1. The formation of very long structures
Tim Nickels and David Dennis
Cambridge University Engineering Department

2. PIV data DNS data Hutchins & Marusic (2007) Dennis (CUED)
Ringuette et al. (2008)
DNS data

3. Very long structures in wall-bounded flows
Structures > 2 d VLSMs up to 20 d
Observed in various studies - DNS and experiment
Evidence is fairly convincing
As yet no definite answer on where they come from

4. 3D measurements of long structures
Many previous experiments - slices
Need for 3D measurements of full structure
Flow 8m
CUED Turbulence Research Water tunnel
Working Section 8m x 900mm x500mm
Maximum speed 1m/s

5. Experimental set-up

6. 3D structure via Taylor’s hypothesis High repetition-rate Stereo PIV (up 1000 vector fields/second)
Flow
Measurement plane
3 components of velocity
3D structure

7. R=4685 A typical 3D packet Side View Top View Flow Flow
Typical angle 11o
Side View
Flow
Top View
Max. width
0.5
Length 2.5

8. Long structures - made from concatenation of smaller “packet” structures
z/
Length 8.4
1.0
0.5 2 4 6 8 10
x/
y/
≈10o
≈10o
0.6 2 4 6 8 10
x/
Isosurfaces of streamwise fluctuation u = -0.1U(free-stream)

9. Likely structure
Appear to be constructed from shorter structures - packets (as suggested by Kim and Adrian (1999))
The important question is “What makes them align?”
…OR IS IT?

10. The first question Is an alignment mechanism necessary?
If we scatter objects randomly on a plane some will align by chance into longer structures
Could this explain VLSMs?

11. A simple statistical model
Single units scattered randomly on a surface (length 2.5 )
Find probability of “alignment” of several units
Compare results with experimental data
Model assumption single structure is always separated from adjacent structure by one width
(so a single structure consists of low speed flanked by high speed).

12. Schematic concept Structure of length 2 units

13. Crude analytical model
Probability of a single unit occurring a=0.(area of all single units over total area) (from experiments - total low speed area over total area)
Probability of a structure of exactly n units in length is
n ≥ 1

14. Results of analytical model

15. Simple “simulation”

17. Conclusions 3D nature of very long structures measured
Long structures seem to consist of shorter packets
Statistical estimates suggest that alignments may be explained by chance
At least chance alignment must be considered as a possibility