The flying hot wire and related instrumentation

A flying hot-wire technique is proposed for studies of separated turbulent flow in wind tunnels. The technique avoids the problem of signal rectification in regions of high turbulence level by moving the probe rapidly through the flow on the end of a rotating arm. New problems which arise include control of effects of torque variation on rotor speed, avoidance of interference from the wake of the moving arms, and synchronization of data acquisition with rotation. Solutions for these problems are described. The self-calibrating feature of the technique is illustrated by a sample X-array calibration

Testing for Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe Data: Minkowski Functionals and the Length of the Skeleton

The three Minkowski functionals and the recently defined length of the skeleton are estimated for the co-added first-year Wilkinson Microwave Anisotropy Probe (WMAP) data and compared with 5000 Monte Carlo simulations, based on Gaussian fluctuations with the a-priori best-fit running-index power spectrum and WMAP-like beam and noise properties. Several power spectrum-dependent quantities, such as the number of stationary points, the total length of the skeleton, and a spectral parameter, gamma, are also estimated. While the area and length Minkowski functionals and the length of the skeleton show no evidence for departures from the Gaussian hypothesis, the northern hemisphere genus has a chi^2 that is large at the 95% level for all scales. For the particular smoothing scale of 3.40 degrees FWHM it is larger than that found in 99.5% of the simulations. In addition, the WMAP genus for negative thresholds in the northern hemisphere has an amplitude that is larger than in the simulations with a significance of more than 3 sigma. On the smallest angular scales considered, the number of extrema in the WMAP data is high at the 3 sigma level. However, this can probably be attributed to the effect of point sources. Finally, the spectral parameter gamma is high at the 99% level in the northern Galactic hemisphere, while perfectly acceptable in the southern hemisphere. The results provide strong evidence for the presence of both non-Gaussian behavior and an unexpected power asymmetry between the northern and southern hemispheres in the WMAP data.Comment: 17 pages, 10 figures, accepted for publication in Ap

New approaches to probing Minkowski functionals

We generalize the concept of the ordinary skew-spectrum to probe the effect of non-Gaussianity on the morphology of cosmic microwave background (CMB) maps in several domains: in real space (where they are commonly known as cumulant-correlators), and in harmonic and needlet bases. The essential aim is to retain more information than normally contained in these statistics, in order to assist in determining the source of any measured non-Gaussianity, in the same spirit as Munshi & Heavens skew-spectra were used to identify foreground contaminants to the CMB bispectrum in Planck data. Using a perturbative series to construct the Minkowski functionals (MFs), we provide a pseudo-C based approach in both harmonic and needlet representations to estimate these spectra in the presence of a mask and inhomogeneous noise. Assuming homogeneous noise, we present approximate expressions for error covariance for the purpose of joint estimation of these spectra. We present specific results for four different models of primordial non-Gaussianity local, equilateral, orthogonal and enfolded models, as well as non-Gaussianity caused by unsubtracted point sources. Closed form results of nextorder corrections to MFs too are obtained in terms of a quadruplet of kurt-spectra. We also use the method of modal decomposition of the bispectrum and trispectrum to reconstruct the MFs as an alternative method of reconstruction of morphological properties of CMB maps. Finally, we introduce the odd-parity skew-spectra to probe the odd-parity bispectrum and its impact on the morphology of the CMB sky. Although developed for the CMB, the generic results obtained here can be useful in other areas of cosmology

Computational Study of Turbulent-Laminar Patterns in Couette Flow

Turbulent-laminar patterns near transition are simulated in plane Couette flow using an extension of the minimal flow unit methodology. Computational domains are of minimal size in two directions but large in the third. The long direction can be tilted at any prescribed angle to the streamwise direction. Three types of patterned states are found and studied: periodic, localized, and intermittent. These correspond closely to observations in large aspect ratio experiments.Comment: 4 pages, 5 figure

General Statistical properties of the CMB Polarization field

The distribution of the polarization of the Cosmic Microwave Background (CMB) in the sky is determined by the hypothesis of random Gaussian distribution of the primordial density perturbations. This hypotheses is well motivated by the inflationary cosmology. Therefore, the test of consistency of the statistical properties of the CMB polarization field with the Gaussianity of primordial density fluctuations is a realistic way to study the nature of primordial inhomogeneities in the Universe. This paper contains the theoretical predictions of the general statistical properties of the CMB polarization field. All results obtained under assumption of the Gaussian nature of the signal. We pay the special attention to the following two problems. First, the classification and statistics of the singular points of the polarization field where polarization is equal to zero. Second, the topology of contours of the value of the degree of polarization. We have investigated the percolation properties for the zones of ``strong'' and ``weak'' polarization. We also have calculated Minkowski functionals for the CMB polarization field. All results are analytical.Comment: Latex, 22 pages, including 5 figure

Flying-Hot-Wire Study of 2-Dimensional Mean Flow Past an NACA 4412 Airfoil at Maximum Lift

