The Scaling Structure of the Velocity Statistics in Atmospheric Boundary Layer

The statistical objects characterizing turbulence in real turbulent flows differ from those of the ideal homogeneous isotropic model.They containcontributions from various 2d and 3d aspects, and from the superposition ofinhomogeneous and anisotropic contributions. We employ the recently introduceddecomposition of statistical tensor objects into irreducible representations of theSO(3) symmetry group (characterized by $j$ and $m$ indices), to disentangle someof these contributions, separating the universal and the asymptotic from the specific aspects of the flow. The different $j$ contributions transform differently under rotations and so form a complete basis in which to represent the tensor objects under study. The experimental data arerecorded with hot-wire probes placed at various heights in the atmospheric surfacelayer. Time series data from single probes and from pairs of probes are analyzed to compute the amplitudes and exponents of different contributions to the second order statistical objects characterized by $j=0$, $j=1$ and $j=2$. The analysis shows the need to make a careful distinction between long-lived quasi 2d turbulent motions (close to the ground) and relatively short-lived 3d motions. We demonstrate that the leading scaling exponents in the three leading sectors ($j = 0, 1, 2$) appear to be different butuniversal, independent of the positions of the probe, and the large scaleproperties. The measured values of the exponent are $\zeta^{(j=0)}_2=0.68 \pm 0.01$, $\zeta^{(j=1)}_2=1.0\pm 0.15$ and $\zeta^{(j=2)}_2=1.38 \pm 0.10$. We present theoretical arguments for the values of these exponents usingthe Clebsch representation of the Euler equations; neglecting anomalous corrections, the values obtained are 2/3, 1 and 4/3 respectively.Comment: PRE, submitted. RevTex, 38 pages, 8 figures included . Online (HTML) version of this paper is avaliable at http://lvov.weizmann.ac.il

Correlation functions in isotropic and anisotropic turbulence: the role of the symmetry group

The theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state. Real turbulent flows exhibit the effects of anisotropic forcing. The analysis of correlation functions and structure functions in isotropic and anisotropic situations is facilitated and made rational when performed in terms of the irreducible representations of the relevant symmetry group which is the group of all rotations SO(3). In this paper we firstly consider the needed general theory and explain why we expect different (universal) scaling exponents in the different sectors of the symmetry group. We exemplify the theory context of isotropic turbulence (for third order tensorial structure functions) and in weakly anisotropic turbulence (for the second order structure function). The utility of the resulting expressions for the analysis of experimental data is demonstrated in the context of high Reynolds number measurements of turbulence in the atmosphere.Comment: 35 pages, REVTEX, 1 figure, Phys. Rev. E, submitte

Identification and Calculation of the Universal Maximum Drag Reduction Asymptote by Polymers in Wall Bounded Turbulence

Drag reduction by polymers in wall turbulence is bounded from above by a universal maximal drag reduction (MDR) velocity profile that is a log-law, estimated experimentally by Virk as $V^+(y^+)\approx 11.7 \log y^+ -17$. Here $V^+(y)$ and $y^+$ are the mean streamwise velocity and the distance from the wall in "wall" units. In this Letter we propose that this MDR profile is an edge solution of the Navier-Stokes equations (with an effective viscosity profile) beyond which no turbulent solutions exist. This insight rationalizes the universality of the MDR and provides a maximum principle which allows an ab-initio calculation of the parameters in this law without any viscoelastic experimental input.Comment: 4 pages, 1 fig. Phys. Rev. Letts., submitte

Energy Spectra of Quantum Turbulence: Large-scale Simulation and Modeling

In $2048^3$ simulation of quantum turbulence within the Gross-Pitaevskii equation we demonstrate that the large scale motions have a classical Kolmogorov-1941 energy spectrum E(k) ~ k^{-5/3}, followed by an energy accumulation with E(k) ~ const at k about the reciprocal mean intervortex distance. This behavior was predicted by the L'vov-Nazarenko-Rudenko bottleneck model of gradual eddy-wave crossover [J. Low Temp. Phys. 153, 140-161 (2008)], further developed in the paper.Comment: (re)submitted to PRB: 5.5 pages, 4 figure

Colloquium: Theory of Drag Reduction by Polymers in Wall Bounded Turbulence

The flow of fluids in channels, pipes or ducts, as in any other wall-bounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases many-folds when the fluid flow turns from laminar to turbulent. A major technological problem is how to reduce this drag in order to minimize the expense of transporting fluids like oil in pipelines, or to move ships in the ocean. It was discovered in the mid-twentieth century that minute concentrations of polymers can reduce the drag in turbulent flows by up to 80%. While experimental knowledge had accumulated over the years, the fundamental theory of drag reduction by polymers remained elusive for a long time, with arguments raging whether this is a "skin" or a "bulk" effect. In this colloquium review we first summarize the phenomenology of drag reduction by polymers, stressing both its universal and non-universal aspects, and then proceed to review a recent theory that provides a quantitative explanation of all the known phenomenology. We treat both flexible and rod-like polymers, explaining the existence of universal properties like the Maximum Drag Reduction (MDR) asymptote, as well as non-universal cross-over phenomena that depend on the Reynolds number, on the nature of the polymer and on its concentration. Finally we also discuss other agents for drag reduction with a stress on the important example of bubbles.Comment: Invited Colloquium Paper for Reviews of Modern Physics, 24 pages, 18 Figs., submitte

