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Sep 18, 2013
09/13

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Victor S. L'vov; Oleksii Rudenko

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The letter considers non-isothermal fluid flows and revises simplifications of basic hydrodynamic equations for such flows arriving eventually to a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of state including both non-ideal gases as well as liquids. The proposed approach is based on a suggested general definition of potential temperature. Special attention is put on the energy conservation principle, and it is shown that the proposed approximation...

Source: http://arxiv.org/abs/0803.2627v1

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Sep 18, 2013
09/13

by
Rama Govindarajan; Victor S. L'vov; Itamar Procaccia

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Motivated by the large effect of turbulent drag reduction by minute concentrations of polymers we study the effects of minor viscosity contrasts on the stability of hydrodynamic flows. The key player is a localized region where the energy of fluctuations is produced by interactions with the mean flow (the "critical layer"). We show that a layer of weakly space-dependent viscosity placed near the critical layer can have very large stabilizing effect on hydrodynamic fluctuations,...

Source: http://arxiv.org/abs/nlin/0105072v1

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Sep 17, 2013
09/13

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Victor S. L'vov; Itamar Procaccia; Vasil Tiberkevich

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In anisotropic turbulence the correlation functions are decomposed in the irreducible representations of the SO(3) symmetry group (with different "angular momenta" $\ell$). For different values of $\ell$ the second order correlation function is characterized by different scaling exponents $\zeta_2(\ell)$. In this paper we compute these scaling exponents in a Direct Interaction Approximation (DIA). By linearizing the DIA equations in small anisotropy we set up a linear operator and...

Source: http://arxiv.org/abs/nlin/0207011v2

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Sep 22, 2013
09/13

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Victor S. L'vov; Anna Pomyalov; Itamar Procaccia; Vasil Tiberkevich

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We address the mechanism of drag reduction by polymers in turbulent wall bounded flows. On the basis of the equations of fluid mechanics we present a quantitative derivation of the "maximum drag reduction (MDR) asymptote" which is the maximum drag reduction attained by polymers. Based on Newtonian information only we prove the existence of drag reduction, and with one experimental parameter we reach a quantitative agreement with the experimental measurements.

Source: http://arxiv.org/abs/nlin/0307034v2

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Sep 23, 2013
09/13

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Emily S. C. Ching; Victor S. L'vov; Evgeni Podivilov; Itamar Procaccia

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We consider turbulent advection of a scalar field $T(\B.r)$, passive or active, and focus on the statistics of gradient fields conditioned on scalar differences $\Delta T(R)$ across a scale $R$. In particular we focus on two conditional averages $\langle\nabla^2 T\big|\Delta T(R)\rangle$ and $\langle|\nabla T|^2\big|\Delta T(R) \rangle$. We find exact relations between these averages, and with the help of the fusion rules we propose a general representation for these objects in terms of the...

Source: http://arxiv.org/abs/chao-dyn/9608008v1

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Sep 17, 2013
09/13

by
Victor S. L'vov; Anna Pomyalov; Vasil Tiberkevich

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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...

Source: http://arxiv.org/abs/nlin/0305019v1

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Sep 18, 2013
09/13

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Victor S. L'vov; Itamar Procaccia; Oleksii Rudenko

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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...

Source: http://arxiv.org/abs/0705.4592v3

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Sep 18, 2013
09/13

by
David Daems; Siegfried Grossmann; Victor S. L'vov; Itamar Procaccia

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It was shown recently that the anomalous scaling of simultaneous correlation functions in turbulence is intimately related to the breaking of temporal scale invariance, which is equivalent to the appearance of infinitely many times scales in the time dependence of time-correlation functions. In this paper we derive a continued fraction representation of turbulent time correlation functions which is exact and in which the multiplicity of time scales is explicit. We demonstrate that this form...

Source: http://arxiv.org/abs/chao-dyn/9811024v1

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Sep 18, 2013
09/13

by
Victor S. L'vov; Itamar Procaccia; Oleksii Rudenko

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Turbulent boundary layers exhibit a universal structure which nevertheless is rather complex, being composed of a viscous sub-layer, a buffer zone, and a turbulent log-law region. In this letter we present a simple analytic model of turbulent boundary layers which culminates in explicit formulae for the profiles of the mean velocity, the kinetic energy and the Reynolds stress as a function of the distance from the wall. The resulting profiles are in close quantitative agreement with...