Hot-wire measurements have been made in the boundary layer, the separated region, and the near wake for flow past an NACA 4412 airfoil at maximum lift. The Reynolds number based on chord was about 1,500,000. Special care was taken to achieve a two-dimensional mean flow. The main instrumentation was a hot-wire probe mounted on the end of a rotating arm. An unexpected effect of rotor interference was identified and brought under control. A digital computer was used to control synchronized sampling at closely spaced points along the probe arc. Ensembles of data were obtained at several thousand locations in the flow field. The data include intermittency, two components of mean velocity, and twelve mean values for double, triple, and quadruple products of two velocity fluctuations. The data are available on punched cards in raw form and also after use of smoothing and interpolation routines to obtain values on a fine rectangular grid aligned with the airfoil chord

A Counts-in-Cells Analysis of Lyman-break Galaxies at z~3

We have measured the counts-in-cells fluctuations of 268 Lyman-break galaxies with spectroscopic redshifts in six 9 arcmin by 9 arcmin fields at z~3. The variance of galaxy counts in cubes of comoving side length 7.7, 11.9, 11.4 h^{-1} Mpc is \sigma_{gal}^2 ~ 1.3\pm0.4 for \Omega_M=1, 0.2 open, 0.3 flat, implying a bias on these scales of \sigma_{gal} / \sigma_{mass} = 6.0\pm1.1, 1.9\pm0.4, 4.0\pm0.7. The bias and abundance of Lyman-break galaxies are surprisingly consistent with a simple model of structure formation which assumes only that galaxies form within dark matter halos, that Lyman-break galaxies' rest-UV luminosities are tightly correlated with their dark masses, and that matter fluctuations are Gaussian and have a linear power-spectrum shape at z~3 similar to that determined locally (\Gamma~0.2). This conclusion is largely independent of cosmology or spectral normalization \sigma_8. A measurement of the masses of Lyman-break galaxies would in principle distinguish between different cosmological scenarios.Comment: Accepted for publication in ApJ, 16 pages including 4 figure

An experimental route to spatiotemporal chaos in an extended 1D oscillators array

We report experimental evidence of the route to spatiotemporal chaos in a large 1D-array of hotspots in a thermoconvective system. Increasing the driving force, a stationary cellular pattern becomes unstable towards a mixed pattern of irregular clusters which consist of time-dependent localized patterns of variable spatiotemporal coherence. These irregular clusters coexist with the basic cellular pattern. The Fourier spectra corresponding to this synchronization transition reveals the weak coupling of a resonant triad. This pattern saturates with the formation of a unique domain of great spatiotemporal coherence. As we further increase the driving force, a supercritical bifurcation to a spatiotemporal beating regime takes place. The new pattern is characterized by the presence of two stationary clusters with a characteristic zig-zag geometry. The Fourier analysis reveals a stronger coupling and enables to find out that this beating phenomena is produced by the splitting of the fundamental spatiotemporal frequencies in a narrow band. Both secondary instabilities are phase-like synchronization transitions with global and absolute character. Far beyond this threshold, a new instability takes place when the system is not able to sustain the spatial frequency splitting, although the temporal beating remains inside these domains. These experimental results may support the understanding of other systems in nature undergoing similar clustering processes.Comment: 12 pages, 13 figure

Particle decay in inflationary cosmology

We investigate the relaxation and decay of a particle during inflation by implementing the dynamical renormalization group. This investigation allows us to give a meaningful definition for the decay rate in an expanding universe. As a prelude to a more general scenario, the method is applied here to study the decay of a particle in de Sitter inflation via a trilinear coupling to massless conformally coupled particles, both for wavelengths much larger and much smaller than the Hubble radius. For superhorizon modes we find that the decay is of the form eta^{Gamma1} with eta being conformal time and we give an explicit expression for Gamma1 to leading order in the coupling which has a noteworthy interpretation in terms of the Hawking temperature of de Sitter space-time. We show that if the mass M of the decaying field is << H then the decay rate during inflation is enhanced over the Minkowski spacetime result by a factor 2H/[pi M]. For wavelengths much smaller than the Hubble radius we find that the decay law is e^{-alpha/[k H C(eta)} with C(eta) the scale factor and alpha determined by the strength of the trilinear coupling. This result suggests a suppression of power for long wavelength modes upon horizon crossing. In all cases we find a substantial enhancement in the decay law as compared to Minkowski space-time. These results suggest potential implications for the spectrum of scalar density fluctuations as well as non-gaussianities.Comment: 19 pages, 1 .eps figure. Improved version to appear in Phys. Rev.

Analytical Model of the Time Developing Turbulent Boundary Layer

We present an analytical model for the time-developing turbulent boundary layer (TD-TBL) over a flat plate. The model provides explicit formulae for the temporal behavior of the wall-shear stress and both the temporal and spatial distributions of the mean streamwise velocity, the turbulence kinetic energy and Reynolds shear stress. The resulting profiles are in good agreement with the DNS results of spatially-developing turbulent boundary layers at momentum thickness Reynolds number equal to 1430 and 2900. Our analytical model is, to the best of our knowledge, the first of its kind for TD-TBL.Comment: 5pages, 9 figs, JETP Letters, submitte