Related papers: Passive scalar turbulence in high dimensions
The field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar advected by the Gaussian velocity field with zero mean and correlation function $\propto\delta(t-t')/k^{d+\eps}$.…
In paper I of this series on fluid turbulence we showed that exact resummations of the perturbative theory of the structure functions of velocity differences result in a finite (order by order) theory. These findings exclude any known…
We investigate the large-scale statistics of a passive scalar transported by a turbulent velocity field. At scales larger than the characteristic lengthscale of scalar injection, yet smaller than the correlation length of the velocity, the…
An analytical solution of the perturbed equations is obtained, which exists in all ergodic models of collisionless spherical stellar systems with a single length parameter. This solution corresponds to variations of this parameter, i.e.,…
The intermittency of a passive scalar advected by three-dimensional Navier-Stokes turbulence at a Taylor-scale Reynolds number of $650$ is studied using direct numerical simulations on a $4096^3$ grid; the Schmidt number is unity. By…
We study a model of fully developed turbulence of a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field theoretic renormalization group. In this approach, scaling properties are related to the fixed…
The 4/5 and 2/3 laws of turbulence can emerge from a theory of 'engineered' random vector fields $\mathcal{X}_{i}(x,t) =X_{i}(x,t)+\tfrac{\theta}{\sqrt{d(d+2)}} X_{i}(x,t)\psi(x)$ existing within $\mathbf{D}\subset\mathbf{R}^{d}$. Here,…
Lagrangian chaos is experimentally investigated in a convective flow by means of Particle Tracking Velocimetry. The Finite Size Lyapunov Exponent analysis is applied to quantify dispersion properties at different scales. In the range of…
The connection between anomalous scaling of structure functions (intermittency) and numerical methods for turbulence simulations is discussed. It is argued that the computational work for direct numerical simulations (DNS) of fully…
Advection of a passive scalar $\theta$ in $d=2$ by a large-scale velocity field rapidly changing in time is considered. The Gaussian feature of the passive scalar statistics in the convective interval was discovered in \cite{95CFKLa}. Here…
We present results of direct numerical simulations of passive scalar advection and diffusion in turbulent rotating flows. Scaling laws and the development of anisotropy are studied in spectral space, and in real space using an axisymmetric…
Approximations to the exact solutions for gravitational instability in the expanding Universe are extremely useful for understanding the evolution of large--scale structure. We report on a series of tests of Newtonian Lagrangian…
We consider the advection of a passive scalar by a divergence free random Gaussian field, white in time and H\"older regular in space (rough Kraichnan's model), a well established synthetic model of passive scalar turbulence. By studying…
A model of the passive vector field advected by the uncorrelated in time Gaussian velocity with power-like covariance is studied by means of the renormalization group and the operator product expansion. The structure functions of the…
Random advection of Lagrangian tracer scalar field $\theta (t,x)$ by a one-dimensional, spatially smooth and short-correlated in time velocity field is considered. Scalar fluctuations are maintained by a source concentrated at the integral…
The dispersion of a passive scalar by wall turbulence, in the limit of infinite Peclet number, is analyzed using frozen velocity fields from the DNS by our group. The Lagrangian trajectories of fluid particles in those fields are integrated…
We perform direct numerical simulation of the incompressible Navier-Stokes equation with forcing at different spatial dimensions and measure turbulent and chaotic properties. Lyapunov exponents, $\lambda$, decrease with dimension, and…
Within the framework of one-dimensional Laval-Dubrulle-Nazarenko type model for the Lagrangian acceleration in developed turbulence studied in the work [A.K. Aringazin and M.I. Mazhitov, cond-mat/0305186] we focus on the effect of…
We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an…
The critical behavior of d-dimensional systems with an n-component order parameter is reconsidered at (m,d,n)-Lifshitz points, where a wave-vector instability occurs in an m-dimensional subspace of ${\mathbb R}^d$. Our aim is to sort out…