667, pp. 135157 (2011).CrossRefGoogle Scholar
Quadrio, M., Ricco, P. and Viotti, C., “Streamwisetravelling waves of spanwise wall velocity for turbulent drag reduction,” Journal of Fluid Mechanics, 627, pp. 161178 (2009).CrossRefGoogle Scholar
Ricco, P. and Hahn, S., “Turbulent drag reduction through rotating discs,” Journal of Fluid Mechanics, 722, pp. 267290 (2013).CrossRefGoogle Scholar
Ricco, P. and Wu, S. L., “On the effects of lateral wall oscillations on a turbulent boundary layer,” Experimental Thermal and Fluid Science, 29(1), pp. 4152 (2004).CrossRefGoogle Scholar
Ricco, P., Ottonelli, C., Hasegawa, Y. and Quadrio, M., “Changes in turbulent dissipation in a channel flow with oscillating walls,” Journal of Fluid Mechanics, 700, pp. 77104 (2012).CrossRefGoogle Scholar
Skote, M., “Comparison between spatial and temporal wall oscillations in turbulent boundary layer flows,” Journal of Fluid Mechanics, 730, pp. 273294 (2013).CrossRefGoogle Scholar
Skote, M., “Scaling of the velocity profile in strongly drag reduced turbulent flows over an oscillating wall,” International Journal of Heat and Fluid Flow, 50, pp. 352358 (2014).CrossRefGoogle Scholar
Skote, M., Mishra, M. and Wu, Y. H., “Drag Reduction of a Turbulent Boundary Layer over an Oscillating Wall and Its Variation with Reynolds Number,” International Journal of Aerospace Engineering, 891037 (2015).CrossRefGoogle Scholar
Skote, M., Mishra, M. and Wu, Y. H., “Wall oscillation induced drag reduction zone in a turbulent boundary layer,” Flow Turbulence and Combustion, 102(3), pp. 641666 (2019).Google Scholar
Touber, E. and Leschziner, M. A., “Near-wall streak modification by spanwise oscillatory wall motion and drag-reduction mechanisms,” Journal of Fluid Mechanics, 693, pp. 150200 (2012).CrossRefGoogle Scholar
Vallikivi, M., Hultmark, M. and Smits, A. J., “Turbulent boundary layer statistics at very high Reynolds number,” Journal of Fluid Mechanics, 779, pp. 371389 (2015).CrossRefGoogle Scholar
Viotti, C., Quadrio, M. and Luchini, P., “Streamwise oscillation of spanwise velocity at the wall of a channel for turbulent drag reduction,” Physics of Fluids, 21(11), 115109 (2009).Google Scholar
Wise, D. J., Alvarenga, C. and Ricco, P., “Spinning out of control: Wall turbulence over rotating discs,” Physics of Fluids, 26(12), 125107 (2014).CrossRefGoogle Scholar
Yakeno, A., Hasegawa, Y. and Kasagi, N., “Modification of quasi-streamwise vortical structure in a drag-reduced turbulent channel flow with spanwise wall oscillation,” Physics of Fluids, 26(8), 085109 (2014).CrossRefGoogle Scholar
Yamamoto, Y. and Tsuji, Y., “Numerical evidence of logarithmic regions in channel flow at Re τ=8000,” Physical Review Fluids, 3(1), 012602 (2018).CrossRefGoogle Scholar
Mizuno, Y. and Jimenez, J., “Wall turbulence without walls,” Journal of Fluid Mechanics, 723, pp. 429455 (2013).CrossRefGoogle Scholar
Zhang, C. and Chernyshenko, S. I., “Quasisteady quasihomogeneous description of the scale interactions in near-wall turbulence,” Physical Review Fluids, 1(1), 014401 (2016).Google Scholar