Multi-Zone Shell Model for Turbulent Wall Bounded Flows

We suggested a \emph{Multi-Zone Shell} (MZS) model for wall-bounded flows accounting for the space inhomogeneity in a "piecewise approximation", in which cross-section area of the flow, $S$, is subdivided into "$j$-zones". The area of the first zone, responsible for the core of the flow, $S_1\simeq S/2$, and areas of the next $j$-zones, $S_j$, decrease towards the wall like $S_j\propto 2^{-j}$. In each $j$-zone the statistics of turbulence is assumed to be space homogeneous and is described by the set of "shell velocities" $u_{nj}(t)$ for turbulent fluctuations of the scale $\propto 2^{-n}$. The MZS-model includes a new set of complex variables, $V_j(t)$, $j=1,2,... \infty$, describing the amplitudes of the near wall coherent structures of the scale $s_j\sim 2^{-j}$ and responsible for the mean velocity profile. Suggested MZS-equations of motion for $u_{nj}(t)$ and $V_j(t)$ preserve the actual conservations laws (energy, mechanical and angular momenta), respect the existing symmetries (including Galilean and scale invariance) and account for the type of the non-linearity in the Navier-Stokes equation, dimensional reasoning, etc. The MZS-model qualitatively describes important characteristics of the wall bounded turbulence, e.g., evolution of the mean velocity profile with increasing Reynolds number, \RE, from the laminar profile towards the universal logarithmic profile near the flat-plane boundary layer as \RE\to \infty.Comment: 27 pages, 17 figs, included, PRE, submitte

Stochastic theory of spin-transfer oscillator linewidths

We present a stochastic theory of linewidths for magnetization oscillations in spin-valve structures driven by spin-polarized currents. Starting from a nonlinear oscillator model derived from spin-wave theory, we derive Langevin equations for amplitude and phase fluctuations due to the presence of thermal noise. We find that the spectral linewidths are inversely proportional to the spin-wave intensities with a lower bound that is determined purely by modulations in the oscillation frequencies. Reasonable quantitative agreement with recent experimental results from spin-valve nanopillars is demonstrated.Comment: Submitted to Physical Review

Velocity and Energy Profiles In Two- vs. Three-Dimensional Channels: Effects of Inverse vs. Direct Energy Cascade

In light of some recent experiments on quasi two-dimensional (2D) turbulent channel flow we provide here a model of the ideal case, for the sake of comparison. The ideal 2D channel flow differs from its 3D counterpart by having a second quadratic conserved variable in addition to the energy, and the latter has an inverse rather than a direct cascade. The resulting qualitative differences in profiles of velocity, V, and energy, K, as a function of the distance from the wall are highlighted and explained. The most glaring difference is that the 2D channel is much more energetic, with K in wall units increasing logarithmically with the Reynolds number \Ret instead of being \Ret-independent in 3D channels.Comment: Theoretical; 4 pages, 3 figures (8 plots); Submitted to Physical Review Letters on 16 February 200

Interaction of ballistic quasiparticles and vortex configurations in superfluid He3-B

The vortex line density of turbulent superfluid He3-B at very low temperature is deduced by detecting the shadow of ballistic quasiparticles which are Andreev reflected by quantized vortices. Until now the measured total shadow has been interpreted as the sum of shadows arising from interactions of a single quasiparticle with a single vortex. By integrating numerically the quasi-classical Hamiltonian equations of motion of ballistic quasiparticles in the presence of nontrivial but relatively simple vortex systems (such as vortex-vortex and vortex-antivortex pairs and small clusters of vortices) we show that partial screening can take place, and the total shadow is not necessarily the sum of the shadows. We have also found that it is possible that, upon impinging on complex vortex configurations, quasiparticles experience multiple reflections, which can be classical, Andreev, or both.Comment: To appear in Phys Rev

One-loop calculations of hyperon polarizabilities under the large N_c consistency condition

The spin-averaged electromagnetic polarizabilities of the hyperons $\Lambda$ and $\Sigma$ are calculated within the one-loop approximation by use of the dispersion theory. The photon and meson couplings to hyperons are determined so as to satisfy the large N_c consistency condition. It is shown that in order for the large N_c consistency condition to hold exotic hyperon states such as $\Sigma^{**}$ with I=2 and J=3/2 are required in the calculation of the magnetic polarizability of the $\Sigma$ state.Comment: 17 pages, REVTeX, no figure