Source: http://arxiv.org/abs/nlin/0606035v2

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Sep 20, 2013
09/13

by
Itai Arad; Victor S. L'vov; Itamar Procaccia

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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...

Source: http://arxiv.org/abs/chao-dyn/9810025v1

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Jul 20, 2013
07/13

by
Susan Kurien; Victor S. L'vov; Itamar Procaccia; K. R. Sreenivasan

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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...

Source: http://arxiv.org/abs/chao-dyn/9906038v1

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Sep 18, 2013
09/13

by
Emily S. C. Ching; Victor S. L'vov; Itamar Procaccia

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Fusion rules in turbulence address the asymptotic properties of many-point correlation functions when some of the coordinates are very close to each other. Here we put to experimental test some non-trivial consequences of the fusion rules for scalar correlations in turbulence. To this aim we examine passive turbulent advection as well as convective turbulence. Adding one assumption to the fusion rules one obtains a prediction for universal conditional statistics of gradient fields. We examine...

Source: http://arxiv.org/abs/chao-dyn/9606017v1

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Sep 20, 2013
09/13

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Victor S. L'vov; Anna Pomyalov; Itamar Procaccia; Vasil Tiberkevich

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The interaction of polymers with turbulent shear flows is examined. We focus on the structure of the elastic stress tensor, which is proportional to the polymer conformation tensor. We examine this object in turbulent flows of increasing complexity. First is isotropic turbulence, then anisotropic (but homogenous) shear turbulence and finally wall bounded turbulence. The main result of this paper is that for all these flows the polymer stress tensor attains a universal structure in the limit of...

Source: http://arxiv.org/abs/nlin/0405022v1

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Jul 19, 2013
07/13

by
Vladimir V. Lebedev; Victor S. L'vov

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We considered symmetry restriction on the interaction coefficients of Kelvin waves and demonstrated that linear in small wave vector asymptotic is not forbidden, as one can expect by naive reasoning.

Source: http://arxiv.org/abs/1005.4575v1

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Sep 23, 2013
09/13

by
Victor S. L'vov; Itamar Procaccia

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In this paper we derive here, on the basis of the NS eqs. a set of fusion rules for correlations of velocity differences when all the separation are in the inertial interval. Using this we consider the standard hierarchy of equations relating the $n$-th order correlations (originating from the viscous term in the NS eq.) to $n+1$'th order (originating from the nonlinear term) and demonstrate that for fully unfused correlations the viscous term is negligible. Consequently the hierarchic chain is...

Source: http://arxiv.org/abs/chao-dyn/9607006v1

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Sep 23, 2013
09/13

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Victor I. Belinicher; Victor S. L'vov; Itamar Procaccia

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This manuscript is a draft of work in progress, meant for network distribution only. It will be updated to a formal preprint when the numerical calculations will be accomplished. In this draft we develop a consistent closure procedure for the calculation of the scaling exponents $\zeta_n$ of the $n$th order correlation functions in fully developed hydrodynamic turbulence, starting from first principles. The closure procedure is constructed to respect the fundamental rescaling symmetry of the...

Source: http://arxiv.org/abs/chao-dyn/9708004v1

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Sep 21, 2013
09/13

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Itai Arad Victor S. L'vov; Evgenii Podivilov; Itamar Procaccia

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Kraichnan's model of passive scalar advection is studied as a case model for understanding the anomalous scaling in the anisotropic sectors. We show here that the solutions of the Kraichnan equation for the $n$ order correlations foliate into sectors that are classified by the irreducible representations of the SO(d) group. We find a discrete spectrum of universal anomalous exponents in every sector. Generically the correlations and structure functions appear as sums over all the contributions,...

Source: http://arxiv.org/abs/chao-dyn/9907017v1

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Sep 23, 2013
09/13

by
Victor S. L'vov; Sergey V. Nazarenko; Grigory E. Volovik

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The spectrum of turbulence in superfluid liquid is modified by the nonlinear energy dissipation caused by the mutual friction between quantized vortices and the normal component of the liquid. In some region of two Reynolds parameters characterizing the flow of a superfluid, we found the new state of the fully developed turbulence. This state displays both the Kolmogorov-Obukhov 5/3-scaling law $E_k \propto k^{-5/3}$ and the new "3-scaling law" $E_k \propto k^{-3}$, each in a well...

