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].

Inverse scattering of 2d photonic structures by layer-stripping

Design and reconstruction of 2d and 3d photonic structures are usually carried out by forward simulations combined with optimization or intuition. Reconstruction by means of layer-stripping has been applied in seismic processing as well as in design and characterization of 1d photonic structures such as fiber Bragg gratings. Layer-stripping is based on causality, where the earliest scattered light is used to recover the structure layer-by-layer. Our set-up is a 2d layered nonmagnetic structure probed by plane polarized harmonic waves entering normal to the layers. It is assumed that the dielectric permittivity in each layer only varies orthogonal to the polarization. Based on obtained reflectance data covering a suitable frequency interval, time-localized pulse data are synthesized and applied to reconstruct the refractive index profile in the leftmost layer by identifying the local, time-domain Fresnel reflection at each point. Once the first layer is known, its impact on the reflectance data is stripped off, and the procedure repeated for the next layer. Through numerical simulations it will be demonstrated that it is possible to reconstruct structures consisting of several layers. The impact of evanescent modes and limited bandwidth is discussed

Evolution of turbulence and in-plane vortices in the near field flow behind multi-scale planar grids

In this experimental work, we carry out detailed two-dimensional particle image velocimetry investigations for the near field wakes behind a conventional and two multi-scale planar grids, using stitched camera fields of view. Statistical independent measurements are conducted focusing on the first few mesh distances downstream of the grid. It is found that the multiple integral length scales originated from the grids loose their importance on the turbulence development after about three mesh distances downstream, much earlier than the distance where the turbulence becomes homogeneous. The largest eddy size, represented by the integral length scales, does not show clear differences in its growth rate among the three grids after an initial development of three times the largest grid size downstream. Nevertheless, when examining individual vortex behaviours using conditional averaging and filtering processes, clear differences are found. The grids are found to have different decay rates of peak vorticity and projected vortex strengths. Despite these differences, the in-plane vorticity correlation function reveals that the mean vortex shape of all the grids shows a universal near-Gaussian pattern which does not change much as the turbulence decays

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

The effect of gain saturation in a gain compensated perfect lens

The transmission of evanescent waves in a gain-compensated perfect lens is discussed. In particular, the impact of gain saturation is included in the analysis, and a method for calculating the fields of such nonlinear systems is developed. Gain compensation clearly improves the resolution; however, a number of nonideal effects arise as a result of gain saturation. The resolution associated with the lens is strongly dependent on the saturation constant of the active medium.Comment: to appear in J. Opt. Soc. Am.

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