Energy Spectra of Superfluid Turbulence in 3^3He

In superfluid $^3$He turbulence is carried predominantly by the superfluid component. To explore the statistical properties of this quantum turbulence and its differences from the classical counterpart we adopt the time-honored approach of shell models. Using this approach we provide numerical simulations of a Sabra-shell model that allows us to uncover the nature of the energy spectrum in the relevant hydrodynamic regimes. These results are in qualitative agreement with analytical expressions for the superfluid turbulent energy spectra that were found using a differential approximation for the energy flux

Universal Model of Finite-Reynolds Number Turbulent Flow in Channels and Pipes

In this Letter we suggest a simple and physically transparent analytical model of the pressure driven turbulent wall-bounded flows at high but finite Reynolds numbers Re. The model gives accurate qualitative description of the profiles of the mean-velocity and Reynolds-stresses (second order correlations of velocity fluctuations) throughout the entire channel or pipe in the wide range of Re, using only three Re-independent parameters. The model sheds light on the long-standing controversy between supporters of the century-old log-law theory of von-K\`arm\`an and Prandtl and proposers of a newer theory promoting power laws to describe the intermediate region of the mean velocity profile.Comment: 4 pages, 6 figs, re-submitted PRL according to referees comment

Phenomenology of Wall Bounded Newtonian Turbulence

We construct a simple analytic model for wall-bounded turbulence, containing only four adjustable parameters. Two of these parameters characterize the viscous dissipation of the components of the Reynolds stress-tensor and other two parameters characterize their nonlinear relaxation. The model offers an analytic description of the profiles of the mean velocity and the correlation functions of velocity fluctuations in the entire boundary region, from the viscous sub-layer, through the buffer layer and further into the log-layer. As a first approximation, we employ the traditional return-to-isotropy hypothesis, which yields a very simple distribution of the turbulent kinetic energy between the velocity components in the log-layer: the streamwise component contains a half of the total energy whereas the wall-normal and the cross-stream components contain a quarter each. In addition, the model predicts a very simple relation between the von-K\'arm\'an slope $\kappa$ and the turbulent velocity in the log-law region $v^+$ (in wall units): $v^+=6 \kappa$. These predictions are in excellent agreement with DNS data and with recent laboratory experiments.Comment: 15 pages, 11 figs, included, PRE, submitte

Statistical Description of Acoustic Turbulence

We develop expressions for the nonlinear wave damping and frequency correction of a field of random, spatially homogeneous, acoustic waves. The implications for the nature of the equilibrium spectral energy distribution are discussedComment: PRE, Submitted. REVTeX, 16 pages, 3 figures (not included) PS Source of the paper with figures avalable at http://lvov.weizmann.ac.il/onlinelist.htm

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

Analytical Model of the Time Developing Turbulent Boundary Layer

We present an analytical model for the time-developing turbulent boundary layer (TD-TBL) over a flat plate. The model provides explicit formulae for the temporal behavior of the wall-shear stress and both the temporal and spatial distributions of the mean streamwise velocity, the turbulence kinetic energy and Reynolds shear stress. The resulting profiles are in good agreement with the DNS results of spatially-developing turbulent boundary layers at momentum thickness Reynolds number equal to 1430 and 2900. Our analytical model is, to the best of our knowledge, the first of its kind for TD-TBL.Comment: 5pages, 9 figs, JETP Letters, submitte

Super Stability of Laminar Vortex Flow in Superfluid 3He-B

Vortex flow remains laminar up to large Reynolds numbers (Re~1000) in a cylinder filled with 3He-B. This is inferred from NMR measurements and numerical vortex filament calculations where we study the spin up and spin down responses of the superfluid component, after a sudden change in rotation velocity. In normal fluids and in superfluid 4He these responses are turbulent. In 3He-B the vortex core radius is much larger which reduces both surface pinning and vortex reconnections, the phenomena, which enhance vortex bending and the creation of turbulent tangles. Thus the origin for the greater stability of vortex flow in 3He-B is a quantum phenomenon. Only large flow perturbations are found to make the responses turbulent, such as the walls of a cubic container or the presence of invasive measuring probes inside the container.Comment: 4 pages, 6 figure

Variable damping and coherence in a high-density magnon gas

We report on the fast relaxation behavior of a high-density magnon gas created by a parametric amplification process. The magnon gas is probed using the technique of spin-wave packet recovery by parallel parametric pumping. Experimental results show a damping behavior which is in disagreement with both the standard model of exponential decay and with earlier observations of non-linear damping. In particular, the inherent magnon damping is found to depend upon the presence of the parametric pumping field. A phenomenological model which accounts for the dephasing of the earlier injected magnons is in good agreement with the experimental data

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

Outliers, Extreme Events and Multiscaling

Extreme events have an important role which is sometime catastrophic in a variety of natural phenomena including climate, earthquakes and turbulence, as well as in man-made environments like financial markets. Statistical analysis and predictions in such systems are complicated by the fact that on the one hand extreme events may appear as "outliers" whose statistical properties do not seem to conform with the bulk of the data, and on the other hands they dominate the (fat) tails of probability distributions and the scaling of high moments, leading to "abnormal" or "multi"-scaling. We employ a shell model of turbulence to show that it is very useful to examine in detail the dynamics of onset and demise of extreme events. Doing so may reveal dynamical scaling properties of the extreme events that are characteristic to them, and not shared by the bulk of the fluctuations. As the extreme events dominate the tails of the distribution functions, knowledge of their dynamical scaling properties can be turned into a prediction of the functional form of the tails. We show that from the analysis of relatively short time horizons (in which the extreme events appear as outliers) we can predict the tails of the probability distribution functions, in agreement with data collected in very much longer time horizons. The conclusion is that events that may appear unpredictable on relatively short time horizons are actually a consistent part of a multiscaling statistics on longer time horizons.Comment: 11 pages, 14 figures included, PRE submitte