Source: http://arxiv.org/abs/nlin/0408048v3

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Sep 22, 2013
09/13

by
Roberto Benzi; Emily S. C. Ching; T. S. Lo; Victor S. L'vov; Itamar Procaccia

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We address the "Additive Equivalence" discovered by Virk and coworkers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wall-bounded flows is limited from above by a very similar Maximum Drag Reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wall-bounded turbulent ensembles, we show that although the microscopic mechanism of attaining the MDR is very different, the macroscopic theory is isomorphic, rationalizing the...

Source: http://arxiv.org/abs/nlin/0501027v1

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Sep 23, 2013
09/13

by
Victor S. L'vov; Evgenii Podivilov; Itamar Procaccia

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On the basis of the Navier-Stokes equations we develop the statistical theory of many space-time correlation functions of velocity differences. Their time dependence is {\em not} scale invariant: $n$-order correlations functions exhibit $n-1$ distinct decorrelation times that are characterized by $n-1$ anomalous dynamical scaling exponents. We derive exact scaling relations that bridge all these dynamical exponents to the static anomalous exponents $\zeta_n$ of the standard structure functions.

Source: http://arxiv.org/abs/chao-dyn/9607011v1

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Sep 18, 2013
09/13

by
Victor S. L'vov; Evgenii Podivilov; Anna Pomyalov; Itamar Procaccia; Damien Vandembroucq

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We introduce a new shell model of turbulence which exhibits improved properties in comparison to the standard (and very popular) GOY model. The nonlinear coupling is chosen to minimize correlations between different shells. In particular the second order correlation function is diagonal in the shell index, the third order correlation exists only between three consecutive shells. Spurious oscillations in the scaling regime, which are an annoying feature of the GOY model, are eliminated by our...

Source: http://arxiv.org/abs/chao-dyn/9803025v2

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118

Jul 20, 2013
07/13

by
Victor S. L'vov; Anna Pomyalov; Itamar Procaccia; Vasil Tiberkevich

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Drag reduction by microbubbles is a promising engineering method for improving ship performance. A fundamental theory of the phenomenon is lacking however, making actual design quite uphazard. We offer here a theory of drag reduction by microbubbles in the limit of very small bubbles, when the effect of the bubbles is mainly to normalize the density and the viscosity of the carrier fluid. The theory culminates with a prediction of the degree of drag reduction given the concentration profile of...

Source: http://arxiv.org/abs/nlin/0406061v2

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54

Sep 19, 2013
09/13

by
Victor S. L'vov; Evgenii Podivilov; Itamar Procaccia

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We show that the Sabra shell model of turbulence, which was introduced recently, displays a Hamiltonian structure for given values of the parameters. As a consequence we compute exactly a one-parameter family of anomalous scaling exponents associated with 4th order correlation functions.

Source: http://arxiv.org/abs/chao-dyn/9804036v1

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Sep 22, 2013
09/13

by
Rama Govindarajan; Victor S. L'vov; Itamar Procaccia

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Motivated by the large effect of turbulent drag reduction by minute concentrations of polymers we study the effects of a weakly space-dependent viscosity on the stability of hydrodynamic flows. In a recent Letter [Phys. Rev. Lett. {\bf 87}, 174501, (2001)] we exposed the crucial role played by a localized region where the energy of fluctuations is produced by interactions with the mean flow (the "critical layer"). We showed that a layer of weakly space-dependent viscosity placed near...

Source: http://arxiv.org/abs/nlin/0205062v1

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55

Sep 18, 2013
09/13

by
Victor S. L'vov; Gijs Ooms; Anna Pomyalov

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We propose a one-fluid analytical model for a turbulently flowing dilute suspension, based on modified Navier-Stokes equation with a $k$-dependent effective density of suspension, $\rho_ {eff}(k)$, and an additional damping term $\propto \gamma_ p(k)$, representing the fluid-particle friction (described by Stokes law). The statistical description of turbulence within the model is simplified by a modification of the usual closure procedure based on the Richardson-Kolmogorov picture of turbulence...

Source: http://arxiv.org/abs/nlin/0210069v2

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Sep 17, 2013
09/13

by
Tov Elperin; Nathan Kleeorin; Michael A. Liberman; Victor S. L'vov; Anna Pomyalov; Igor Rogachevskii

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We analyzed formation of small-scale inhomogeneities of particle spatial distribution (particle clustering) in a turbulent flow. The particle clustering is a consequence of a spontaneous breakdown of their homogeneous space distribution, and is caused by a combined effect of the particle inertia and a finite correlation time of the turbulent velocity field. Theory of the particle clustering is extended to the case when the particle Stokes time is larger than the Kolmogorov time scale, but is...

