150,445 research outputs found
Reynolds number dependence of scalar fluctuations in a high Schmidt number turbulent jet
The scalar rms fluctuations in a turbulent jet were investigated experimentally, using high-resolution, laser-induced fluorescence techniques. The experiments were conducted in a high Schmidt number fluid (water), on the jet centerline, over a jet Reynolds number range of 30003000 or 6500
Stochastic geometric properties of scalar interfaces in turbulent jets
Experiments were conducted in which the behavior of scalar interfaces in turbulent jets was examined, using laser-induced fluorescence (LIF) techniques. The experiments were carried out in a high Schmidt number fluid (water), on the jet centerline, over a jet Reynolds number range of 1000<=Re<=24 000. Both two-dimensional scalar data, c(r,t) at fixed x/d, and one-dimensional scalar data, c(t) at fixed x/d and r/x, were analyzed using standard one- and two-dimensional fractal box-counting algorithms. Careful treatment was given to the handling of noise. Both long and short records as well as off-centerline measurements were also investigated. The important effect of threshold upon the results is discussed. No evidence was found of a constant (power-law) fractal dimension over the range of Reynolds numbers studied. On the other hand, the results are consistent with the computed behavior of a simple stochastic model of interface geometry
A Tale of Two Courts: The Alaska Supreme Court, the United States Supreme Court, and Retroactivity
Measurements of scalar power spectra in high Schmidt number turbulent jets
We report on an experimental investigation of temporal, scalar power spectra of round, high Schmidt number (Sc β 1.9 Γ 10^3), momentum-dominated turbulent jets, for jet Reynolds numbers in the range of 1.25 Γ 10^4 β€ Re β€ 7.2 Γ 10^4. At intermediate scales, we find a spectrum with a slope (logarithmic derivative) that increases in absolute value with Reynolds number, but remains less than 5/3 at the highest Reynolds number in our experiments. At the smallest scales, our spectra exhibit no k^(β1) power-law behaviour, but, rather, seem to be approximated by a log-normal function, over a range of scales exceeding a factor of 40, in some cases
Some consequences of the boundedness of scalar fluctuations
Values of the scalar field c(x,t), if initially bounded, will always be bounded by the limits set by the initial conditions. This observation permits the maximum variance βΌ(cβ²^2) to be computed as a function of the mean value c. It is argued that this maximum should be expected in the limit of infinite Schmidt numbers (zero scalar species diffusivity). This suggests that cβ²/c on the axis of turbulent jets, for example, may not tend to a constant, i.e., independent of x/d, in the limit of very large Schmidt numbers. It also underscores a difficulty with the k^(β1) scalar spectrum proposed by Batchelor [J. Fluid Mech. 5, 113 (1959)]
Turbulent mixing
The ability of turbulent flows to effectively mix entrained fluids to a molecular scale is a vital part of the dynamics of such flows, with wide-ranging consequences in nature and engineering. It is a considerable experimental, theoretical, modeling, and computational challenge to capture and represent turbulent mixing which, for high Reynolds number (Re) flows, occurs across a spectrum of scales of considerable span. This consideration alone places high-Re mixing phenomena beyond the reach of direct simulation, especially in high Schmidt number fluids, such as water, in which species diffusion scales are one and a half orders of magnitude smaller than the smallest flow scales. The discussion below attempts to provide an overview of turbulent mixing; the attendant experimental, theoretical, and computational challenges; and suggests possible future directions for progress in this important field
Robert MacPherson and arithmetic groups
We survey contributions of Robert MacPherson to the theory of arithmetic
groups. There are two main areas we discuss: (i) explicit reduction theory for
Siegel modular threefolds, and (ii) constructions of compactifications of
locally symmetric spaces. The former is joint work with Mark McConnell, the
latter with Lizhen Ji.Comment: Dedicated to Robert MacPherson on the occasion of his 60th birthda
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