Related papers: Fully developed turbulence and the multifractal co…
The appearance of vortex filaments, the power-law dependence of velocity and vorticity correlators and their multiscaling behavior are derived from the Navier-Stokes equation. This is possible due to interpretation of the Navier-Stokes…
The Frisch-Parisi multifractal formalism remains the most compelling rationalisation for anomalous scaling in fully developed turbulence. We now show that this formalism can be adapted locally to reveal the spatial distribution of…
Making use of the exact equations for structure functions, supplemented by the equations for dissipa tive anomaly as well as an estimate for the Lagrangian acceleration of fluid particles, we obtain a main result of the multifractal theory…
The development of turbulence closure models, parametrizing the influence of small non-resolved scales on the dynamics of large resolved ones, is an outstanding theoretical challenge with vast applicative relevance. We present a closure,…
Cellular suspensions such as dense bacterial flows exhibit a turbulence-like phase under certain conditions. We study this phenomenon of "active turbulence" statistically by using numerical tools. Following Wensink et al. [Proc. Natl. Acad.…
We study small-scale and high-frequency turbulent fluctuations in three-dimensional flows under Fourier-mode reduction. The Navier-Stokes equations are evolved on a restricted set of modes, obtained as a projection on a fractal or…
By means of high-resolution numerical simulations, we compare the statistical properties of homogeneous and isotropic turbulence to those of the Navier-Stokes equation where small-scale vortex filaments are strongly depleted, thanks to a…
Lagrangian acceleration has been investigated both experimentally and numerically in the past, and it has been shown to exhibit extreme fluctuations, which have been rationalized as events in which tracer particles get trapped into vortical…
We investigate statistical properties of vorticity fluctuations in fully developed turbulence, which are known to exhibit a strong intermittent behavior. Taking as the starting point the Navier-Stokes equations with a random force term…
The Lagrangian and Eulerian transversal velocity structure functions of fully developed fluid turbulence are found basing on the Navier-Stokes equation. The structure functions are shown to obey the scaling relations inside the inertial…
Fully-developed incompressible Navier-Stokes turbulence in three dimensions is a dissipative dynamical system that exhibits strong departure from absolute equilibrium. Nevertheless, several kinds of representation by Tsallis equilibria have…
Series of lectures on statistical turbulence written for amateurs but not experts. Elementary aspects and problems of turbulence in two and three dimensional Navier-Stokes equation are introduced. A few properties of scalar turbulence and…
In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked…
Turbulent flows exhibit large intermittent fluctuations from inertial to dissipative scales, characterized by multifractal statistics and breaking the statistical self-similarity. It has recently been proposed that the Navier-Stokes…
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…
Building upon the intrinsic properties of Navier-Stokes dynamics, namely the prevalence of intense vortical structures and the interrelationship between vorticity and strain rate, we propose a simple framework to quantify the extreme events…
Contrary to accepted turbulence folklore, which holds that no mathematical relation exists between the Navier-Stokes equations (NSEs) and the multifractal model (MFM) of Parisi and Frisch, we develop a theory that reconciles the MFM with…
The probability density functions measured by Lewis and Swinney for turbulent Couette-Taylor flow, observed by Bodenschatz and co-workers in the Lagrangian measurement of particle accelerations and those obtained in the DNS by Gotoh et al.…
We show that the classical Kolmogorov and Richardson scaling laws in fully developed turbulence are consistent with a random Gaussian force field. Numerical simulations of a shell model approximation to the Navier-Stokes equations suggest…
Mechanical effects that span multiple physical scales -- such as the influence of vanishing molecular viscosity on large-scale flow structures under specific conditions -- play a critical role in real fluid systems. The spin angular…