Scaling and universality in turbulent convection

Anomalous correlation functions of the temperature field in two-dimensional turbulent convection are shown to be universal with respect to the choice of external sources. Moreover, they are equal to the anomalous correlations of the concentration field of a passive tracer advected by the convective flow itself. The statistics of velocity differences is found to be universal, self-similar and close to Gaussian. These results point to the conclusion that temperature intermittency in two-dimensional turbulent convection may be traced back to the existence of statistically preserved structures, as it is in passive scalar turbulence.Comment: 4 pages, 6 figure

Clustering and collisions of heavy particles in random smooth flows

Finite-size impurities suspended in incompressible flows distribute inhomogeneously, leading to a drastic enhancement of collisions. A description of the dynamics in the full position-velocity phase space is essential to understand the underlying mechanisms, especially for polydisperse suspensions. These issues are here studied for particles much heavier than the fluid by means of a Lagrangian approach. It is shown that inertia enhances collision rates through two effects: correlation among particle positions induced by the carrier flow and uncorrelation between velocities due to their finite size. A phenomenological model yields an estimate of collision rates for particle pairs with different sizes. This approach is supported by numerical simulations in random flows.Comment: 12 pages, 9 Figures (revTeX 4) final published versio

Active and Passive Fields in Turbulent Transport: the Role of Statistically Preserved Structures

We have recently proposed that the statistics of active fields (which affect the velocity field itself) in well-developed turbulence are also dominated by the Statistically Preserved Structures of auxiliary passive fields which are advected by the same velocity field. The Statistically Preserved Structures are eigenmodes of eigenvalue 1 of an appropriate propagator of the decaying (unforced) passive field, or equivalently, the zero modes of a related operator. In this paper we investigate further this surprising finding via two examples, one akin to turbulent convection in which the temperature is the active scalar, and the other akin to magneto-hydrodynamics in which the magnetic field is the active vector. In the first example, all the even correlation functions of the active and passive fields exhibit identical scaling behavior. The second example appears at first sight to be a counter-example: the statistical objects of the active and passive fields have entirely different scaling exponents. We demonstrate nevertheless that the Statistically Preserved Structures of the passive vector dominate again the statistics of the active field, except that due to a dynamical conservation law the amplitude of the leading zero mode cancels exactly. The active vector is then dominated by the sub-leading zero mode of the passive vector. Our work thus suggests that the statistical properties of active fields in turbulence can be understood with the same generality as those of passive fields.Comment: 13 pages, 13 figures, submitted to Phys. Rev.

Two-dimensional elastic turbulence

We investigate the effect of polymer additives on a two-dimensional Kolmogorov flow at very low Reynolds numbers by direct numerical simulations of the Oldroyd-B viscoelastic model. We find that above the elastic instability threshold the flow develops the elastic turbulence regime recently observed in experiments. We observe that both the turbulent drag and the Lyapunov exponent increase with Weissenberg, indicating the presence of a disordered, turbulent-like mixing flow. The energy spectrum develops a power-law scaling range with an exponent close to the experimental and theoretical expectations

Acceleration statistics of heavy particles in turbulence

We present the results of direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, up to resolution $512^3$ ($R_\lambda\approx 185$). Following the trajectories of up to 120 million particles with Stokes numbers, $St$, in the range from 0.16 to 3.5 we are able to characterize in full detail the statistics of particle acceleration. We show that: ({\it i}) The root-mean-squared acceleration $a_{\rm rms}$ sharply falls off from the fluid tracer value already at quite small Stokes numbers; ({\it ii}) At a given $St$ the normalised acceleration $a_{\rm rms}/(\epsilon^3/\nu)^{1/4}$ increases with $R_\lambda$ consistently with the trend observed for fluid tracers; ({\it iii}) The tails of the probability density function of the normalised acceleration $a/a_{\rm rms}$ decrease with $St$. Two concurrent mechanisms lead to the above results: preferential concentration of particles, very effective at small $St$, and filtering induced by the particle response time, that takes over at larger $St$.Comment: 10 pages, 3 figs, 2 tables. A section with new results has been added. Revised version accepted for pubblication on Journal of Fluid Mechanic

Small scale statistics of viscoelastic turbulence

The small scale statistics of homogeneous isotropic turbulence of dilute polymer solutions is investigated by means of direct numerical simulations of a simplified viscoelastic fluid model. It is found that polymers only partially suppress the turbulent cascade below the Lumley scale, leaving a remnant energy flux even for large elasticity. As a consequence, fluid acceleration in viscoelastic flows is reduced with respect to Newtonian turbulence, whereas its rescaled probability density is left unchanged. At large scales the velocity field is found to be unaffected by the presence of polymers.Comment: 7 pages, 4 figure

Reliability of Early Fetal Echocardiography for Congenital Heart Disease Detection: A Preliminary Experience and Outcome Analysis of 102 Fetuses to Demonstrate the Value of a Clinical Flow-Chart Designed for At-Risk Pregnancy Management

Early fetal echocardiography (EFEC) is a fetal cardiac ultrasound analysis performed between the 12th and 16th week of pregnancy (compared with the usual 18-22 weeks). In the last 10 years, the introduction of “aneuploidy sonographic markers” in screening for cardiac defects has led to a shift from late second to end of the first trimester or beginning of the second trimester of pregnancy for specialist fetal echocardiography. In this prospective study, early obstetric screening was performed between January 2014 and October 2015, using “aneuploidy sonographic markers” following SIEOG Guidelines 2014. These parameters were then collected and strategically combined in an evaluation score to select the group of pregnancies for performing EFEC, in accordance with the American Society of Echocardiography guidelines for fetal Echocardiography. All second-level examinations were performed transabdominally using a 3D convex volumetric probe with frequency range of 4-8 MHz (Accuvix – Samsung). The outcome data included transabdominal fetal echocardiography from 18 weeks to term and after birth. Overall, 99 pregnant women in the first trimester underwent EFEC (95 singleton and 4 twin pregnancies). Specifically, 30 fetuses were evaluated for extra-cardiac anomalies evidenced by obstetric screening (30%), 25 for family history of congenital heart diseases (25%), 8 for family history of genetic-linked diseases (8%), 4 for heart diseases suspected by obstetric screening (4%) and 19 by normal screening (19%). Was detected 11 (10.7%) CHD, when EFEC detected CHD, were compared to those performed later in pregnancy (18 weeks GA-term), a high degree of diagnosis correspondence was evidenced. The higher sensitivity value of EFEC vs late-FE, in comparison with the post-natal value, coupled with the high EFEC specificity shown vs both the end points, enabled us to consider it as a really reliable diagnostic technology, at least in perienced hands. The introduction of a key combination of the more sensitive obstetric and cardiologic variables should facilitate the formulation of a possible flow-chart as a guide for CHD at-risk pregnancies

Kolmogorov's law for two-dimensional electron-magnetohydrodynamic turbulence

The analogue of the Kolmogorov's four-fifths law is derived for two-dimensional, homogeneous, isotropic EMHD turbulence in the energy cascade inertial range. Direct numerical simulations for the freely decaying case show that this relation holds true for different values of the adimensional electron inertial length scale, $d_e$. The energy spectrum is found to be close to the expected Kolmogorov spectrum.Comment: 9 pages RevTeX, 3 PostScript figure