Singular structure at the turbulent/non-turbulent interface of a jet

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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

PRL 95 (2005) 174501
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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?

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Turbulence modeling problem
(1) ?T const
(2) ?T e2/?
u'v'?T (?U/?y)
?T ?0
no growth
U
?T

• add small ?T to allow growth, or
• growth due to numerical diffusion

?T ? 0, butno turbulence
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Combined PIV/LIF measurement of a self-similar
turbulent jet
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(No Transcript)
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Detection of the interface
Threshold level Prasad Sreenivasan, EiF 7
(1989) 259
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Conditional sampling with respect to the interface
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Results vorticity
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Results conditional statistics
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Super-layer jump condition
I
V
T
turbulent transport
See e.g. W.C. Reynolds, JFM 54 (1972) 481
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Results velocity jump condition
(Kovasznay et al. ?U 0)
Turner
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Results mass flux - engulfment
Total mass within boundary envelope
Engulfed mass within boundary envelope
See also Mathew Basu, PoF 14 (2002) 2065
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Results length scales
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Results enstrophy transport
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Eddy viscosity in the outer jet region
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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 (?T) retains a small constant value in
  outer jet region Prandtl was right !!!