Freely-Decaying, Homogeneous Turbulence Generated by Multi-scale Grids

We investigate wind tunnel turbulence generated by both conventional and multi-scale grids. Measurements were made in a tunnel which has a large test-section, so that possible side wall effects are very small and the length assures that the turbulence has time to settle down to a homogeneous shear-free state. The conventional and multi-scale grids were all designed to produce turbulence with the same integral scale, so that a direct comparison could be made between the different flows. Our primary finding is that the behavior of the turbulence behind our multi-scale grids is virtually identical to that behind the equivalent conventional grid. In particular, all flows exhibit a power-law decay of energy, $u^2 \sim t^{-n}$, where $n$ is very close to the classical Saffman exponent of $n = 6/5$. Moreover, all spectra exhibit classical Kolmogorov scaling, with the spectra collapsing on the integral scales at small $k$, and on the Kolmogorov micro-scales at large $k$. Our results are at odds with some other experiments performed on similar multi-scale grids, where significantly higher energy decay exponents and turbulence levels have been reported.Comment: 19 pages, 18 figure

The non-local nature of structure functions

Kolmogorov’s two-thirds, h(Dv)2i e2/3r2/3, and five-thirds, E e2/3k−5/3, laws are formally equivalent in the limit of vanishing viscosity, n!0. However, for most Reynolds numbers encountered in laboratory scale experiments, or numerical simulations, it is invariably easier to observe the five-thirds law. By creating artificial fields of isotropic turbulence composed of a random sea of Gaussian eddies whose size and energy distribution can be controlled, we show why this is the case. The energy of eddies of scale, s, is shown to vary as s2/3, in accordance with Kolmogorov’s 1941 law, and we vary the range of scales, g = smax/smin, in any one realisation from g = 25 to g = 800. This is equivalent to varying the Reynolds number in an experiment from Rl = 60 to Rl = 600. While there is some evidence of a five-thirds law for g > 50 (Rl > 100), the two-thirds law only starts to become apparent when g approaches 200 (Rl 240). The reason for this discrepancy is that the second-order structure function is a poor filter, mixing information about energy and enstrophy, and from scales larger and smaller than r. In particular, in the inertial range, h(Dv)2i takes the form of a mixed power-law, a1+a2r2+a3r2/3, where a2r2 tracks the variation in enstrophy and a3r2/3 the variation in energy. These findings are shown to be consistent with experimental data where the polution of the r2/3 law by the enstrophy contribution, a2r2, is clearly evident. We show that higherorder structure functions (of even order) suffer from a similar deficiency. (See also [2].

A study of convection velocities in a zero pressure gradient turbulent boundary layer

Time-resolved DPIV measurements performed in wall parallel planes at several wall normal locations in a turbulent boundary layer (TBL) are used to illuminate the distribution of wall parallel velocities in a three-dimensional energy spectrum over streamwise, spanwise, and temporal wavelengths. To our knowledge, this is the first time this type of spectral distribution has been reported. Slices of the 3D spectrum can give insight into the propagation of different scales in the ow as well as the streamwise and spanwise extent of dominant scales. Measurements were performed at three wall normal locations, y^+ = 34; 108; and 278, in a zero pressure gradient TBL at Re_τ = 470 . Two high speed cameras placed side-by-side in the streamwise direction give a 10δ streamwise field of view with a time step of Δt^+ = 0:5 between consecutive fields. Far from the wall the convection velocities of all scales are very close to the local mean velocity in agreement with the work of Dennis and Nickels, while at y^+ = 34 it was found that all measured scales in the flow convect faster than the local mean in agreement with Krogstad et. al. The variation of the convection velocity with scale and distance from the wall will be discussed

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

Renormalization group in the infinite-dimensional turbulence: third-order results

The field theoretic renormalization group is applied to the stochastic Navier-Stokes equation with the stirring force correlator of the form k^(4-d-2\epsilon) in the d-dimensional space, in connection with the problem of construction of the 1/d expansion for the fully developed fluid turbulence beyond the scope of the standard epsilon expansion. It is shown that in the large-d limit the number of the Feynman diagrams for the Green function (linear response function) decreases drastically, and the technique of their analytical calculation is developed. The main ingredients of the renormalization group approach -- the renormalization constant, beta function and the ultraviolet correction exponent omega, are calculated to order epsilon^3 (three-loop approximation). The two-point velocity-velocity correlation function, the Kolmogorov constant C_K in the spectrum of turbulent energy and the inertial-range skewness factor S are calculated in the large-d limit to third order of the epsilon expansion. Surprisingly enough, our results for C_K are in a reasonable agreement with the existing experimental estimates.Comment: 30 pages with EPS figure

Did the Draupner wave occur in a crossing sea?

