A note on dissipation in helical turbulence

In helical turbulence a linear cascade of helicity accompanying the energy cascade has been suggested. Since energy and helicity have different dimensionality we suggest the existence of a characteristic inner scale, $\xi=k_H^{-1}$, for helicity dissipation in a regime of hydrodynamic fully developed turbulence and estimate it on dimensional grounds. This scale is always larger than the Kolmogorov scale, $\eta=k_E^{-1}$, and their ratio $\eta / \xi$ vanishes in the high Reynolds number limit, so the flow will always be helicity free in the small scales.Comment: 2 pages, submitted to Phys. Fluid

On the dual cascade in two-dimensional turbulence

We study the dual cascade scenario for two-dimensional turbulence driven by a spectrally localized forcing applied over a finite wavenumber range [k_\min,k_\max] (with k_\min > 0) such that the respective energy and enstrophy injection rates $\epsilon$ and $\eta$ satisfy k_\min^2\epsilon\le\eta\le k_\max^2\epsilon. The classical Kraichnan--Leith--Batchelor paradigm, based on the simultaneous conservation of energy and enstrophy and the scale-selectivity of the molecular viscosity, requires that the domain be unbounded in both directions. For two-dimensional turbulence either in a doubly periodic domain or in an unbounded channel with a periodic boundary condition in the across-channel direction, a direct enstrophy cascade is not possible. In the usual case where the forcing wavenumber is no greater than the geometric mean of the integral and dissipation wavenumbers, constant spectral slopes must satisfy $\beta>5$ and $\alpha+\beta\ge8$, where $-\alpha$ ($-\beta$) is the asymptotic slope of the range of wavenumbers lower (higher) than the forcing wavenumber. The influence of a large-scale dissipation on the realizability of a dual cascade is analyzed. We discuss the consequences for numerical simulations attempting to mimic the classical unbounded picture in a bounded domain.Comment: 22 pages, to appear in Physica

The Exact N-point Generating Function in Polyakov-Burgers Turbulence

We find the exact N-point generating function in Polyakov's approach to Burgers turbulence.Comment: 7 pages,Latex,no figure

The reflection-antisymmetric counterpart of the K\'arm\'an-Howarth dynamical equation

We study the isotropic, helical component in homogeneous turbulence using statistical objects which have the correct symmetry and parity properties. Using these objects we derive an analogue of the K\'arm\'an-Howarth equation, that arises due to parity violation in isotropic flows. The main equation we obtain is consistent with the results of O. Chkhetiani [JETP, 63, 768, (1996)] and V.S. L'vov et al. [chao-dyn/9705016, (1997)] but is derived using only velocity correlations, with no direct consideration of the vorticity or helicity. This alternative formulation offers an advantage to both experimental and numerical measurements. We also postulate, under the assumption of self-similarity, the existence of a hierarchy of scaling exponents for helical velocity correlation functions of arbitrary order, analogous to the Kolmogorov 1941 prediction for the scaling exponents of velocity structure function.Comment: 24 pages, 1 figure. Version 2 (Final). To be published in Physica

Direct Numerical Simulations of the Navier-Stokes Alpha Model

We explore the utility of the recently proposed alpha equations in providing a subgrid model for fluid turbulence. Our principal results are comparisons of direct numerical simulations of fluid turbulence using several values of the parameter alpha, including the limiting case where the Navier-Stokes equations are recovered. Our studies show that the large scale features, including statistics and structures, are preserved by the alpha models, even at coarser resolutions where the fine scales are not fully resolved. We also describe the differences that appear in simulations. We provide a summary of the principal features of the alpha equations, and offer some explanation of the effectiveness of these equations used as a subgrid model for three-dimensional fluid turbulence

