1. Singular structure at the turbulent/non-turbulent interface of a jet
J. Westerweel, J.C.R. Hunt, A. Petracci, R. Delfos
Delft University of Technology, The Netherlands
J.M. Pedersen
Technical University of Denmark
C. Fukushima
Hiroshima Institute of Technology, Japan
Stirring & Mixing in Turbulence, Lorentz Center, Leiden, Aug , 2006
PRL 95 (2005)

2. Turbulent/non-turbulent interfaces
free turbulent flows: bounded by regions of irrotational flow
how does the interface remain sharp?
how does irrotational fluid become turbulent?
‘engulfment’ vs. ‘nibbling’
how related to outward propagation of interface?
how to represent the interface in turbulence model?

3. Turbulence modeling problem
– u'v'=T (U/y)
(1) T = const
(2) T ~ e2/
T 0
no growth U T
add small T to allow growth, or
growth due to numerical diffusion
T  0, but no turbulence

4. Combined PIV/LIF measurement of a self-similar turbulent jet

6. Detection of the interface
1. binarization
5. superimpose
vorticity
6. determine
conditional
flow statistics
y – yi
3. detect boundary
4. save outmost points
2. remove disconnected
objects
Threshold level: Prasad & Sreenivasan, EiF 7 (1989) 259

7. Conditional sampling with respect to the interface

8. Results: vorticity

9. Results: conditional statistics

10. Super-layer jump conditionV T
turbulent
transport
See e.g.: W.C. Reynolds, JFM 54 (1972) 481

11. Results: velocity jump condition
(Kovasznay et al.: U ~ 0)
Turner:

12. Results: mass flux - engulfment
Total mass within boundary envelope
Engulfed mass within boundary envelope
See also: Mathew & Basu, PoF 14 (2002) 2065

13. Results: length scales

14. Results: enstrophy transport

15. Eddy viscosity in the outer jet region

16. Conclusions
Experimental data support presence of a discontinuity in axial velocity;
Boundary propagation (Eb) given by superlayer jump condition matches entrainment velocity;
Interface associated with a shear layer with ‘constant’ strength;
Length scales of conditional velocity fluctuations increase proportional to distance from interface;
Zero turbulent transport of enstrophy across interface;
Kolmogorov-scale nibbling appears to be the dominant process;
Implications for turbulence modeling: eddy viscosity (νT) retains a small constant value in outer jet region: Prandtl was right !!!