Rahul R. Prasad

QUANTITATIVE THREE-DIMENSIONAL IMAGING AND THE STRUCTURE OF PASSIVE SCALAR FIELDS IN FULLY TURBULENT FLOWS

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. Turbulence jets and wakes at moderate Reynolds numbers are used as examples

The measurement and interpretation of fractal dimensions of the scalar interface in turbulent flows

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.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 (logarit...

Scalar interfaces in digital images of turbulent flows

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.

New results on the fractal and multifractal structure of the large Schmidt number passive scalars in fully turbulent flows

Abstract By measuring concentration fluctuations of a dye with very fine spatial and temporal resolution in typical unconfined turbulent water flows, we obtain the fractal dimension characteristic of the scalar interface in the range between Kolmogorov and Batchelor scales. We use one-dimensional intersection methods and invoke Taylors hypothesis, but both of them are amply justified. We obtain a theoretical estimate for the fractal dimension by modifying our earlier arguments for finite (though large) Schmidt number effects. Finally, the multifractal characteristics of the scalar dissipation rate in the same scale range are also presented.

The fractal geometry of interfaces and the multifractal distribution of dissipation in fully turbulent flows

We describe scalar interfaces in turbulent flowsvia elementary notions from fractal geometry. It is shown by measurement that these interfaces possess a fractal dimension of 2.35±0.05 in a variety of flows, and it is demonstrated that the uniqueness of this number is a consequence of the physical principle of Reynolds number similarity. Also, the spatial distribution of scalar and energy dissipation in physical space is shown to be multifractal. We compare thef(α) curves obtained from one- and two-dimensional cuts in several flows, and examine their value in describing features of turbulence in the three-dimensional physical space.

Theoretical and experimental study of rotation in a vacuum‐arc centrifuge

Measurements of rotation frequency, plasma potential, ion temperature, and density in a vacuum‐arc centrifuge are described. The vacuum‐arc centrifuge is a magnetized plasma column 1 m long, 5 cm in diameter, with ne ∼1014 cm−3, and Ti ∼3 eV. The source of this plasma column is a vacuum‐arc discharge between a negatively biased cathode and a grounded‐mesh anode 6 cm downstream of it. This source plasma region is at one end of a 2‐m‐long vacuum vessel. An externally applied axial magnetic field collimates the plasma, which streams through the anode mesh and induces rotation. Rigid–rotor frequencies ∼105 rad s−1 lead to radial centrifugal separation between isotopes. A piezoelectrically scanned Fabry–Perot interferometer is used to measure ion temperature and rotation frequency. Langmuir probes are also used to corroborate these rotation measurements, and to measure the plasma potential and ion‐density profiles. These measurements lead to scaling laws for the rotation. The scaling laws are compared with the...

Quantitative x‐ray emission from a DPF device

The x‐ray emission was measured from a Dense Plasma Focus (DPF) device. The high density plasma is generated by an electrical discharge in rarefied‐neon gas between electrodes in a Mather‐type plasma focus configuration. A curved‐crystal x‐ray spectrograph, a pinhole camera, and an active‐filtered photodiode were the diagnostics viewing the axial output of the pinched‐plasma region. The x‐ray pinhole images indicate a pinched volume roughly 8 mm in length with a nearly circular cross section of about 300 μm in diameter. The digitized spectral traces were computer processed to obtain absolute x‐ray line intensities. The neon plasma yielded 10–15 J of K‐shell radiation into 4π with the hydrogenlike and heliumlike alpha lines totaling 55%–65% of the total spectral emission. The x‐ray emission of the DPF device was studied as a function of discharge current and anode diameter.

Space and time resolved electron density and current measurements in a dense plasma focus Z-pinch

Plasma density and current profiles in a Z-pinch are important parameters to understand the implosion and radiation physics. This paper describes measurements of electron density and current at radii of /spl ges/200 /spl mu/m from the axis of a dense plasma focus (DPF) pinch plasma that is imploded by a /spl ap/0.3 MA current pulse. These measurements use laser interferometry and polarimetry. The electromagnetic wave propagating through a current carrying plasma will change its phase, polarization state, and propagation direction. Refraction by electrons bends the wave fronts and changes the propagation direction; Faraday rotation due to the magnetic field and electron density rotates the laser polarization vector. By measuring these quantities simultaneously, the magnetic field and electron density can be separately determined. Although the DPF used here is a low current device, the measured densities (/spl les/10/sup 20/ cm/sup -3/) and magnetic fields (/spl sim/100 T) are similar to values expected just outside higher current but larger radius Z-pinches, so this technique should be applicable there as well. The techniques described here do not require access to the core of the pinch to work; just outside these pinches the coronal density and self-magnetic field are high enough to give reliable data but not so high as to make the measurements difficult.

Z pinch imploding plasma density profile measurements using a two-frame laser shearing interferometer

A laser shearing interferometer (LSI) was used to make spatially and temporally resolved measurements of the electron density profile in an imploding z pinch. Experiments were conducted on the 0.7-MA/250-ns Hawk machine, the 2.5-MA/100-ns ACE-4 machine, and the 3.8-MA/190-ns Double Eagle machine. Time and space resolved measurements of the current and plasma density are needed for better understanding of the implosion dynamics and stagnation physics of z pinches. The electron density profile can be obtained using an LSI. The LSI passes a short pulse, collimated laser beam across the imploding z pinch, which distorts the laser wavefront. the maximum wavefront distortion occurs where the density gradient is highest, such as across the current sheath. After passing through the pinch, the distorted wavefronts are split into two beams that are laterally displaced relative to one other. This shearing causes interference between these two wavefronts and produces an interferogram, from which the plasma density profiles are derived. In the experiments, a 150-ps laser pulse was split into two pulses with an interpulse delay of several tens. of nanoseconds. This pulse pair gave two snap shots of the electron density profiles during the 100-300-ns implosions. From these interferograms, electron densities and implosion velocities of the imploding plasmas were derived, the current sheath was observed, and the plasma ionization states, growth rates, and wavelengths of instabilities were estimated. The results motivate construction of an upgraded instrument with four or more frames and with an added laser polarimetry measurement (Faraday rotation) capability to obtain both electron and current profiles.

Laser wavefront analyzer for imploding plasma density and current profile measurements

The laser wavefront analyzer (LWA) consists of a polarized laser beam pulse that traverses an imploding z-pinch, and a microlens array that focuses the laser beam into a large number (104) of very tiny spots. LWA image analysis determines the refractive bending angles (due to density gradients) and Faraday rotation angles (due to the magnetic field-density integral) throughout the plasma cross section. Electron density and current distributions are derived from LWA data in an imploding gas-puff z-pinch plasma.