The clustering instability of inertial particles spatial distribution in turbulent flows

A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia and a finite correlation time of the velocity field. The crucial parameter for the clustering instability is a size of the particles. The critical size is estimated for a strong clustering (with a finite fraction of particles in clusters) associated with the growth of the mean absolute value of the particles number density and for a weak clustering associated with the growth of the second and higher moments. A new concept of compressibility of the turbulent diffusion tensor caused by a finite correlation time of an incompressible velocity field is introduced. In this model of the velocity field, the field of Lagrangian trajectories is not divergence-free. A mechanism of saturation of the clustering instability associated with the particles collisions in the clusters is suggested. Applications of the analyzed effects to the dynamics of droplets in the turbulent atmosphere are discussed. An estimated nonlinear level of the saturation of the droplets number density in clouds exceeds by the orders of magnitude their mean number density. The critical size of cloud droplets required for clusters formation is more than $20 \mu$m.Comment: REVTeX 4, 15 pages, 2 figures(included), PRE submitte

Anomalous scaling, nonlocality and anisotropy in a model of the passively advected vector field

A model of the passive vector quantity advected by a Gaussian time-decorrelated self-similar velocity field is studied; the effects of pressure and large-scale anisotropy are discussed. The inertial-range behavior of the pair correlation function is described by an infinite family of scaling exponents, which satisfy exact transcendental equations derived explicitly in d dimensions. The exponents are organized in a hierarchical order according to their degree of anisotropy, with the spectrum unbounded from above and the leading exponent coming from the isotropic sector. For the higher-order structure functions, the anomalous scaling behavior is a consequence of the existence in the corresponding operator product expansions of ``dangerous'' composite operators, whose negative critical dimensions determine the exponents. A close formal resemblance of the model with the stirred NS equation reveals itself in the mixing of operators. Using the RG, the anomalous exponents are calculated in the one-loop approximation for the even structure functions up to the twelfth order.Comment: 37 pages, 4 figures, REVTe

Energy- and flux-budget turbulence closure model for stably stratified flows. Part II: the role of internal gravity waves

We advance our prior energy- and flux-budget turbulence closure model (Zilitinkevich et al., 2007, 2008) for the stably stratified atmospheric flows and extend it accounting for additional vertical flux of momentum and additional productions of turbulent kinetic energy, turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). Main effects of IGW are following: the maximal value of the flux Richardson number (universal constant 0.2-0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. In the heterogeneous stratification, when IGW propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. IGW also reduce anisotropy of turbulence and increase the share of TPE in the turbulent total energy. Depending on the direction (downward or upward), IGW either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.Comment: 37 pages, 5 figures, revised versio

Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence

The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. The velocity field is Gaussian, $\delta$-correlated in time, and scales with a positive exponent $\xi$. Explicit inertial-range expressions for the magnetic correlation functions are obtained; they are represented by superpositions of power laws with non-universal amplitudes and universal (independent of the anisotropy and forcing) anomalous exponents. The complete set of anomalous exponents for the pair correlation function is found non-perturbatively, in any space dimension $d$, using the zero-mode technique. For higher-order correlation functions, the anomalous exponents are calculated to $O(\xi)$ using the renormalization group. The exponents exhibit a hierarchy related to the degree of anisotropy; the leading contributions to the even correlation functions are given by the exponents from the isotropic shell, in agreement with the idea of restored small-scale isotropy. Conversely, the small-scale anisotropy reveals itself in the odd correlation functions : the skewness factor is slowly decreasing going down to small scales and higher odd dimensionless ratios (hyperskewness etc.) dramatically increase, thus diverging in the $r\to 0$ limit.Comment: 25 pages Latex, 1 Figur

Antisemitism and the Russian Revolution

Book synopsis: When the Bolsheviks came to power in 1917, they announced the overthrow of a world scarred by exploitation and domination. In the very moment of revolution, these sentiments were put to the test as antisemitic pogroms swept the former Pale of Settlement. The pogroms posed fundamental questions of the Bolshevik project, revealing the depth of antisemitism within sections of the working class, peasantry and Red Army. Antisemitism and the Russian Revolution offers the first book-length analysis of the Bolshevik response to antisemitism. Contrary to existing understandings, it reveals this campaign to have been led not by the Party leadership, as is often assumed, but by a loosely connected group of radicals who mobilized around a Jewish political subjectivity. By examining pogroms committed by the Red Army, Brendan McGeever also uncovers the explosive overlap between revolutionary politics and antisemitism, and the capacity for class to become racialized in a moment of crisis