Mixing and the Geometry of Isosurfaces in Turbulent Jets

Citation

Catrakis, Haris J. (1996) Mixing and the Geometry of Isosurfaces in Turbulent Jets. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/GPS6-DW08. https://resolver.caltech.edu/CaltechETD:etd-03312005-152819

Abstract

Experiments have been conducted to investigate mixing and the geometry of scalar isosurfaces in turbulent jets. Specifically, images of the jet-fluid concentration in the far-field of round, liquid-phase, turbulent jets have been recorded at high resolution and signal-to-noise ratio using laser-induced-fluorescence digital-imaging techniques, in the Reynolds number range 4.5 x 10³ ≤ Re ≤ 18 x 10³. 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 other scalar-field and scalar-isosurface measures. Classical as well as fractal measures of the 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 behavior 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. A lognormal model of scales is proposed. The data also indicate a lognormal distribution of size of the isoscalar islands and lakes, and a powerlaw distribution of shape complexity, with values of the latter that increase with increasing size.

Thesis Files