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

Topological Structure of the QCD Vacuum Revealed by Overlap Fermions

Overlap fermions preserve a remnant of chiral symmetry on the lattice. They are a powerful tool to investigate the topological structure of the vacuum of Yang-Mills theory and full QCD. Recent results concerning the localization of topological charge and the localization and local chirality of the overlap eigenmodes are reported. The charge distribution is radically different, if a spectral cut-off for the Dirac eigenmodes is applied. The density q(x) is changing from the scale-a charge density (with full lattice resolution) to the ultraviolet filtered charge density. The scale-a density, computed on the Linux cluster of LRZ, has a singular, sign-coherent global structure of co-dimension 1 first described by the Kentucky group. We stress, however, the cluster properties of the UV filtered topological density resembling the instanton picture. The spectral cut-off can be mapped to a bosonic smearing procedure. The UV filtered field strength reveals a high degree of (anti)selfduality at "hot spots" of the action. The fermionic eigenmodes show a high degree of local chirality. The lowest modes are seen to be localized in low-dimensional space-time regions.Comment: 13 pages, 11 figures, accepted to appear in the Proceedings of "HLRB, KONWIHR and Linux-Cluster: Review, Results and Future Projects Workshop", Leibniz Rechenzentrum Munich, December 200

Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence. Dynamical-system approaches suggest that invariant solutions to the Navier–Stokes equations, such as traveling waves and relative periodic orbits in pipe flow, act as building blocks of the disordered dynamics. While recent studies have shown how transient chaos arises from such solutions, the ensuing dynamics lacks the strong fluctuations in size, shape and speed of the turbulent spots observed in experiments. We here show that chaotic spots with distinct dynamical and kinematic properties merge in phase space and give rise to the enhanced spatio-temporal patterns observed in pipe flow. This paves the way for a dynamical-system foundation to the phenomenology of turbulent-laminar patterns in wall-bounded extended shear flows.Peer ReviewedPostprint (published version

Cover illustration: Non-premixed hydrocarbon flame

This year’s cover illustration, reproduced here as figure 1, depicts an image formed by a short-time (1/1000 s) exposure of a non-premixed hydrocarbon flame. The flow is driven by the buoyancy forces generated by the density difference from the combustion heat release and resulting temperature rise. The Reynolds number for this buoyancy-induced, turbulent flow is relatively low, estimated at a few thousand

Turbulence, fractals, and mixing

Proposals and experiment 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, D_d(λ). 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, D_d(λ), 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

The small-scale structure of the fluctuating passive scalar field in a turbulent boundary layer

Issued as final reportNational Science Foundatio

Scale distributions and fractal dimensions in turbulence

A new geometric framework connecting scale distributions to coverage statistics is employed to analyze level sets arising in turbulence as well as in other phenomena. A 1D formalism is described and applied to Poisson, lognormal, and power-law statistics. A d-dimensional generalization is also presented. Level sets of 2D spatial measurements of jet-fluid concentration in turbulent jets are analyzed to compute scale distributions and fractal dimensions. Lognormal statistics are used to model the level sets at inner scales. The results are in accord with data from other turbulent flows