Flow, Turbulence and Combustion

, Volume 100, Issue 2, pp 391–416 | Cite as

Streamwise Vortices and Velocity Streaks in a Locally Drag-Reduced Turbulent Boundary Layer



This work aims to understand the changes associated with the near-wall streaky structures in a turbulent boundary layer (TBL) where the local skin-friction drag is substantially reduced. The Reynolds number is R e 𝜃 = 1000 based on the momentum thickness or R e τ = 440 based on the friction velocity of the uncontrolled flow. The TBL is perturbed via a local surface oscillation produced by an array of spanwise-aligned piezo-ceramic (PZT) actuators and measurements are made in two orthogonal planes using particle image velocimetry (PIV). Data analyses are conducted using the vortex detection, streaky structure identification, spatial correlation and proper orthogonal decomposition (POD) techniques. It is found that the streaky structures are greatly modified in the near-wall region. Firstly, the near-wall streamwise vortices are increased in number and swirling strength but decreased in size, and are associated with greatly altered velocity correlations. Secondly, the velocity streaks grow in number and strength but contract in width and spacing, exhibiting a regular spatial arrangement. Other aspects of the streaky structures are also characterized; they include the spanwise gradient of the longitudinal fluctuating velocity and both streamwise and spanwise integral length scales. The POD analysis indicates that the turbulent kinetic energy of the streaky structures is reduced. When possible, our results are compared with those obtained by other control techniques such as a spanwise-wall oscillation, a spanwise oscillatory Lorentz force and a transverse traveling wave.


Turbulent boundary layer control Streamwise vortices Velocity streaks 


Latin symbols


Peak-to-peak oscillation amplitude at the actuator tip

\(A_{\omega _{x} } \)

Size of streamwise vortex


Velocity gradient tensor


Oscillation frequency


Height of vortex center


= δ /𝜃, Shape factor, where δ and 𝜃 are displacement and momentum thicknesses, respectively


Transverse spacing of adjacent vortex centers


Number of vortex center


= U 𝜃/ν, Reynolds number based on momentum thickness


= u τ δ/ν, Reynolds number based on friction velocity


Spacing of adjacent streaks

U, U

Local mean and free-stream streamwise velocities, respectively


Streamwise fluctuating velocity


\(= \sqrt {\overline \tau _{w} /\rho } ,\) friction velocity


Streak width


Perturbed spanwise velocity


Spanwise fluctuating velocity


Streamwise direction


Wall-normal direction


Spanwise direction

Greek symbols


Boundary layer thickness defined by the location where U = 99% U


Momentum thickness


= (ω x / |ω x |)λ c i , signed swirling strength


Real eigenvalue


Vortex strength as indicated by eigenvalue of the local velocity gradient tensor




Wall-normal fluctuating velocity


Flow density

\(\overline \tau _{w} \)

Averaged wall shear stress

ϕi, i+1

(i = 1, 2, …, 15), phase shift between adjacent actuator


Streamwise vorticity


Wall-normal vorticity



Particle image velocimetry


Proper orthogonal decomposition


Turbulent boundary layer


Turbulent kinetic energy



Normalization by wall units

Ensemble average



YZ wishes to acknowledge support given to him from NSFC through grant 11632006, from RGC of HKSAR through grant PolyU 5329/11E. H.L.B. would like to acknowledge support given to him from NSFC through grant 11302062 and from State Key Laboratory of Aerodynamics through grant SKLA20130102.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • H. L. Bai
    • 1
    • 2
    • 3
  • Y. Zhou
    • 1
  • W. G. Zhang
    • 2
  • R. A. Antonia
    • 4
  1. 1.Institute for Turbulence-Noise-Vibration Interaction and Control, Shenzhen Graduate SchoolHarbin Institute of TechnologyShenzhenChina
  2. 2.State Key Laboratory of AerodynamicsMianyangChina
  3. 3.Department of Civil and Environmental EngineeringHong Kong University of Science and TechnologyKowloonChina
  4. 4.School of EngineeringUniversity of NewcastleCallaghanAustralia

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