Mixing in turbulent jets: scalar measures and isosurface geometry

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 4.5 × 10^3 ≤ Re ≤ 18 × 10^3, 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