Skip to main content Accessibility help

Modelling turbulent skin-friction control using linearized Navier–Stokes equations

  • C. A. Duque-Daza (a1) (a2), M. F. Baig (a1), D. A. Lockerby (a1), S. I. Chernyshenko (a3) and C. Davies (a4)...


Linearized Navier–Stokes equations are solved to investigate the impact on the growth of near-wall turbulent streaks that arises from streamwise-travelling waves of spanwise wall velocity. The percentage change in streak amplification due to the travelling waves, over a range of wave parameters, is compared to published direct numerical simulation (DNS) predictions of turbulent skin-friction reduction; a clear correlation between the two is observed. Linearized simulations at a much higher Reynolds number, more relevant to aerospace applications, produce results that show no marked differences to those obtained at low Reynolds number. It is also observed that there is a close correlation between DNS data of drag reduction and a very simple characteristic of the ‘generalized’ Stokes layer generated by the streamwise-travelling waves.


Corresponding author

Email address for correspondence:


Hide All
1. Auteri, F., Baron, A., Belan, M., Campanardi, G. & Quadrio, M. 2010 Experimental assessment of drag-reduction by travelling waves in a turbulent pipe flow. Phys. Fluids 22, 115103.
2. Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in a viscous shear flow. Phys. Fluids 4, 16371650.
3. Butler, K. M. & Farrell, B. F. 1993 Optimal perturbations and streak spacing in wall-bounded turbulent shear flows. Phys. Fluids 4, 774777.
4. Chernyshenko, S. I. & Baig, M. F. 2005 The mechanism of streak formation in near-wall turbulence. J. Fluid Mech. 544, 99131.
5. Choi, J. I., Xu, C. X. & Sung, H. J. 2002 Drag-reduction by spanwise wall-oscillation in wall-bounded flows. AIAA J. 40, 842850.
6. Cossu, C., Pujals, G. & Depardon, S. 2009 Optimal transient growth and very large-scale structures in turbulent boundary layers. J. Fluid Mech. 619, 7994.
7. Davies, C. & Carpenter, P. W. 2001 A novel velocity-vorticity formulation of the Navier–Stokes equations with application to boundary layer disturbance evolution. J. Comput. Phys. 172, 119165.
8. Henningson, D. S. 1996 Comment on ‘transition in shear flows. Nonlinear normality versus non-normal linearity’. Phys. Fluids 8, 22572258.
9. Henningson, D. S., Lundbladh, A. & Johansson, A. V 1993 A mechanism for bypass-transition from localized disturbances in wall-bounded shear flows. J. Fluid Mech. 250, 169207.
10. Jung, W. J., Mangiavacchi, N. & Akhavan, R. 1992 Suppression of turbulence in wall-bounded flows by high-frequency spanwise oscillations. Phys. Fluids A 4, 16051607.
11. Karnidakis, G. E. & Choi, K.-S. 2003 Mechanisms on transverse motions in turbulent wall-flows. Annu. Rev. Fluid Mech. 35, 4562.
12. Kline, S. J., Reynolds, W. C., Schraun, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741773.
13. Landahl, M. T. 1989 Boundary layer turbulence regarded as a driven linear system. Physica D 37, 1119.
14. Lockerby, D. A., Carpenter, P. W. & Davies, C. 2005 Control of sublayer streaks using microjet actuators. AIAA J. 43, 18781886.
15. Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22, 065103.
16. Nagib, H. M. & Chauhan, K. A. 2008 Variations of Von-Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.
17. Quadrio, M. & Ricco, P. 2011 The laminar generalized Stokes layer and turbulent drag-reduction. J. Fluid Mech. 667, 135157.
18. Quadrio, M., Ricco, P & Viotti, C. 2009 Streamwise travelling waves of spanwise wall-velocity for turbulent drag-reduction. J. Fluid Mech. 627, 161178.
19. Ricco, P. & Quadrio, M. 2008 Wall-oscillation conditions for drag-reduction in turbulent channel flow. Intl J. Heat Fluid Flow 29, 601612.
20. Waleffe, F. 1995 Transition in shear flows. Nonlinear normality versus non-normal linearity. Phys. Fluids 7, 3060.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed