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Sep 18, 2013
09/13

by
Victor S. L'vov

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A variation principle is suggested to find self-similar solitary solutions (``solitons'') of shell model of turbulence. For the Sabra shell model the shape of the solitons is approximated by rational trial functions with relative accuracy of O(0.001). It is found how the soliton shape, propagation time $t_n$ and the dynamical exponent $z_0$ (which governs the time rescaling of the solitons in different shells) depend on parameters of the model. For a finite interval of $z$ the author discovered...

Source: http://arxiv.org/abs/nlin/0105015v1

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Sep 22, 2013
09/13

by
Victor S. L'vov; Itamar Procaccia

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We propose a scheme for the calculation from the NS equations of the scaling exponents $\zeta_n$ of the $n$th order correlators in fully developed hydrodynamic turbulence. The scheme is nonperturbative and constructed to respect the fundamental rescaling symmetry of the Euler equation. It constitutes an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of $\zeta_n$. As a consequence $\zeta_n$ are determined by solvability conditions and not...

Source: http://arxiv.org/abs/chao-dyn/9707015v1

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Sep 23, 2013
09/13

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Elena Kartashova; Victor S. L'vov

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The dynamics of nonlinear atmospheric planetary waves is determined by a small number of independent wave clusters consisting of a few connected resonant triads. We classified the different types of connections between neighboring triads that determine the general dynamics of a cluster. Each connection type corresponds to substantially different scenarios of energy flux among the modes. The general approach can be applied directly to various mesoscopic systems with 3-mode interactions,...

Source: http://arxiv.org/abs/0801.3374v2

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Sep 18, 2013
09/13

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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 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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Sep 18, 2013
09/13

by
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 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 18, 2013
09/13

by
Victor S. L'vov; Sergey Nazarenko

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We present two phenomenological models for 2D turbulence in which the energy spectrum obeys a nonlinear fourth-order and a second-order differential equations respectively. Both equations respect the scaling properties of the original Navier-Stokes equations and it has both the -5/3 inverse-cascade and t -3 direct-cascade spectra. In addition, the fourth order equation has Raleigh-Jeans thermodynamic distributions, as exact steady state solutions. We use the fourth-order model to derive a...

Source: http://arxiv.org/abs/nlin/0605003v2

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Sep 21, 2013
09/13

by
Victor S. L'vov; Anna Pomyalov

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We suggested a one-fluid model of a turbulent dilute suspension which accounts for the ``two-way'' fluid-particle interactions by $k$-dependent effective density of suspension and additional damping term in the Navier-Stokes equation. We presented analytical description of the particle modification of turbulence including scale invariant suppression of a small $k$ part of turbulent spectrum (independent of the particle response time) and possible enhancemenent of large $k$ region [up to the...

Source: http://arxiv.org/abs/nlin/0203016v1

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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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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 22, 2013
09/13

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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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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 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 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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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 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 18, 2013
09/13

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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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Jul 20, 2013
07/13

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

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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...

Source: http://arxiv.org/abs/nlin/0009049v1

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Sep 19, 2013
09/13

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

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We address the dynamical and statistical description of stably stratified turbulent boundary layers with the important example of the atmospheric boundary layer with a stable temperature stratification in mind. Traditional approaches to this problem, based on the profiles of mean quantities, velocity second-order correlations, and dimensional estimates of the turbulent thermal flux run into a well known difficulty, predicting the suppression of turbulence at a small critical value of the...

Source: http://arxiv.org/abs/nlin/0610056v4

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Sep 21, 2013
09/13

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

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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...

Source: http://arxiv.org/abs/0902.2715v1

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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 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 18, 2013
09/13

by
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 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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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 17, 2013
09/13

by
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 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
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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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 20, 2013
09/13

by
Ryu Numasato; Makoto Tsubota; Victor S. L'vov

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We numerically study two-dimensional quantum turbulence with a Gross--Pitaevskii model. With the energy initially accumulated at large scale, quantum turbulence with many quantized vortex points is generated. Due to the lack of enstrophy conservation in this model, direct energy cascade with a Kolmogorov--Obukhov energy spectrum $E(k) \propto k^{-5/3}$ is observed, which is quite different from two-dimensional incompressible classical turbulence in the decaying case. A positive value for the...