Source: http://arxiv.org/abs/nlin/0305017v2

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Sep 19, 2013
09/13

by
Adrienne L. Fairhall; Victor S. L'vov; Itamar Procaccia

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A recent theoretical development in the understanding of the small-scale structure of Navier-Stokes turbulence has been the proposition that the scales $\eta_n(R)$ that separate inertial from viscous behavior of many-point correlation functions depend on the order $n$ and on the typical separations $R$ of points in the correlation. This is a proposal of fundamental significance in itself but it also has implications for the inertial range scaling behaviour of various correlation functions. This...

Source: http://arxiv.org/abs/chao-dyn/9709034v1

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Sep 18, 2013
09/13

by
Victor S. L'vov; Itamar Procaccia; Damien Vandembroucq

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In a series of recent works it was proposed that shell models of turbulence exhibit inertial range scaling exponents that depend on the nature of the dissipative mechanism. If true, and if one could imply a similar phenomenon to Navier-Stokes turbulence, this finding would cast strong doubts on the universality of scaling in turbulence. In this Letter we propose that these ``nonuniversalities'' are just corrections to scaling that disappear when the Reynolds number goes to infinity.

Source: http://arxiv.org/abs/chao-dyn/9803014v1

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Sep 18, 2013
09/13

by
Victor S. L'vov; Anna Pomyalov; Itamar Procaccia

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The statistics of 2-dimensional turbulence exhibit a riddle: the scaling exponents in the regime of inverse energy cascade agree with the K41 theory of turbulence far from equilibrium, but the probability distribution functions are close to Gaussian like in equilibrium. The skewness $\C S \equiv S_3(R)/S^{3/2}_2(R)$ was measured as $\C S_{\text{exp}}\approx 0.03$. This contradiction is lifted by understanding that 2-dimensional turbulence is not far from a situation with equi-partition of...

Source: http://arxiv.org/abs/nlin/0202049v2

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Sep 20, 2013
09/13

by
Yacine Amarouchene; Daniel Bonn; Hamid Kellay; Ting-Shek Lo; Victor S. L'vov; Itamar Procaccia

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We present experimental and theoretical results addressing the Reynolds number (Re) dependence of drag reduction by sufficiently large concentrations of rod-like polymers in turbulent wall-bounded flows. It is shown that when Re is small the drag is {\em enhanced}. On the other hand when Re increases the drag is reduced and eventually the Maximal Drag Reduction (MDR) asymptote is attained. The theory is shown to be in excellent agreement with experiments, rationalizing and explaining all the...

Source: http://arxiv.org/abs/nlin/0607006v1

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Sep 20, 2013
09/13

by
Yuriy M. Bunkov; Victor S. L'vov; Grigory E. Volovik

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In this Letter we discussed the parametric instability of texture of homogeneous (in time) spin precession, explaining how spatial inhomogeneity of the texture may change the threshold of the instability in comparison with idealized spatial homogeneous case, considered in our JETP Letter \textbf{83}, 530 (2006), cond-mat/0605386. This discussion is inspired by critical Comment of I.A. Fomin (cond-mat/0606760) related to the above questions. In addition we considered here results of direct...

Source: http://arxiv.org/abs/nlin/0608032v1

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Sep 18, 2013
09/13

by
Elena Kartashova; Victor S. L'vov

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We suggest a way of rationalizing an intra-seasonal oscillations (IOs) of the Earth atmospheric flow as four meteorological relevant triads of interacting planetary waves, isolated from the system of all the rest planetary waves. Our model is independent of the topography (mountains, etc.) and gives a natural explanation of IOs both in the North and South Hemispheres. Spherical planetary waves are an example of a wave mesoscopic system obeying discrete resonances that also appears in other...

Source: http://arxiv.org/abs/nlin/0606058v3

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Sep 22, 2013
09/13

by
Itamar Procaccia; Victor S. L'vov; Roberto Benzi

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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...

Source: http://arxiv.org/abs/nlin/0702034v1

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Sep 21, 2013
09/13

by
Narimasa Sasa; Takuma Kano; Masahiko Machida; Victor S. L'vov; Oleksii Rudenko; Makoto Tsubota

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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.

