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

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 ≃ 1.9 × 10^3), momentum-dominated turbulent jets, for jet Reynolds numbers in the range of 1.25 × 10^4 ≤ Re ≤ 7.2 × 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^(−1) 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 ∼(c′^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 c′/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^(−1) scalar spectrum proposed by Batchelor [J. Fluid Mech. 5, 113 (1959)]

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

Review of the tribe Melolonthini in the southeastern United States (Coleoptera: Scarabaeidae: Melolonthinae)

This paper reviews the tribe Melolonthini (Scarabaeidae, Melolonthinae) in the southeastern United States, primarily in the states of Mississippi, Alabama, Georgia, and northern Florida. Four new species are described: Gronocarus inornatus, Hypothyce burnei, Polyphylla donaldsoni, and Polyphylla woodruffi. One new synonymy is made: Gronocarus multispinosus Howden is synonymized under Gronocarus autumnalis Schaeffer. Description of the previously unknown female is made for Polyphylla brownae Young. New collection records are presented for many species. Comments on natural histories and a key to species (omitting only species of the genus Phyllophaga Harris) in this region are presented

New record for Tesarius Rakovic in South America (Coleoptera: Scarabaeidae: Aphodiinae: Psammodiini)

The genus Tesarius Rakovic (1981) is an interesting group of wingless, nearly eyeless (yet probably functionally blind), sand dune-dwelling scarabs. There are presently 5 species in the genus, T. sulcipennis (Lea 1904) from Tasmania and 4 species in western North America. One of these native North American species, T. caelatus (LeConte 1857) has been found in Britain (Johnson 1975). The genus is reviewed by Rakovic (1981, 1984), who provides a key to species