Source: http://arxiv.org/abs/1002.3667v1

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Sep 20, 2013
09/13

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

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We discuss a simple analytical model of the turbulent boundary layer (TBL) over flat plane. The model offers an analytical description of the profiles of mean velocity and turbulent activity in the entire boundary region, from the viscous sub-layer, through the buffer layer further into the log-law turbulent region. In contrast to various existing interpolation formulas the model allows one to generalize the description of simple TBL of a Newtonian fluid for more complicated flows of turbulent...

Source: http://arxiv.org/abs/nlin/0404010v1

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Sep 22, 2013
09/13

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

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We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of the stable atmospheric boundary layer in mind is addressed. Traditional approaches to this problem, based on the profiles of mean quantities, velocity second-order correlations, and dimensional estimates of the turbulent thermal flux run into a well...

Source: http://arxiv.org/abs/0812.4017v1

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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 20, 2013
09/13

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

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We consider superfluid turbulence near absolute zero of temperature generated by classical means, e.g. towed grid or rotation but not by counterflow. We argue that such turbulence consists of a {\em polarized} tangle of mutually interacting vortex filaments with quantized vorticity. For this system we predict and describe a bottleneck accumulation of the energy spectrum at the classical-quantum crossover scale $\ell$. Demanding the same energy flux through scales, the value of the energy at the...

Source: http://arxiv.org/abs/nlin/0612018v5

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Sep 23, 2013
09/13

by
T. S. Lo; Victor S. L'vov; Itamar Procaccia

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Drag reduction in stationary turbulent flows by bubbles is sensitive to the dynamics of bubble oscillations. Without this dynamical effect the bubbles only renormalize the fluid density and viscosity, an effect that by itself can only lead to a small percentage of drag reduction. We show in this paper that the dynamics of bubbles and their effect on the compressibility of the mixture can lead to a much higher drag reduction.

Source: http://arxiv.org/abs/nlin/0511006v1

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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
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 23, 2013
09/13

by
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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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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Sep 21, 2013
09/13

by
Victor S. L'vov; Anna Pomyalov; Antonino Ferrante; Said Elghobashi

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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...

Source: http://arxiv.org/abs/0706.0422v1

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Sep 18, 2013
09/13

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

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The major difficulty in developing theories for anomalous scaling in hydrodynamic turbulence is the lack of a small parameter. In this Letter we introduce a shell model of turbulence that exhibits anomalous scaling with a tunable small parameter. The small parameter $\epsilon$ represents the ratio between deterministic and random components in the coupling between $N$ identical copies of the turbulent field. We show that in the limit $N\to \infty$ anomalous scaling sets in proportional to...

Source: http://arxiv.org/abs/chao-dyn/9903030v1

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Sep 22, 2013
09/13

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

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We consider shell models that display an inverse energy cascade similar to 2-dimensional turbulence (together with a direct cascade of an enstrophy-like invariant). Previous attempts to construct such models ended negatively, stating that shell models give rise to a "quasi-equilibrium" situation with equipartition of the energy among the shells. We show analytically that the quasi-equilibrium state predicts its own disappearance upon changing the model parameters in favor of the...

Source: http://arxiv.org/abs/nlin/0201020v1

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Sep 20, 2013
09/13

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

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The anomalous scaling behavior of the n-th order correlation functions ${\cal F}_n$ of the Kraichnan model of turbulent passive scalar advection is believed to be dominated by the homogeneous solutions (zero-modes) of the Kraichnan equation $\hat{\cal B}_n {\cal F}_n=0$. Previous analysis found zero-modes in perturbation theory in a small parameter. We present non-perturbative analysis of the simplest (non-trivial) case of n=3 and compare the results with the perturbative predictions.

Source: http://arxiv.org/abs/chao-dyn/9610016v1

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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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42

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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58

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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6.0

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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51

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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50

Sep 22, 2013
09/13

by
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