Joint statistics between temperature and its dissipation rate components in a round jet

J. Mi, R. A. Antonia, and F. Anselme

Fracture Surfaces as Multiscaling Graphs

Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of materials, paper) are analyzed as self-affine graphs $h(x)$ of height $h$ as a function of length $x$. We show that these are multiscaling, in the sense that $n^{th}$ order moments of the height fluctuations across any distance $\ell$ scale with a characteristic exponent that depends nonlinearly on the order of the moment. Having demonstrated this, one rules out a widely held conjecture that fracture in 2D belongs to the universality class of directed polymers in random media. In fact, 2D fracture does not belong to any of the known kinetic roughening models. The presence of multiscaling offers a stringent test for any theoretical model; we show that a recently introduced model of quasi-static fracture passes this test.Comment: 4 pages, 5 figure

On the numerical modelling of the Jet Erosion Test

International audienceEvaluating the erodibility of a soil, both in terms of erosion threshold (initiation) and erosion rate (progression), is critical for the evaluation of the safety of water retaining structures. Indeed different soils can erode at different rates. However, the relationship between the erosion parameters and the geotechnical and chemical properties of soils remains largely unknown. The jet erosion test appears to be an efficient and simple means for quantifying the two erosion parameters involved. The first parameter is the critical stress while the second parameter is the erosion coefficient. A simplified model of this test has been drawn up by G. Hanson et al. to interpret the experimental curves. Few attempts have been made so far to model the whole process, however. The aim of this study is to simulate the impinging jet and to take into account the erosion of the soil by means of computational fluid dynamics (CFD) numerical modelling. The key point was the time dependence of the problem, due to erosion processes, however the turbulent flow could be considered as steady because of the assumption of low kinetics erosion assumption. The results of the present modelling study are compared to the simplified model and to experimental data. This comparison is a first confirmation of the validity of the simplified model as a means of assessing the critical stress and the erosion coefficient with jet erosion tests

Aeroacoustic source analysis in a corrugated flow pipe

International audienceThis study is focused on a phenomenon often encountered in flow carrying pipes, since flow instabilities caused by geometric features may generate acoustic signals and thereafter interact with these signals in such a way that powerful pure tones are produced. A modern example is found in the so-called " singing risers " , or the gas pipes connecting gas production platforms to the transport network. But the flow generated resonance in a fully corrugated circular pipe may be silenced by the addition of relatively low frequency flow oscillations induced by an acoustic generator. Experiments reported here, aimed at investigating in more detail the coupling between the flow in the pipe, the acoustically generated flow oscillations and the emitted resulting noise, are performed in a specifically designed facilit

Double scaling and intermittency in shear dominated flows

The Refined Kolmogorov Similarity Hypothesis is a valuable tool for the description of intermittency in isotropic conditions. For flows in presence of a substantial mean shear, the nature of intermittency changes since the process of energy transfer is affected by the turbulent kinetic energy production associated with the Reynolds stresses. In these conditions a new form of refined similarity law has been found able to describe the increased level of intermittency which characterizes shear dominated flows. Ideally a length scale associated with the mean shear separates the two ranges, i.e. the classical Kolmogorov-like inertial range, below, and the shear dominated range, above. However, the data analyzed in previous papers correspond to conditions where the two scaling regimes can only be observed individually. In the present letter we give evidence of the coexistence of the two regimes and support the conjecture that the statistical properties of the dissipation field are practically insensible to the mean shear. This allows for a theoretical prediction of the scaling exponents of structure functions in the shear dominated range based on the known intermittency corrections for isotropic flows. The prediction is found to closely match the available numerical and experimental data.Comment: 7 pages, 3 figures, submitted to PR

Multifractality of the Feigenbaum attractor and fractional derivatives

It is shown that fractional derivatives of the (integrated) invariant measure of the Feigenbaum map at the onset of chaos have power-law tails in their cumulative distributions, whose exponents can be related to the spectrum of singularities $f(\alpha)$. This is a new way of characterizing multifractality in dynamical systems, so far applied only to multifractal random functions (Frisch and Matsumoto (J. Stat. Phys. 108:1181, 2002)). The relation between the thermodynamic approach (Vul, Sinai and Khanin (Russian Math. Surveys 39:1, 1984)) and that based on singularities of the invariant measures is also examined. The theory for fractional derivatives is developed from a heuristic point view and tested by very accurate simulations.Comment: 20 pages, 5 figures, J.Stat.Phys. in pres

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

Experimental assessment of a new form of scaling law for near-wall turbulence

Scaling laws and intermittency in the wall region of a turbulent flow are addressed by analyzing moderate Reynolds number data obtained by single component hot wire anemometry in the boundary layer of a flat plate. The paper aims in particular at the experimental validation of a new form of refined similarity recently proposed for the shear dominated range of turbulence, where the classical Kolmogorov-Oboukhov inertial range theory is inappropriate. An approach inspired to the extended self-similarity allows for the extraction of the different power laws for the longitudinal structure functions at several wall normal distances. A double scaling regime is found in the logarithmic region, confirming previous experimental results. Approaching the wall, the scaling range corresponding to the classical cascade-dominated range tends to disappear and, in the buffer layer, a single power law is found to describe the available range of scales. The double scaling is shown to be associated with two different forms of refined similarity. The classical form holds below the shear scale L s . The other, originally introduced on the basis of DNS data for a turbulent channel, is experimentally confirmed to set up above L s . Given the experimental diffulties in the evaluation of the instantaneous dissipation rate, some care is devoted to check that its one-dimensional surrogate does not bias the results. The increased intermittency as the wall is approached is experimentally found entirely consistent with the failure of the refined Kolmogorov-Oboukhov similarity and the establishment of its new form near the wall.Comment: 27 pages, 9 figure

Measurement of Lagrangian velocity in fully developed turbulence

We have developed a new experimental technique to measure the Lagrangian velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler tracking. This method yields a direct access to the velocity of a single particule at a turbulent Reynolds number $R_{\lambda} = 740$. Its dynamics is analyzed with two decades of time resolution, below the Lagrangian correlation time. We observe that the Lagrangian velocity spectrum has a Lorentzian form $E^{L}(\omega) = u_{rms}^{2} T_{L} / (1 + (T_{L}\omega)^{2})$, in agreement with a Kolmogorov-like scaling in the inertial range. The probability density function (PDF) of the velocity time increments displays a change of shape from quasi-Gaussian a integral time scale to stretched exponential tails at the smallest time increments. This intermittency, when measured from relative scaling exponents of structure functions, is more pronounced than in the Eulerian framework.Comment: 4 pages, 5 figures. to appear in PR

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