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CATRAKIS, H. J. & DIMOTAKIS, P. E. 1996
"Mixing in turbulent jets: scalar measures and isosurface geometry,"
*J. Fluid Mech.* **317**, 369-406.

**Abstract**

Experiments have been conducted to investigate mixing and the
geometry of scalar isosurfaces in turbulent jets. Specifically,
we have obtained high-resolution, high-signal-to-noise-ratio
images of the jet-fluid concentration in the far field of round,
liquid-phase, turbulent jets, in the Reynolds number range
4.5x10^{3} <= Re <= 18x10^{3}, using
laser-induced-fluorescence imaging techniques. Analysis of these
data indicates that this Reynolds-number range spans a mixing
transition in the far field of turbulent jets. This is manifested
in the probability-density function of the scalar field, as well
as in measures of the scalar isosurfaces. Classical as well as
fractal measures of these isosurfaces have been computed, from
small to large spatial scales, and are found to be functions of
both scalar threshold and Reynolds number. The coverage of level
sets of jet-fluid concentration in the two-dimensional images is
found to possess a scale-dependent-fractal dimension that
increases continuously with increasing scale, from near unity, at
the smallest scales, to 2, at the largest scales. The geometry of
the scalar isosurfaces is, therefore, more complex than power-law
fractal, exhibiting an increasing complexity with increasing
scale. This behaviour necessitates a scale-dependent
generalization of power-law-fractal geometry. A connection
between scale-dependent-fractal geometry and the distribution of
scales is established and used to compute the distribution of
spatial scales in the flow.

Fig. 3
Jet-fluid concentration on the far-field (z/d_{j}=275) of a
turbulent jet at *Re*=4.5x10^{3}.

Fig. 4
Jet-fluid concentration on the far-field (z/d_{j}=275) of a
turbulent jet at *Re=9.0x10*^{3}.

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Fig. 5
Jet-fluid concentration on the far-field (z/d_{j}=275) of a
turbulent jet at *Re*=18x10^{3}.

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