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Turbulent boundary layer structure

Shear velocity, u*u* = √τo/ρ

0 hR Sτ γ=

= cross-sectional area/wetted perimeter

Shear velocity, u*u* = √τo/ρ

Turbulent boundary layer structure over a FLAT bed

Classic research by the groups of Kline (Stanford) and Grass (UCL)

Tony Grass (UCL)JFM 1971

Used H2 bubbles over different bed roughness

Burst and sweeps

Grass, 1971

+U’-U’

+v’

-v’

If U’ and v’ are deviation of downstream and vertical velocity from their mean (+ve v = upwards)

12

3 4

2 = bursts4 = sweeps1 = outward interactions3 = inward interactions

Define a ‘hole’ size to exclude small

events Quadrant Analysis

Tb=fU/Y~5

Jackson, 1975, 1976

Burst period

Smith and Metzler, 1983

Planform characteristics…Smith and Metzler, 1983

Smith and Metzler, 1983

H2 bubblewire

low-speedstreaks

flow

time

Looking down onto the channel bed

Low speed streak spacing, λ+:

λ+ = λ.u*/ν

where λ = streak spacingu* = shear velocity

ν = kinematic viscosity

λ+ = λ.u*/ν ≅ 100

Smith and Metzler, 1983

Smith and Metzler, 1983

Smith and Metzler, 1983

Smith and Metzler, 1983

The burst-sweep cycle (from Allen, 1984) - hairpins

The earlier work of Kline and

colleagues

Smith et al., 1991

Generation of secondary hairpin vortices (Smith et al., 1991)

Turbulent Boundary Layer Structure (Robinson, 1991)

Robinson, 1991

Turbulent Boundary Layer Structure (Robinson, 1991)

Wall-attached hairpin

Adrian et al., 2000

Adrian, 2007

More complex packets of vortices

Adrian, 2007

A model of vortex packets

Spanwise merger of hairpins by vortex reconnection of legs

Adrian, 2007

Adrian, 2007

Movie 1

Movie 2

transitions to turbulence

Links to Large-Scale-Motions (Falco, 1977)

streaks

entrainment patch

movie

Adrian, 2007

Long streaks of low-momentum fluid in streamwise-spanwise planes of boundary layer flow at y/δ = 0.2 and Reθ = 2216. The red (blue) contours represent regions of swirling strength.

Adrian, 2007

Summary sketch of the organization of hairpins and packets in a boundary layer.

Adrian, 2007

References***Adrian, R.L. (2007) Hairpin vortex organization in wall turbulence, Physics of Fluids, 19, 041301.****Marusic, I. (2009) Unravelling turbulence near walls, Journal of Fluid Mechanics, 630, 1-4.*

Grass, A.J. (1971) Structural features of turbulent flow over smooth & rough boundaries, J. Fluid Mechanics, 50, 233-255.Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. (1967) The structure of turbulent boundary layers. Journal of Fluid Mechanics, 30, 741-773. Robinson, S. K. (1991) Coherent motion in the turbulent boundary layer. Ann. Rev. Fluid Mech. 3, 601-639.Smith, C.R. and Metzler, S.P. (1983) The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer, Journal of Fluid Mechanics, 129, 27-54.Smith, C.R. (1996), Coherent flow structures in smooth-wall turbulent boundary layers: Facts, mechanisms and speculation. in Coherent Flow Structures in open channels edited by P.J. Ashworth, S.J. Bennett, J.L. Best, and S.J. McLelland, pp. 1-39, John Wiley and Sons.

Next weeks seminars

Alex: Head, M.R., and P. Bandyopadhyay (1981), New aspects of turbulent boundary layer structure, Journal of Fluid Mechanics, 107, 297-338.Justin: Adrian, R. J., C. D. Meinhart and C. D. Tomkins (2000), Vortex organization in the outer region of the turbulent boundary layer, Journal of Fluid Mechanics, 422, 1-54. Ron: 2 papers in Science!Marusic et al., (2010) Predictive model for wall-bounded turbulent flow, Science, 329, 9 July 2010.Adrian, R.J. (2010) Closing in on models of wall turbulence, Science, 329, 9 July 2010.

NOTE: These can be large papers!: start with Intro, Conclusions and Discussion: reviewers can then focus in on

papers