Eulerian and Lagrangian views of a turbulent boundary layer flow using time-resolved tomographic PIV


Coherent structures and their time evolution in the logarithmic region of a turbulent boundary layer investigated by means of 3D space–time correlations and time-dependent conditional averaging techniques are the focuses of the present paper. Experiments have been performed in the water tunnel at TU Delft measuring the particle motion within a volume of a turbulent boundary layer flow along a flat plate at a free-stream velocity of 0.53 m/s at Re θ = 2,460 based on momentum thickness by using time-resolved tomographic particle image velocimetry (PIV) at 1 kHz sampling rate and particle tracking velocimetry (PTV). The obtained data enable an investigation into the flow structures in a 3D Eulerian reference frame within time durations corresponding to 28 δ/U. An analysis of the time evolution of conditional averages of vorticity components representing inclined hairpin-like legs and of Q2- and Q4-events has been performed, which gives evidence to rethink the early stages of the classical hairpin development model for high Reynolds number TBLs. Furthermore, a PTV algorithm has been applied on the time sequences of reconstructed 3D particle image distributions identifying thousands of particle trajectories that enable the calculation of probability distributions of the three components of Lagrangian accelerations.

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Direct numerical simulations


Hot-wire anemometry


Laser Doppler anemometry


Linear stochastic estimation


Multiplicative algebraic reconstruction technique


Probability density function


Particle image velocimetry


Particles per pixel


Particle tracking velocimetry


Root mean square


(Turbulent) boundary layer


Time resolved


Wall units

t :


u, v, w :

Instantaneous velocity components in x- (streamwise), y- (wall normal) and z-(spanwise) directions

u′, v′, w′ :

Fluctuation velocity components

u+, v+, w+:

Instantaneous velocity components based on u τ

x, y, z:

Streamwise, wall normal and spanwise coordinates

ax, ay, az:

Components of Lagrangian acceleration

x+, y+, z+:

Distances in wall units based on u τ

kx, ky, kz:

Wavenumbers in x-, y- and z-direction

u τ :

Skin friction velocity


Kolmogorov length scale

τ η :

Kolomogorov time scale

Re θ :

Reynolds number based on momentum thickness of boundary layer

Re τ :

Reynolds number based on u τ and δ

c f :

Skin friction coefficient

f :

Focal length

f # :

Aperture stop


Quadrants of instantaneous Reynolds stress u′v′

Q, R:

Invariants of the velocity gradient tensor

U :

Free-stream velocity


Boundary layer thickness (0.99U )

δ0 = 2.6 mm:

(Boundary layer thickness at tripping)

λ2 :

Measure of swirl strength (second negative eigenvalue of S² + Ω²)

R ij :

Space–(time) correlation function (i and j scalars e.g. u′, v′ or w′)

k x ϕ ij :

Pre-multiplied cross- or co-spectrum


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The authors wish to thank Prof. Dr. I. Marusic for providing the hot-wire cross- spectra.

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Correspondence to A. Schröder.

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Schröder, A., Geisler, R., Staack, K. et al. Eulerian and Lagrangian views of a turbulent boundary layer flow using time-resolved tomographic PIV. Exp Fluids 50, 1071–1091 (2011).

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  • Particle Image Velocimetry
  • Direct Numerical Simulation
  • Turbulent Boundary Layer
  • Particle Tracking Velocimetry
  • Particle Image Velocimetry Data