Source: http://arxiv.org/abs/1008.3050v2

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Sep 18, 2013
09/13

by
Victor S. L'vov; Itamar Procaccia

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The main difficulty of statistical theories of fluid turbulence is the lack of an obvious small parameter. In this paper we show that the formerly established fusion rules can be employed to develop a theory in which Kolmogorov's statistics of 1941 acts as the zero order, or background statistics, and the anomalous corrections to the K41 scaling exponents $\zeta_n$ of the $n$th order structure functions can be computed analytically. The crux of the method consists of renormalizing a 4-point...

Source: http://arxiv.org/abs/nlin/0005025v2

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Jul 24, 2013
07/13

by
Victor S. L'vov; Sergey V. Nazarenko; Oleksii Rudenko

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We revise the theory of superfluid turbulence near the absolute zero of temperature and suggest a model with differential approximation for the energy fluxes in the k-space carried by the collective hydrodynamic motions of quantized vortex lines and by their individual uncorrelated motions known as Kelvin waves. The model predicts energy spectra of the hydrodynamic and the Kelvin waves components of the system, which experience a smooth crossover between different regimes of motion over a...

Source: http://arxiv.org/abs/0807.1258v1

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Sep 18, 2013
09/13

by
Elisabetta De Angelis; Carlo Casciola; Victor S. L'vov; Anna Pomyalov; Itamar Procaccia; Vasil Tiberkevich

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Drag reduction by polymers in turbulent flows raises an apparent contradiction: the stretching of the polymers must increase the viscosity, so why is the drag reduced? A recent theory proposed that drag reduction in agreement with experiments is consistent with the effective viscosity growing linearly with the distance from the wall. With this self consistent solution the reduction in the Reynolds stress overwhelms the increase in viscous drag. In this Letter we show, using Direct Numerical...

Source: http://arxiv.org/abs/nlin/0401005v1

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Sep 22, 2013
09/13

by
Victor S. L'vov; Anna Pomyalov; Itamar Procaccia; Oleksii Rudenko

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Finite-dimensional wave turbulence refers to the chaotic dynamics of interacting wave `clusters' consisting of finite number of connected wave triads with exact three-wave resonances. We examine this phenomenon using the example of atmospheric planetary (Rossby) waves. It is shown that the dynamics of the clusters is determined by the types of connections between neighboring triads within a cluster; these correspond to substantially different scenarios of energy flux between different triads....

Source: http://arxiv.org/abs/0906.2852v1

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Sep 18, 2013
09/13

by
Victor S. L'vov; Sergei V. Nazarenko; L. Skrbek

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We suggest a "minimal model" for the 3D turbulent energy spectra in superfluids, based on their two-fluid description. We start from the Navier-Stokes equation for the normal fluid and from the coarse-grained hydrodynamic equation for the superfluid component (obtained from the Euler equation for the superfluid velocity after averaging over the vortex lines) and introduce a mutual friction coupling term, proportional to the counterflow velocity, the average superfluid vorticity and to...

Source: http://arxiv.org/abs/nlin/0606002v1

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Sep 21, 2013
09/13

by
Victor S. L'vov; Anna Pomyalov; Itamar Procaccia

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The Taylor hypothesis which allows surrogating spatial measurements requiring many experimental probes by time series from one or two probes is examined on the basis of a simple analytic model of turbulent statistics. The main points are as follows: (i) The Taylor hypothesis introduces systematic errors in the evaluation of scaling exponents. (ii) When the mean wind $\bar{V}_0$ is not infinitely larger than the root-mean-square longitudinal turbulent fluctuations $v_T$, the effective Taylor...

Source: http://arxiv.org/abs/chao-dyn/9905031v1

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Jun 28, 2018
06/18

by
Dmytro Khomenko; Victor S. L'vov; Anna Pomyalov; Itamar Procaccia

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In mechanically driven superfluid turbulence the mean velocities of the normal- and superfluid components are known to coincide: $\mathbf U_{\text{n}} =\mathbf U_{\text{s}}$. Numerous laboratory, numerical and analytical studies showed that under these conditions the mutual friction between the normal- and superfluid velocity components couples also their fluctuations: $\mathbf u'_{\text{n}}(\mathbf r,t) \approx \mathbf u'_{\text{s}}(\mathbf r,t)$ almost at all scales. In this paper we show...

Topics: Condensed Matter, Other Condensed Matter

Source: http://arxiv.org/abs/1509.03566

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54

Sep 21, 2013
09/13

by
Victor S. L'vov; Evgenii Podivilov; Itamar Procaccia

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All statistical models of turbulence take into account Kolmogorov's exact result known as the "4/5 law" which stems from energy conservation. This law states that the energy flux expressed as a spatial derivative of the 3rd order velocity correlator equals the rate of energy dissipation. We have found an additional exact result which stems from the conservation of helicity in turbulence without inversion symmetry. It equates the flux of helicity expressed as a second spatial...

