Generalized scaling in fully developed turbulence

Physical Review E, 2001

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.

Physics of Fluids, 2006

We present an extension of the Kármán-Howarth theorem to the Lagrangian averaged magnetohydrodynamic (LAMHD−α) equations. The scaling laws resulting as a corollary of this theorem are studied in numerical simulations, as well as the scaling of the longitudinal structure function exponents indicative of intermittency. Numerical simulations for a magnetic Prandtl number equal to unity are presented both for freely decaying and for forced two dimensional MHD turbulence, solving directly the MHD equations, and employing the LAMHD−α equations at 1/2 and 1/4 resolution. Linear scaling of the third-order structure function with length is observed. The LAMHD−α equations also capture the anomalous scaling of the longitudinal structure function exponents up to order 8.

Fluid Dynamics Research, 1999

We brie y present some results about scaling laws in a turbulent channel ow. We analyse the scaling exponents of channel ow turbulence by using data from direct numerical simulations.

Physics of Fluids, 2002

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 difficulties 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.

Physical Review E, 2004

It is shown that the heart rate variability (HRV) in healthy and diseased humans possesses a hierarchical structure of the She-Leveque (SL) form. This structure, first found in measurements in turbulent fluid flows, implies further details in the HRV multifractal scaling. The potential of diagnosis is also discussed based on the characteristics derived from the SL hierarchy.

Physical Review E, 2002

It is shown that the two remarkable properties of turbulence, the Extended Self-Similarity (ESS) [R.

Physical Review E, 2003

We analyze velocity fluctuations in turbulent Rayleigh-Bénard convection. The velocity measurements were taken at the center of an aspect-ratio-one convection cell filled with water. The measured probability density functions of the velocity difference over a time interval are found to change with , indicating that the velocity fluctuations are intermittent. The velocity intermittency can be well characterized by the She-Leveque hierarchical structure. Our analyses further show that the vertical velocity component has distinct statistical features from the horizontal components. This result indicates that the vertical direction is special and buoyancy is important even at the center of the convection cell.

Journal of Statistical Physics, 2015

We present a detailed review of some of the most recent developments on Eulerian and Lagrangian turbulence in homogeneous and isotropic statistics. In particular, we review phenomenological and numerical results concerning the issue of universality with respect to the large scale forcing and the viscous dissipative physics. We discuss the state-of-the-art of numerical versus experimental comparisons and we discuss the dicotomy between phenomenology based on coherent structures or on statistical approaches. A detailed discussion of finite Reynolds effects is also presented.

Physics of Fluids

In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with She and Leveque's predictions [Phys. Rev. Lett. 72, 336-339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate. This is unlike in hydrodynamic turbulence where the energy flux and the dissipation rate are equal.

Journal of Statistical Physics, 2009

We review the Parisi-Frisch [1] MultiFractal formalism for Navier-Stokes turbulence with particular emphasis on the issue of statistical fluctuations of the dissipative scale. We do it for both Eulerian and Lagrangian Turbulence. We also show new results concerning the application of the formalism to the case of Shell Models for turbulence. The latter case will allow us to discuss the issue of Reynolds number dependence and the role played by vorticity and vortex filaments in real turbulent flows.

Physical Review Letters, 2008

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Water Resources Research, 1999

The coupling of hydrological distributed models to numerical weather prediction outputs is an important issue for hydrological applications such as forecasting of flood events. Downscaling meteorological predictions to the hydrological scales requires the resolution of two fundamental issues regarding precipitation, namely, (1) understanding the statistical properties and scaling laws of rainfall fields and (2) validation of downscaling models that are able to preserve statistical characteristics observed in real precipitation. In this paper we discuss the first issue by introducing a new multifractal model that appears particularly suitable for random generation of synthetic rainfall. We argue that the results presented in this paper may be also useful for the solution of the second question. Statistical behavior of rainfall in time is investigated through a highresolution time series recorded in Genova (Italy). The multifractal analysis shows the presence of a temporal threshold, localized around 15-20 hours, which separates two ranges of anomalous scaling laws. Synthetic time series, characterized by very similar scaling laws to the observed one, are generated with the multifractal model. The potential of the model for extreme rainfall event distributions is also discussed. The multifractal analysis of Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment (GATE) radar fields have shown that statistical properties of rainfall in space depend on time durations over which precipitation is accumulated. Further analysis of some rainfall fields produced with a meteorological limited area model exhibited the same anomalous scaling as the GATE fields.

