Related papers: Euler equations and turbulence: analytical approac…
The statistics of the energy and helicity fluxes in isotropic turbulence are studied using high resolution direct numerical simulation. The scaling exponents of the energy flux agree with those of the transverse velocity structure functions…
Active fluids exhibit spontaneous flows with complex spatiotemporal structure, which have been observed in bacterial suspensions, sperm cells, cytoskeletal suspensions, self-propelled colloids, and cell tissues. Despite occurring in the…
The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a…
Polyakov recently showed how to use conformal field theory to describe two-dimensional turbulence. Here we construct an infinite hierarchy of solutions, both for the constant enstrophy flux cascade, and the constant energy flux cascade. We…
This work analyses the homogeneous isotropic turbulence by means of the equivalence between Euler and Lagrange representations of motion, adopting the bifurcation rates associated with Navier--Stokes and kinematic equations, and an…
Two-dimensional electrostatic turbulence in magnetized weakly-collisional plasmas exhibits a cascade of entropy in phase space [Phys. Rev. Lett. 103, 015003 (2009)]. At scales smaller than the gyroradius, this cascade is characterized by…
We perform a unique direct numerical simulation of Euler turbulence using delta-correlated velocity field as an initial condition, and report a full range of $k^2$ and $k$ energy spectra for 3D and 2D flows respectively, zero energy flux,…
This work makes analytic progress in the deterministic study of turbulence in Hamiltonian systems by identifying two types of energy cascade solutions and the corresponding large- and small-scale structures they generate. The first cascade…
Active matter systems display a fascinating range of dynamical states, including stationary patterns and turbulent phases. While the former can be tackled with methods from the field of pattern formation, the spatio-temporal disorder of the…
High resolution numerical simulations of stationary inverse energy cascade in two-dimensional turbulence are presented. Deviations from Gaussianity of velocity differences statistics are quantitatively investigated. The level of statistical…
We propose a new perspective on Turbulence using Information Theory. We compute the entropy rate of a turbulent velocity signal and we particularly focus on its dependence on the scale. We first report how the entropy rate is able to…
Starting from the classical formulation of the weak turbulence theory in a density stratified fluid, we derive a simplified version of the kinetic equation of internal gravity wave turbulence. This equation allows us to uncover scaling laws…
We study shell models that conserve the analogues of energy and enstrophy, hence designed to mimic fluid turbulence in 2D. The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous…
Recent results suggest that highly active, chaotic, non-equilibrium states of living fluids might share much in common with high Reynolds number, inertial turbulence. We now show, by using a hydrodynamical model, the onset of intermittency…
A scale invariant, selfsimilar atmospheric eddy continuum exists in the planetary atmospheric boundary layer spanning several orders of magnitude in scales and gives rise to the observed fractal geometry for the global cloud cover pattern.…
The bottleneck pileup in the energy spectrum is investigated for several two-dimensional (2D) turbulence systems by numerical simulation using high-order diffusion terms to amplify the effect, which is weak for normal diffusion. For 2D…
This paper concerns modeling of the evolution of intermittency region between two weakly miscible phases due to temporal and spatial variations of its characteristic length scale. First, the need of a more general description allowing for…
Some important concepts in the nonstandard analysis theory of turbulence are presented in this article. The structure of point, on which differential equations are defined, is analyzed. The distinction between the uniform point and the…
For a particular choice of the smoothing kernel, it is shown that the system of partial differential equations governing the vortex-blob method corresponds to the averaged Euler equations. These latter equations have recently been derived…
Turbulence is defined as an eddy-like state of fluid motion where the inertial-vortex forces of the eddies are larger than any other forces that tend to damp the eddies out. By this definition, turbulence always cascades from small scales…