Study of the origin of three dimensional structures and chaos in an externally forced free shear layer

Experiments on an externally forced free shear layer are performed which study the origin of three-dimensional structures and chaos in shear flows. Transition routes between the laminar two-dimensional stages of shear flows and their final complex three-dimensional stages are examined. Two avenues of investigation are pursued. First, the general idea of a multi-frequency route to chaos is examined which treats the shear flow as an open dynamical system. An attempt is made to apply concepts from nonlinear dynamics to these systems. Secondly, a new approach to generating three-dimensional structures in shear flows which involves the creation of a spatial shear in the frequency of external perturbations is presented. In these experiments, a variety of vortex reconnection behaviors is observed at the discontinuity

Probability density function of turbulent velocity fluctuation

The probability density function (PDF) of velocity fluctuations is studied experimentally for grid turbulence in a systematical manner. At small distances from the grid, where the turbulence is still developing, the PDF is sub-Gaussian. At intermediate distances, where the turbulence is fully developed, the PDF is Gaussian. At large distances, where the turbulence has decayed, the PDF is hyper-Gaussian. The Fourier transforms of the velocity fluctuations always have Gaussian PDFs. At intermediate distances from the grid, the Fourier transforms are statistically independent of each other. This is the necessary and sufficient condition for Gaussianity of the velocity fluctuations. At small and large distances, the Fourier transforms are dependent.Comment: 7 pages, 8 figures in a PS file, to appear in Physical Review

Extended self-similarity of the small-scale cosmic microwave background anisotropy

The Extended Self-Similarity (ESS) of cosmic microwave background (CMB) radiation has been studied using recent data obtained by the space-craft based Wilkinson Microwave Anisotropy Probe. Using the ESS and the high angular scale resolution (arcminutes) of the data it is shown that the CMB temperature space {\it increments} exhibit considerable and systematic declination from Gaussianity for high order moments at the small angular scales. Moreover, the CMB space increment ESS exponents have remarkably close values to the ESS exponents observed in turbulence (in magnetohydrodynamic turbulence)

Yakhot's model of strong turbulence: A generalization of scaling models of turbulence

We report on some implications of the theory of turbulence developed by V. Yakhot [V. Yakhot, Phys. Rev. E {\bf 57}(2) (1998)]. In particular we focus on the expression for the scaling exponents $\zeta_{n}$. We show that Yakhot's result contains three well known scaling models as special cases, namely K41, K62 and the theory by V. L'vov and I. Procaccia [V. L'vov & I. Procaccia, Phys. Rev. E {\bf 62}(6) (2000)]. The model furthermore yields a theoretical justification for the method of extended self--similarity (ESS).Comment: 8 page

Probability density function of turbulent velocity fluctuations in rough-wall boundary layer

The probability density function of single-point velocity fluctuations in turbulence is studied systematically using Fourier coefficients in the energy-containing range. In ideal turbulence where energy-containing motions are random and independent, the Fourier coefficients tend to Gaussian and independent of each other. Velocity fluctuations accordingly tend to Gaussian. However, if energy-containing motions are intermittent or contaminated with bounded-amplitude motions such as wavy wakes, the Fourier coefficients tend to non-Gaussian and dependent of each other. Velocity fluctuations accordingly tend to non-Gaussian. These situations are found in our experiment of a rough-wall boundary layer.Comment: 6 pages, to appear in Physical Review

Synthesis of Na+/Ca2+ ions modified TiO2 xerogels through co precipitation method

747-751We report a facile method for the synthesis of Na+/Ca2+ ions modified TiO2 xerogels by coprecipitation followed by calcination process. The resultant materials are well characterized by powder X-ray diffraction, Raman spectroscopy, ultraviolet-visible diffuse reflectance spectroscopy and high resolution transmission electron microscopy. Presence of sodium and calcium ions can influence the crystallinity of rutile TiO2. The photocatalytic performances of bare rutile TiO2 along with modified materials such as Na-TiO2, Ca-TiO2, Na-Ca-TiO2 materials are evaluated by calculating the amount of hydrogen evolved during the photocatalytic decomposition of water under light irradiation.This study will be effective informulating the effect of alkali/alkaline earth metal ions on the photocatalytic activity of rutile TiO2

Local properties of extended self-similarity in 3D turbulence

Using a generalization of extended self-similarity we have studied local scaling properties of 3D turbulence in a direct numerical simulation. We have found that these properties are consistent with lognormal-like behavior of energy dissipation fluctuations with moderate amplitudes for space scales $r$ beginning from Kolmogorov length $\eta$ up to the largest scales, and in the whole range of the Reynolds numbers: $50 \leq R_{\lambda} \leq 459$. The locally determined intermittency exponent $\mu(r)$ varies with $r$; it has a maximum at scale $r=14 \eta$, independent of $R_{\lambda}$.Comment: 4 pages, 5 figure

Vortex tubes in velocity fields of laboratory isotropic turbulence: dependence on the Reynolds number

The streamwise and transverse velocities are measured simultaneously in isotropic grid turbulence at relatively high Reynolds numbers, Re(lambda) = 110-330. Using a conditional averaging technique, we extract typical intermittency patterns, which are consistent with velocity profiles of a model for a vortex tube, i.e., Burgers vortex. The radii of the vortex tubes are several of the Kolmogorov length regardless of the Reynolds number. Using the distribution of an interval between successive enhancements of a small-scale velocity increment, we study the spatial distribution of vortex tubes. The vortex tubes tend to cluster together. This tendency is increasingly significant with the Reynolds number. Using statistics of velocity increments, we also study the energetical importance of vortex tubes as a function of the scale. The vortex tubes are important over the background flow at small scales especially below the Taylor microscale. At a fixed scale, the importance is increasingly significant with the Reynolds number.Comment: 8 pages, 3 PS files for 8 figures, to appear in Physical Review

Experiments on the Forced Wake of an Airfoil

Presented here is an experimental effort which attempts to understand the nature of the wake of an airfoil in a controlled environment. The frequency of oscillation in the wake (the vortex shedding frequency) is controlled through the introduction of an external perturbation. Strip heaters are used to introduce waves into the top and bottom boundary layers of a thin symmetric airfoil which are amplified and introduced to the wake. The linear and nonlinear interactions of these waves in the wake are studied in detail. Three modes of interaction have been observed through flow visualization and velocity measurements: frequency locking in which the vortex shedding frequency is the same as the forcing frequency, quasiperiodic vortex interaction in which periodic clusters of vortices are observed in the wake, and chaotic vortex interaction in which the vortices in the wake have a three dimensional random structure