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

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

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

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

Experimental set-up

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

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

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)

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?

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?

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).

Schematic concept Structure of length 2 units

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

Results of analytical model

Simple “simulation”

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