Related papers: Is Turbulence as Simple as Tossing a Coin?
New aspects of turbulence are uncovered if one considers flow motion from the perspective of a fluid particle (known as the Lagrangian approach) rather than in terms of a velocity field (the Eulerian viewpoint). Using a new experimental…
A relation between intermittency and clustering phenomena in velocity field has been revealed for homogeneous fluid turbulence. It is described how the intermittency exponent can be split into sum of two other exponents. One of these…
This is an idiosyncratic survey of statistical fluid mechanics centering on the Hopf functional differential equation. Using the Burgers equation for illustration we review several functional integration approaches to theory of turbulence.…
We analyse the tumbling of small non-spherical, axisymmetric particles in random and turbulent flows. We compute the orientational dynamics in terms of a perturbation expansion in the Kubo number, and obtain the tumbling rate in terms of…
In this contribution, I give an overview of the various approaches toward the numerical modelling of turbulence, particularly, in the interstellar medium. The discussion is placed in a physical context, i. e. computational problems are…
Predicting how much mixing occurs when a given amount of energy is injected into a Boussinesq fluid is a longstanding problem in stratified turbulence. The huge number of degrees of freedom involved in those processes renders extremely…
The use of Fermat-Torricelli points can be an effective mathematical tool for analyzing numerical series that have a large variance, a pronounced nonlinear trend, or do not have a normal distribution of a random variable. Linear…
The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation,…
In this article, I would like to express some of my views on the nature of turbulence. These views are mainly drawn from the author's recent results on chaos in partial differential equations \cite{Li04}. Fluid dynamicists believe that…
To describe the small-scale intermittency of turbulence, a self-similarity is assumed for the probability density function of a logarithm of the rate of energy dissipation smoothed over a length scale among those in the inertial range. The…
We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with a single free relaxation time that depends on space and time. A proper kinetic equation is constructed from averaging the…
In this work, I derive the time-dependent probability density function of classical observables using the Hamiltonian mechanics approach, extending the notion of fluctuation theorems for any observables. In particular, the time-dependent…
Time evolution equation for the Probability Distribution Function (PDF) is derived for system of weakly interacting waves. It is shown that a steady state for such system may correspond to strong intermittency.
Turbulent flows play an important role in many aspects of nature and technics from sea storms to transport of particles or chemicals. Transport of energy from large scales to small fluctuations is the essential feature of three-dimensional…
Prediction is a fundamental objective of science. It is more difficult for chaotic and complex systems like turbulence. Here we use information theory to quantify spatial prediction using experimental data from a turbulent soap film. At…
In this note, we propose a new idea by analyzing the basic disturbance equations, and give starting equations for understanding the instability phenomena of laminar flows and transition to turbulence. It is considered that there is an…
We consider a stochastic version of the point vortex system, in which the fluid velocity advects single vortices intermittently for small random times. Such system converges to the deterministic point vortex dynamics as the rate at which…
The statistical properties of turbulence are considered to be universal at sufficiently small length scales, i. e., independent of boundary conditions and large-scale forces acting on the fluid. Analyzing data from numerical simulations of…
This paper is devoted to a statistical analysis of the fluctuations of velocity and acceleration produced by a random distribution of point vortices in two-dimensional turbulence. We show that the velocity probability density function…
The effect of Eulerian intermittency on the Lagrangian statistics of relative dispersion in fully developed turbulence is investigated. A scaling range spanning many decades is achieved by generating a multi-affine synthetic velocity field…