Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows

Abstract

The three-dimensional turbulent field of a passive scalar has been mapped quantitatively by obtaining, effectively instantaneously, several closely spaced parallel two-dimensional images; the two-dimensional images themselves have been obtained by laser-induced fluorescence. Turbulent jets and wakes at moderate Reynolds numbers are used as examples. The working fluid is water. The spatial resolution of the measurements is about four Kolmogorov scales. The first contribution of this work concerns the three-dimensional nature of the boundary of the scalar-marked regions (the ‘scalar interface’). It is concluded that interface regions detached from the main body are exceptional occurrences (if at all), and that in spite of the large structure, the randomness associated with small-scale convolutions of the interface are strong enough that any two intersections of it by parallel planes are essentially uncorrelated even if the separation distances are no more than a few Kolmogorov scales. The fractal dimension of the interface is determined directly by box-counting in three dimensions, and the value of 2.35 ± 0.04 is shown to be in good agreement with that previously inferred from two-dimensional sections. This justifies the use of the method of intersections. The second contribution involves the joint statistics of the scalar field and the quantity χ* (or its components), χ* being the appropriate approximation to the scalar ‘dissipation’ field in the inertial–convective range of scales. The third aspect relates to the multifractal scaling properties of the spatial intermittency of χ*; since all three components of χ* have been obtained effectively simultaneously, inferences concerning the scaling properties of the individual components and their sum have been possible. The usefulness of the multifractal approach for describing highly intermittent distributions of χ* and its components is explored by measuring the so-called singularity spectrum (or the f(α)-curve) which quantifies the spatial distribution of various strengths of χ*. Also obtained is a time sequence of two-dimensional images with the temporal resolution on the order of a few Batchelor timescales; this enables us to infer features of temporal intermittency in turbulent flows, and qualitatively the propagation speeds of the scalar interface. Finally, a few issues relating to the resolution effects have been addressed briefly by making point measurements with the spatial and temporal resolutions comparable with the Batchelor lengthscale and the corresponding timescale.

Dynamic Closure of Scalar Dissipation Rate for Large Eddy Simulations of Turbulent Premixed Combustion: A Direct Numerical Simulations Analysis

“…5i) does not depend on any empirical parametersation of β c similar to Eq. 5iv but inherently accounts for [29][30][31][32][33][34], may not be suitable for SDRÑ c modelling and this behaviour perhaps arises due to multi-fractal nature of SDR, which was observed previously for passive scalar mixing [57][58][59][60][61]. By contrast, both static and dynamic versions of the LES-G model (i.e.…”

“…α D does not change between actual and test filter scales) that has been invoked while deriving Eq. 4 may not be strictly valid, as SDR for passive scalars is known to exhibit multi-fractal nature [57,58,60,61] and a similar behaviour is likely to be present also for reacting flows. Thus, a single power-law exponent may not be suitable to describe the statistical behaviour of N c .…”

The effect of bivalve excurrent jet dynamics on mass transfer in a benthic boundary layer

“…see Prasad and Sreenivasan 1990;Koochesfahani and Dimotakis 1985;O'Riordan 1993) was used to obtain spatially resolved information about the timeaveraged growth of the concentration boundary layer above the bed. In this technique, fluorescent dye is illuminated with a thin sheet of laser light and a CCD-video camera is used to capture images pf dyed excurrent jet flows.…”

Fractals in wave processes

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