Fractal and multifractal characteristics of a scalar dispersed in a turbulent jet

Flohr, Peter; Olivari, D.

doi:10.1016/0167-2789(94)90264-x

Cited by 17 publications

(14 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Their study visualized planar sections of a turbulent jet with a passive scalar (smoke) advected by the jet flow. The fractal dimension of the level sets of scalar concentration estimated by Flohr and Olivari [18] goes down with concentration, similar to our late-time results.…”

Section: Observations and Analysissupporting

confidence: 79%

“…Some of this decrease is caused by mixing of curtain material with air, some may also be an effect of the loss of resolution. Here, we must note an interesting parallel with the work of Flohr and Olivari [18]. Their study visualized planar sections of a turbulent jet with a passive scalar (smoke) advected by the jet flow.…”

Section: Observations and Analysismentioning

confidence: 94%

“…The multiscale nature of turbulence and apparent geometric complexity of turbulent flows attracted the attention of Mandelbrot [12], who suggested that the geometric structure of turbulence is fractal. Subsequent studies [14][15][16][17][18] showed that it is indeed possible to quantify the geometry of turbulent flows with power-law statistics in terms of a constant fractal dimension over a considerable range of scales. It is also of interest that in Mandelbrot's book [12], the opening of the chapter on turbulence (chapter 10 in the 1983 edition) mentions that transition to turbulence is likely to have 'fractal aspects of great importance, but they have not been clarified enough to be discussed here'.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Shock-driven gas curtain: fractal dimension evolution in transition to turbulence

Vorobieff

Rightley

Benjamin

1999

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

We present estimates of the Hausdorff fractal dimension of a planar section of the interfaces on the sides of a thin curtain of heavy gas (SF 6 ) embedded in air and accelerated with a planar shock wave at Mach 1.2. As the Richtmyer-Meshkov instability develops, eventually leading to a transition to turbulence in the curtain, the fractal dimension of the interfaces increases from an initial value not exceeding 1.10 to a maximum value 1.36 ± 0.07. This value is close to that experimentally measured for fully developed turbulence. The growth of the fractal dimension is closely related to mixing in the flow. It represents an important and previously unmeasured property in the transition to turbulence due to Richtmyer-Meshkov instability.

show abstract

Section: Observations and Analysissupporting

confidence: 79%

Section: Observations and Analysismentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Shock-driven gas curtain: fractal dimension evolution in transition to turbulence

Vorobieff

Rightley

Benjamin

1999

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…curvature, in the coverage plots]" but attributed this to "the small range between integral and Kolmogorov scales at the Reynolds numbers of [the] experiments". Flohr & Olivari (1994) analysed isoscalar surfaces in gas-phase turbulent jets and reported "constant [PLF] scaling behaviour over a wide range [of scales]" with a threshold-dependent PLF dimension exhibiting a maximum value. For the outer isoscalar surfaces, they suggested a PLF dimension of D2 = 1.30 f 0.05. suggested a PLF dimension of 0 3 = 2.35 f 0.05 for outer isoscalar surfaces in turbulent jets, with PLF scaling "over much of the interval between the integral scale and the Kolmogorov scale," and a PLF dimension of 0 3 = 2.67 f 0.05 for inner isoscalar surfaces in turbulent jets, in a scaling range "smaller" than that for the outer isosurfaces, indicating the degree of confidence of his results as "fairly certain".…”

Section: Nd(jl)mentioning

confidence: 99%

Mixing in turbulent jets: scalar measures and isosurface geometry

Catrakis

Dimotakis

1996

J. Fluid Mech.

View full text Add to dashboard Cite

Experiments have been conducted to investigate mixing and the geometry of scalar isosurfaces in turbulent jets. Specifically, we have obtained high-resolution, highsignal-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 x lo3 < Re < 18 x lo3, 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 scaledependent generalization of power-law-fractal geometry. A connection between scaledependent-fractal geometry and the distribution of scales is established and used to compute the distribution of spatial scales in the flow.

show abstract

“…The 1994 update of this work identified the estimate of D3 = 813 as a sharp estimate (rather than an upper bound), in the limit of Sc 4 os. Flohr & Olivari (1994) analyzed isoscalar surfaces in gas-phase turbulent jets and reported, "constant scaling behavior over a wide range [of scales]," with a An analysis of the (temporal) evolution of a line element in grid-generated turbulence was reported by Villermaux & Gagne (1994). Their measurements of the wrinkling of a smoke filament, shed from a thin wire downstream of a grid in a wind tunnel, were interpreted in terms of a fitted power-law coverage dimension that increased (linearly) with the distance downstream from a thin wire.…”

Section: An Overview Of Reports On Fractals For Turbulencementioning

confidence: 99%

Turbulence, Fractals, and Mixing

Dimotakis

Catrakis

1999

Mixing

View full text Add to dashboard Cite

Proposals and experiment a1 evidence, from both numerical simulations and laboratory experiments, regarding the behavior of level sets in turbulent flows are reviewed. Isoscalar surfaces in turbulent flows, at least in liquid-phase turbulent jets, where extensive experiments have been undertaken, appear to have a geometry that is more complex than (constant-D) fractal. Their description requires an extension of the original, scale-invariant, fractal framework that can be cast in terms of a variable (scale-dependent) coverage dimension, Dd(X). The extension to a scale-dependent framework allows level-set coverage statistics to be related to other quantities of interest. In addition to the pdf of point-spacings (in 1-D), it can be related to the scale-dependent surface-to-volume (perimeter-to-area in 2-D) ratio, as well as the distribution of distances to the level set. The application of this framework to the study of turbulent -jet mixing indicates that isoscalar geometric measures are both threshold and Reynolds-number dependent. As regards mixing, the analysis facilitated by the new tools, as well as by other criteria, indicates enhanced mixing with increasing Reynolds number, at least for the range of Reynolds numbers investigated. This results in a progressively less-complex level-set geometry, at least in liquid-phase turbulent jets, with increasing Reynolds number. In liquid-phase turbulent jets, the spacings in one-dimensional records, as well as the size distribution of individual "islands" and "lakes" in two-dimensional isoscalar slices, are found in accord with lognormal statistics in the inner-scale range. The coverage dimension, Dd(X), derived from such sets is also in accord with lognormal statistics, in the inner-scale range. Preliminary three-dimensional (2-D space + time) isoscalar-surface data provide further evidence of a complex level-set geometrical structure in scalar fields generated by turbulence, at least in the case of turbulent jets.

show abstract

Fractal and multifractal characteristics of a scalar dispersed in a turbulent jet

Cited by 17 publications

References 13 publications

Shock-driven gas curtain: fractal dimension evolution in transition to turbulence

Shock-driven gas curtain: fractal dimension evolution in transition to turbulence

Mixing in turbulent jets: scalar measures and isosurface geometry

Turbulence, Fractals, and Mixing

Contact Info

Product

Resources

About