Physical Review E, 1997

We investigate the scaling properties of the velocity circulation of a turbulent shear flow. We evaluate, using extended self-similarity, the circulation scaling exponents both at maximum and minimum shear regions. We show that the anomalous component of the velocity circulation and the anomalous component of the velocity structure functions are equal. ͓S1063-651X͑97͒11202-8͔

Physical Review E, 1998

It is often taken for granted that the analysis of multifractals with fixed-size algorithms leads to faithful results although this is not the case in practice. We present a novel and self-consistent way to obtain from a partition sum S q (l) the spectrum of singularities f (α) and its confidence intervals. With this tool we gain new insights into the intricacies of fixed-size algorithms and propose consequent improvements. We give a numerical analysis of the Hénon attractor which displays theoretical predictions of a phase transitionlike plateau.

Physical Review E, 2000

The statistical properties of the streamwise velocity fluctuations in a fully developed turbulent channel flow are studied experimentally by means of single hot wire measurements. The intermittency features, studied through the scaling of the moments of the velocity structure function computed using the extended selfsimilarity and through the probability density function of the wavelet coefficients, are found to be dependent on the distance from the wall. The maximum intermittency effects are observed in the region between the buffer layer and the inner part of the logarithmic region where it is known that the bursting phenomenon, related to coherent structures such as low speed streaks and streamwise vortices, is the dominant dynamical feature. An eduction technique based on wavelet transform for identification of organized motion is developed and used to analyze the turbulent signals. Streamwise velocity conditional averages computed on events educed with the proposed method are reported. Events responsible for intermittency are found to consist of regions of high velocity gradients and are directly correlated with the observed increase of intermittency close to the wall.

Physical review. E, 2018

Using direct numerical simulations, we study the statistical properties of reversals in two-dimensional Rayleigh-Bénard convection for infinite Prandtl number. We find that the large-scale circulation reverses irregularly, with the waiting time between two consecutive genuine reversals exhibiting a Poisson distribution on long timescales, while the interval between successive crossings on short timescales shows a power-law distribution. We observe that the vertical velocities near the sidewall and at the center show different statistical properties. The velocity near the sidewall shows a longer autocorrelation and 1/f^{2} power spectrum for a wide range of frequencies, compared to shorter autocorrelation and a narrower scaling range for the velocity at the center. The probability distribution of the velocity near the sidewall is bimodal, indicating a reversing velocity field. We also find that the dominant Fourier modes capture the dynamics at the sidewall and at the center very wel...

Physics of Fluids, 2010

We present results of a high resolution numerical study of two dimensional (2d) Rayleigh-Taylor turbulence using a recently proposed thermal lattice Boltzmann method (LBT). The goal of our study is both methodological and physical. We assess merits and limitations concerning small-and large-scale resolution/accuracy of the adopted integration scheme. We discuss quantitatively the requirements needed to keep the method stable and precise enough to simulate stratified and unstratified flows driven by thermal active fluctuations at high Rayleigh and high Reynolds numbers. We present data with spatial resolution up to 4096 × 10000 grid points and Rayleigh number up to Ra ∼ 10 11. The statistical quality of the data allows us to investigate velocity and temperature fluctuations, scale-by-scale, over roughly four decades. We present a detailed quantitative analysis of scaling laws in the viscous, inertial and integral range, supporting the existence of a Bolgiano-like inertial scaling, as expected in 2d systems. We also discuss the presence of small/large intermittent deviation to the scaling of velocity/temperature fluctuations and the Rayleigh dependency of gradients flatness.

Physics of Fluids, 2006

Physics of Fluids, 2001

A unified framework for velocity structure functions, sign-singular cancellation measures, multifractal measures of the energy dissipation and absolute values of the velocity derivative ͑''vorticity''͒, and the two-scale velocity structure functions is suggested. The scaling behavior of these measures within the inertial subrange is considered and tested using one-dimensional ͑1-D͒ velocity measurements from a high Re jet flow. In these tests we used the phase-randomization procedure that appears to be an effective tool in identifying the effects of turbulence intermittency and spectral energy flux. A number of relationships between turbulence scaling exponents are derived and tested.

