We present measurements of the curve of / vs a from two-dimensional sections of the "dissipation" field of concentration fluctuations, and from one-dimensional sections of the dissipation field of passive temperature fluctuations, in turbulent jets. The results confirm the universality of the dissipation rate X of scalar fluctuations and the applicability of Taylor's hypothesis, and show that the curve of/vs a is the same for different components of X, that the additive properties of f(a) apply to intersections, and that the intermittency exponent of X is considerably higher than that for the turbulent kinetic-energy dissipation.

It is well recognized that both trabecular bone density and structure affect the overall bone quality and strength. In this study the aim is to quantify variations in the structural network of trabeculae using the concepts of fractal geometry. Fractal objects are objects that appear statistically similar over a range of scales. Typically fractals do not have smooth surfaces, but instead have rather complex structures with highly convoluted surfaces. Associated with every fractal is a characteristic dimension, called the fractal dimension. In this study, techniques of fractal analysis were used to characterize the trabecular bone matrix on digital images acquired by quantitative computed tomography (QCT) of dried excised human vertebral bodies (density ranging from 76-220 mg/cc) and photomicrography of transiliac crest biopsies. An automatic boundary tracking algorithm was used to identify the trabecular-bone and bone marrow interface, and a box-counting algorithm was used to estimate the fractal dimension of the trabecular boundary. Using this technique for fractal objects, if the boundary being analyzed is covered with boxes of differing sizes, epsilon, then the number of boxes N required to cover the surface increases indefinitely according to the relation N = epsilon-D, where D is the fractal dimension. Using this relationship in a preliminary study on five specimens we have found that the trabecular-bone boundary is fractal in nature. Using photomicrographs of iliac crest biopsies, it is found that the fractal dimension changes with the fractional trabecular bone content.(ABSTRACT TRUNCATED AT 250 WORDS)

Abstract.A scalar interface is defined as the surface separating the scalar-marked regions of a turbulent flow from the rest. The problem of determining the two-dimensional intersections of scalar interfaces is examined, taking as a specific example digital images of an axisymmetric jet visualized by laser-induced fluorescence. The usefulness of gradient and Laplacian techniques for this purpose is assessed, and it is shown that setting a proper threshold on the pixel intensity works well if the signal/noise ratio is high. Two methods of determining the proper threshold are presented, and the results are discussed. As one application of the technique, the fractal dimension of the scalar interface is calculated.

One of the recently established results concerns the fractal-like properties of surfaces such as the turbulent/nonturbulent interface. Although several confirmations have been reported in recent literature, enough discussion does not exist on how various flow features as well as measurement techniques affect the fractal dimension obtained; nor, in one place, is there a full discussion of the physical interpretation of such measurements. This paper serves these two purposes by examining in detail the specific case of the interface of scalar-marked regions (scalar interface) in turbulent shear flows. Dimension measurements have been made in two separate scaling regimes, one of which spans roughly between the integral and Kolmogorov scales (the K range), and the other between the Kolmogorov and Batchelor scales (the B range). In the K range, the fractal dimension is 2.36±0.05 to high degree of reliability. This is also the dimension of the vorticity interface. The dimension in the B range approaches (logarithmically) the value 3 in the limit of infinite Schmidt number, and is 2.7±0.03 when the diffusing scalar in water is sodium fluorescein (Schmidt number of the order 1000). Among the effects considered are those of (a) the flow Reynolds number, (b) developing regions such as the vicinity of a jet nozzle or a wake generator, (c) the free-stream and other noise effects, (d) the validity of the method of intersections usually invoked to relate the dimension of a fractal object to that of its intersections, (e) the effect of intersections by ‘‘slabs’’ of finite thickness and ‘‘lines’’ of finite width, and (f) the computational algorithm used for fractal dimension measurement, etc. The authors’ previous arguments concerning the physical meaning of the fractal dimension of surfaces in turbulent flows are recapitulated and amplified. In so doing, turbulent mixing is examined, and by invoking Reynolds and Schmidt numbers similarities, the fractal dimensions of scalar interfaces are deduced when the Schmidt number is small, unity, and large.

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.

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Ignition of imploding inertial confinement capsules requires, among other things, controlling the symmetry with high accuracy and fidelity. We have used gated x-ray imaging, with 10 μm and 70 ps resolution, to detect the x-ray emission from the imploded core of symmetry capsules at the National Ignition Facility. The measurements are used to characterize the time dependent symmetry and the x-ray bang time of the implosion from two orthogonal directions. These measurements were one of the primary diagnostics used to tune the parameters of the laser and Hohlraum to vary the symmetry and x-ray bang time of the implosion of cryogenically cooled ignition scale deuterium/helium filled plastic capsules. Here, we will report on the successful measurements performed with up to 1.2 MJ of laser energy in a fully integrated cryogenics gas-filled ignition-scale Hohlraum and capsule illuminated with 192 smoothed laser beams. We will describe the technique, the accuracy of the technique, and the results of the variation in symmetry with tuning parameters, and explain how that set was used to predictably tune the implosion symmetry as the laser energy, the laser cone wavelength separation, and the Hohlraum size were increased to ignition scales. We will also describe how to apply that technique to cryogenically layered tritium-hydrogen-deuterium capsules.

The National Ignition Facility has been used to compress deuterium-tritium to an average areal density of ~1.0±0.1 g cm(-2), which is 67% of the ignition requirement. These conditions were obtained using 192 laser beams with total energy of 1-1.6 MJ and peak power up to 420 TW to create a hohlraum drive with a shaped power profile, peaking at a soft x-ray radiation temperature of 275-300 eV. This pulse delivered a series of shocks that compressed a capsule containing cryogenic deuterium-tritium to a radius of 25-35 μm. Neutron images of the implosion were used to estimate a fuel density of 500-800 g cm(-3).