Source: http://arxiv.org/abs/chao-dyn/9705016v2

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Sep 21, 2013
09/13

by
Claudio Ferrari; Badr Kaoui; Victor S. L'vov; Itamar Procaccia; Oleksii Rudenko; J. H. M. ten Thije Boonkkamp; Federico Toschi

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We developed a model for the enhancement of the heat flux by spherical and elongated nano- particles in sheared laminar flows of nano-fluids. Besides the heat flux carried by the nanoparticles the model accounts for the contribution of their rotation to the heat flux inside and outside the particles. The rotation of the nanoparticles has a twofold effect, it induces a fluid advection around the particle and it strongly influences the statistical distribution of particle orientations. These...

Source: http://arxiv.org/abs/1204.2694v1

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Sep 19, 2013
09/13

by
Victor S. L'vov; Ruben Pasmanter; Anna Pomyalov; Itamar Procaccia

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The weak version of universality in turbulence refers to the independence of the scaling exponents of the $n$th order strcuture functions from the statistics of the forcing. The strong version includes universality of the coefficients of the structure functions in the isotropic sector, once normalized by the mean energy flux. We demonstrate that shell models of turbulence exhibit strong universality for both forced and decaying turbulence. The exponents {\em and} the normalized coefficients are...

Source: http://arxiv.org/abs/nlin/0302042v1

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Sep 20, 2013
09/13

by
Victor S. L'vov; Anna Pomyalov; Itamar Procaccia; Sergej S. Zilitinkevich

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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...

Source: http://arxiv.org/abs/nlin/0506058v1

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Sep 22, 2013
09/13

by
Vladimir V. Lebedev; Victor S. L'vov

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It is shown that statistical properties of developed hydrodynamic turbulence are characterized by an infinite set of independent anomalous exponents which describes the scaling behavior of hydrodynamic fields constructed from the second and larger powers of the velocity derivatives. A physical mechanism responsible for anomalous scaling, ``telescopic multi-step eddy interaction", is discovered and investigated. The essence of this mechanism is the existence of a very large number...

Source: http://arxiv.org/abs/chao-dyn/9410003v1

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49

Sep 18, 2013
09/13

by
Victor S. L'vov; Itamar Procaccia

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It is shown that the idea that scaling behavior in turbulence is limited by one outer length $L$ and one inner length $\eta$ is untenable. Every n'th order correlation function of velocity differences $\bbox{\cal F}_n(\B.R_1,\B.R_2,\dots)$ exhibits its own cross-over length $\eta_{n}$ to dissipative behavior as a function of, say, $R_1$. This length depends on $n$ {and on the remaining separations} $R_2,R_3,\dots$. One result of this Letter is that when all these separations are of the same...

Source: http://arxiv.org/abs/chao-dyn/9606018v1

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Sep 23, 2013
09/13

by
Victor S. L'vov; . Yu. L'vov; A. C. Newell; V. Zakharov

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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 discussed

Source: http://arxiv.org/abs/chao-dyn/9607007v1

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Sep 22, 2013
09/13

by
Adrienne L. Fairhall; Barak Galanti; Victor S. L'vov; Itamar Procaccia

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We present results from direct numerical simulations of the Kraichnan model for passive scalar advection by a rapidly-varying random scaling velocity field for intermediate values of the velocity scaling exponent. These results are compared with the scaling exponents predicted for this model by Kraichnan. Further, we test the recently proposed fusion rules which govern the scaling properties of multi-point correlations, and present results on the linearity of the conditional statistics of the...

Source: http://arxiv.org/abs/chao-dyn/9707003v1

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Sep 20, 2013
09/13

by
Victor S. L'vov; Daniela Pierotti; Anna Pomyalov; Itamar Procaccia

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We present a model of hydrodynamic turbulence for which the program of computing the scaling exponents from first principles can be developed in a controlled fashion. The model consists of $N$ suitably coupled copies of the "Sabra" shell model of turbulence. The couplings are chosen to include two components: random and deterministic, with a relative importance that is characterized by a parameter called $\epsilon$. It is demonstrated, using numerical simulations of up to 25 copies...

Source: http://arxiv.org/abs/chao-dyn/9810021v1