Phase diagram of solution of oppositely charged polyelectrolytes

We study a solution of long polyanions (PA) with shorter polycations (PC) and focus on the role of Coulomb interaction. A good example is solutions of DNA and PC which are widely studied for gene therapy. In the solution, each PA attracts many PCs to form a complex. When the ratio of total charges of PA and PC in the solution, $x$, equals to 1, complexes are neutral and they condense in a macroscopic drop. When $x$ is far away from 1, complexes are strongly charged. The Coulomb repulsion is large and free complexes are stable. As $x$ approaches to 1, PCs attached to PA disproportionate themselves in two competing ways. One way is inter-complex disproportionation, in which PCs make some complexes neutral and therefore condensed in a macroscopic drop while other complexes become even stronger charged and stay free. The other way is intra-complex disproportionation, in which PCs make one end of a complex neutral and condensed in a small droplet while the rest of the complex forms a strongly charged tail. Thus each complex becomes a "tadpole". These two ways can also combine together to give even lower free energy. We get a phase diagram of PA-PC solution in a plane of $x$ and inverse screening radius of the monovalent salt, which includes phases or phase coexistence with both kinds of disproportionation.Comment: 29 pages, 10 figures. Major change in results and tex

Scaling and correlation analysis of galactic images

Different scaling and autocorrelation characteristics and their application to astronomical images are discussed: the structure function, the autocorrelation function, Fourier spectra and wavelet spectra. We recommend as the optimal mathematical tool the wavelet spectrum with a suitable choice of the analysing wavelet. We introduce the wavelet cross-correlation function which enables to study the correlation between images as a function of scale. The wavelet cross-correlation coefficient strongly depends on the scale. The classical cross-correlation coefficient can be misleading if a bright, extended central region or an extended disk exists in the galactic images. An analysis of the scaling and cross-correlation characteristics of 9 optical and radio maps of the nearby spiral galaxy NGC 6946 is presented. The wavelet spectra allow to separate structures on different scales like spiral arms and diffuse extended emission. Only the images of thermal radio emission and Halpha emission give indications of 3-dimensional Kolmogorov-type turbulence on the smallest resolved scales (160-800 pc). The cross-correlations between the images of NGC 6946 show strong similarities between the images of total radio emission, red light and mid-infrared dust emission on all scales. The best correlation is found between total radio emission and dust emission. Thermal radio continuum and Halpha emission are best correlated on a scale of about 1' \simeq 1.6 kpc, the typical width of a spiral arm. On a similar scale, the images of polarised radio and Halpha emission are anticorrelated, which remains undetected with classical ross-correlation analysis.Comment: 15 pages with 12 figures. Accepted for publication in MNRA

Effects of forcing in three dimensional turbulent flows

We present the results of a numerical investigation of three-dimensional homogeneous and isotropic turbulence, stirred by a random forcing with a power law spectrum, $E_f(k)\sim k^{3-y}$. Numerical simulations are performed at different resolutions up to $512^3$. We show that at varying the spectrum slope $y$, small-scale turbulent fluctuations change from a {\it forcing independent} to a {\it forcing dominated} statistics. We argue that the critical value separating the two behaviours, in three dimensions, is $y_c=4$. When the statistics is forcing dominated, for $y<y_c$, we find dimensional scaling, i.e. intermittency is vanishingly small. On the other hand, for $y>y_c$, we find the same anomalous scaling measured in flows forced only at large scales. We connect these results with the issue of {\it universality} in turbulent flows.Comment: 4 pages, 4 figure

Field-Theoretic Simulations of Polyelectrolyte Complexation

We briefly discuss our recent field-theoretic study of polyelectrolyte complexation, which occurs in solutions of two oppositely charged polyelectrolytes. Charged systems require theoretical methods beyond the mean-field (or self-consistent field) approximation; indeed, mean-field theory is qualitatively incorrect for such polyelectrolyte solutions. Both analytical (one-loop) and numerical (complex Langevin) methods to account for charge correlations are discussed. In particular, the first application of field-theoretic simulations to polyelectrolyte systems is reported. The polyelectrolyte charge-charge correlation length and a phase diagram are provided; effects of charge redistribution are qualitatively explored.Comment: 7 pages, 3 figures, 3 equations, LaTeX; accepted to Journal of Polymer Science B: Polymer Physics; v2: a revised and expanded version, 6 paragraphs of text and about 20 references adde

Self-sustained oscillations in homogeneous shear flow

Generation of the large-scale coherent vortical structurs in homogeneous shear flow couples dynamical processes of energy and enstrophy production. In the large rate of strain limit, the simple estimates of the contributions to the energy and enstrophy equations result in a dynamical system, describing experimentally and numerically observed self-sustained non-linear oscillations of energy and enstrophy. It is shown that the period of these oscilaltions is independent upon the box size and the energy and enstrophy fluctuations are strongly correlated.Comment: 10 pages 6 figure