Related papers: Chaos and information in two dimensional turbulenc…
We consider a chain of oscillators with hyperbolic chaos coupled via diffusion. When the coupling is strong the chain is synchronized and demonstrates hyperbolic chaos so that there is one positive Lyapunov exponent. With the decay of the…
A deterministic multi-scale dynamical system is introduced and discussed as prototype model for relative dispersion in stationary, homogeneous and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and…
The anomalous scaling phenomena of three-dimensional passive scalar turbulence are studied using high resolution direct numerical simulation. The inertial range scaling exponents of the passive scalar increment and the scalar dissipation…
We apply a simple method to provide explicit expressions for different scaling exponents in intermittent fully developed turbulence, that before were only given through a Legendre transform. This includes predictability exponents for…
Turbulence is a fundamental flow phenomenon, typically anisotropic at large scales and approximately isotropic at small scales. The classical Kolmogorov scaling laws (2/3, -5/3 and 4/5) have been well-established for turbulence without…
It is generally believed that the dynamics of simple fluids can be considered to be chaotic, at least to the extent that they can be modeled as classical systems of particles interacting with short range, repulsive forces. Here we give a…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
The statistical properties of the dissipation process constrain the analysis of large scale numerical simulations of three dimensional incompressible magnetohydrodynamic (MHD) turbulence, such as those of Biskamp and Muller [Phys. Plasmas…
Competition between two main attractors of the distributed chaos, one associated with translational symmetry (homogeneity) and another associated with rotational symmetry (isotropy), has been studied in freely decaying turbulence. It is…
Universal properties of turbulence have been associated traditionally with very high Reynolds numbers, but recent work has shown that the onset of the power-laws in derivative statistics occurs at modest microscale Reynolds numbers of the…
Shell model turbulence is a simplified mathematical framework that captures essential features of incompressible fluid turbulence such as the energy cascade, intermittency and anomalous scaling of the fluid observables. We perform a…
We propose explicit forms for the steady state distributions governing fully developed turbulence in two and three spatial dimensions. We base our proposals on the crucial importance of the area and volume preserving diffeomorphisms in the…
A new scaling theory for spinodal decomposition in the inertial hydrodynamic regime is presented. The scaling involves three relevant length scales, the domain size, the Taylor microscale and the Kolmogorov dissipation scale. This allows…
Using a multi-scaled, chaotic flow known as the KS model of turbulence, we investigate the dependence of Lyapunov exponents on various characteristics of the flow. We show that the KS model yields a power law relation between the Reynolds…
Macroscopic systems subjected to injection and dissipation of energy can exhibit complex spatiotemporal behaviors as result of dissipative self-organization. Here, we report a one and two dimensional pattern forming set up, which exhibits a…
Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on…
Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov's $k^{-5/3}$ scaling is derived for the energy inertial range. A related modification is found…
We investigate the laws that rule the behavior of the largest Lyapunov exponent (LLE) in many particle systems with long range interactions. We consider as a representative system the so-called Hamiltonian alpha-XY model where the…
Understanding and quantifying chaos from data remains challenging. We present a data-driven method for estimating the largest Lyapunov exponent (LLE) from one-dimensional chaotic time series using machine learning. A predictor is trained to…
We investigate spectral properties of buoyancy driven bubbly flows. Using high-resolution numerical simulations and phenomenology of homogeneous turbulence, we identify the relevant energy transfer mechanisms. We find: (a) At high enough…