Physical Review E, 1999

The exit-time statistics of experimental turbulent data is analyzed. By looking at the exit-time moments ͑inverse structure functions͒ it is possible to have a direct measurement of scaling properties of the laminar statistics. It turns out that the inverse structure functions show a much more extended intermediate dissipative range than the structure functions, leading to the first clear evidence of the existence of such a range of scales.

Physical Review E, 2002

We measure temperature fluctuations in the Rayleigh-Bénard apparatus, which is a closed cylindrical container with the bottom wall heated and the top wall cooled. The aspect ratio, which is the diameter-to-height ratio of the apparatus, is unity. The Rayleigh number is 1.5ϫ10 11. The working fluid is cryogenic helium gas. We compute temperature structure functions up to order 16, and use extended self-similarity to obtain scaling exponents in the Bolgiano regime. In contrast to passive scalars, the scaling exponents tend not to saturate with the order of the structure function, suggesting the absence of ramplike structures in temperature traces of convective motion.

Journal of Statistical Physics, 2007

An analytic perturbation theory is suggested in order to find finite-size corrections to the scaling power laws. In the frame of this theory it is shown that the first order finite-size correction to the scaling power laws has following form S(r) ∼ = cr α 0 [ln(r/η)] α 1 , where η is a finite-size scale (in particular for turbulence, it can be the Kolmogorov dissipation scale). Using data of laboratory experiments and numerical simulations it is shown shown that a degenerate case with α0 = 0 can describe turbulence statistics in the near-dissipation range r > η, where the ordinary (power-law) scaling does not apply. For moderate Reynolds numbers the degenerate scaling range covers almost the entire range of scales of velocity structure functions (the log-corrections apply to finite Reynolds number). Interplay between local and non-local regimes has been considered as a possible hydrodynamic mechanism providing the basis for the degenerate scaling of structure functions and extended self-similarity. These results have been also expanded on passive scalar mixing in turbulence. Overlapping phenomenon between local and non-local regimes and a relation between position of maximum of the generalized energy input rate and the actual crossover scale between these regimes are briefly discussed.

Physical Review E, 2002

Properties of the mean wind in thermal convection, especially the abrupt reversal of its direction at high Rayleigh numbers, are studied. Measurements made in a closed cylindrical container of aspect ratio 1 are analyzed, and both the long-term and short-term behaviors of the direction reversals are discussed. A first look at the data suggests a Brownian-type process in action, but a closer look suggests the existence of hierarchical features with time scales extending roughly over a decade and a half. A physical model consistent with experimental observations is presented, and the origin of the cutoff scales is discussed. It appears that the generation of the wind as well as the reversal of its direction can be understood in terms of the imbalance between buoyancy effects and friction.

Andrologia

Portulaca oleracea contains a wide range of chemical constituents, including flavonoids, alkaloids, polysaccharides, fatty acids, terpenoids, sterols, proteins, vitamins, and minerals. These chemical constituents are linked to the plant’s diverse pharmacological properties, such as antimicrobial and antioxidant activities. Therefore, this study is aimed at evaluating the effect of adding two concentrations (50 or 100 μg/mL) of Portulaca oleracea leaf ethanolic extracts in a native form (POLE) or nanoformulation (POLENF) on the antioxidant status of sperm medium to improve goat sperm freezability. Semen was evaluated postequilibration (5°C for 2 h), postthawing, and 2 h postincubation (37°C and 5% CO2). Phytochemical analysis showed the presence of 30 compounds in POLE, including phenolic acids and flavonoids and their glucosides. Total flavonoids were higher in POLE than in POLENF. Both extracts showed strong free radical scavenging capacity by the 2,2-diphenyl-1-picryl-hydrazyl-hyd...

Physical Review E, 2002

An example of a combination of Kolmogorov three-dimensional properties with Alfve ´n two-dimensional properties in solar-wind plasma is given using recent data obtained with the Advanced Composition Explorer satellite at the L1 libration point. Both spectral and moments scaling analyses are used to demonstrate the possibility of such a combination. Two-decade scaling and the large number of the scaling exponents under consideration indicate the robustness of this observation.