The ‘New Year Wave’ was recorded at the Draupner platform in the North Sea and is a rare high quality measurement of a ‘freak’ or ‘rogue’ wave. The wave has been the subject of much interest and numerous studies. Despite this, the event has still not been satisfactorily explained. One piece of information which was not directly measured at the platform, but which is vital to understanding the nonlinear dynamics is the wave’s directional spreading. This paper investigates the directionality of the Draupner wave and concludes it might have resulted from two wave-groups crossing, whose mean wave directions were separated by about 90◦ or more. This result has been deduced from a set-up of the low frequency second order difference waves under the giant wave, which can be explained only if two wave systems are propagating at such an angle. To check whether second order theory is satisfactory for such a highly non-linear event, we have run numerical simulations using a fully non-linear potential flow solver, which confirm the conclusion deduced from the second order theory. This is backed up by a hindcast from ECMWF which shows swell waves propagating at ∼ 80◦ to the wind sea. Other evidence which supports our conclusion are the measured forces on the structure, the magnitude of the second order sum waves and some other instances of freak waves occurring in crossing sea states

Lattice dynamical analogies and differences between SrTiO3 and EuTiO3 revealed by phonon-dispersion relations and double-well potentials

A comparative analysis of the structural phase transitions of EuTiO3 and SrTiO3 (at TS = 282 and 105 K, respectively) is made on the basis of phonon-dispersion and density functional calculations. The phase transition of EuTiO3 is predicted to arise from the softening of a transverse acoustic zone-boundary mode caused by the rotations of the TiO6 octahedra, as also found for the phase transition of SrTiO3. While the temperature dependence of the soft mode is similar in both compounds, their elastic properties differ drastically due to a large difference in the double-well potentials associated with the soft zone boundary-acoustic mode.Comment: 16 pages, 6 figure

Disorder and diffuse scattering in single-chirality (TaSe4_4)2_2I crystals

The quasi-one-dimensional chiral compound (TaSe$_4$)$_2$I has been extensively studied as a prime example of a topological Weyl semimetal. Upon crossing its phase transition temperature $T_\textrm{CDW}$ $\approx$ 263 K, (TaSe$_4$)$_2$I exhibits incommensurate charge density wave (CDW) modulations described by the well-defined propagation vector $\sim$(0.05, 0.05, 0.11), oblique to the TaSe$_4$ chains. Although optical and transport properties greatly depend on chirality, there is no systematic report about chiral domain size for (TaSe$_4$)$_2$I. In this study, our single-crystal scattering refinements reveal a bulk iodine deficiency, and Flack parameter measurements on multiple crystals demonstrate that separate (TaSe$_4$)$_2$I crystals have uniform handedness, supported by direct imaging and helicity dependent THz emission spectroscopy. Our single-crystal X-ray scattering and calculated diffraction patterns identify multiple diffuse features and create a real-space picture of the temperature-dependent (TaSe$_4$)$_2$I crystal structure. The short-range diffuse features are present at room temperature and decrease in intensity as the CDW modulation develops. These transverse displacements, along with electron pinning from the iodine deficiency, help explain why (TaSe$_4$)$_2$I behaves as an electronic semiconductor at temperatures above and below $T_\textrm{CDW}$, despite a metallic band structure calculated from density functional theory of the ideal structure.Comment: 24 pages, 20 figures, 3 table

Rapid ethical assessment on informed consent content and procedure in Hintalo-Wajirat, Northern Ethiopia: a qualitative study

Background Informed consent is a key component of bio-medical research involving human participants. However, obtaining informed consent is challenging in low literacy and resource limited settings. Rapid Ethical Assessment (REA) can be used to contextualize and simplify consent information within a given study community. The current study aimed to explore the effects of social, cultural, and religious factors during informed consent process on a proposed HPV-serotype prevalence study. Methodology A qualitative community-based REA was conducted in Adigudom and Mynebri Kebeles, Northern Ethiopia, from July to August 2013. Data were collected by a multi-disciplinary team using open ended questions concerning informed consent components in relation to the parent study. The team conducted one-to-one In-Depth Interviews (IDI) and Focus Group Discussions (FGDs) with key informants and community members to collect data based on the themes of the study. Tape recorded data were transcribed in Tigrigna and then translated into English. Data were categorized and thematically analyzed using open coding and content analysis based on pre-defined themes. Results The REA study revealed a number of socio-cultural issues relevant to the proposed study. Low community awareness about health research, participant rights and cervical cancer were documented. Giving a vaginal sample for testing was considered to be highly embarrassing, whereas giving a blood sample made participants worry that they might be given a result without the possibility of treatment. Verbal consent was preferred to written consent for the proposed study. Conclusion This rapid ethical assessment disclosed important socio-cultural issues which might act as barriers to informed decision making. The findings were important for contextual modification of the Information Sheet, and to guide the best consent process for the proposed study. Both are likely to have enabled participants to understand the informed consent better and consequently to comply with the study