Related papers: Hidden scale invariance of turbulence in a shell m…
We demonstrate that like in the forward cascade of three dimensional turbulence that displays intermittency (lack of self-similarity) due to the concentration of energy dissipation in a small set of fractal dimension less than three, the…
Turbulent flows in three dimensions are characterized by the transport of energy from large to small scales through the energy cascade. Since the small scales are the result of the nonlinear dynamics across the scales, they are often…
A three-layer asymptotic structure for turbulent pipe flow is proposed, revealing in terms of intermediate variables, the existence of a Reynolds-number invariant logarithmic region. It provides a theoretical foundation for addressing…
The multifractal theory of turbulence is used to investigate the energy cascade in the Northwestern Atlantic ocean. The statistics of singularity exponents of velocity gradients computed from in situ measurements are used to show that the…
The dynamics of small-scale structures in free-surface turbulence is crucial to large-scale phenomena in natural and industrial environments. Here we conduct experiments on the quasi-flat free surface of a zero-mean-flow turbulent water…
For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a new, and yet simple, tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the…
Extensive experimental evidence highlight that scalar turbulence exhibits anomalous diffusion and stronger intermittency levels at small scales compared to that in fluid turbulence. This renders the corresponding subgrid-scale dynamics…
We extend the analysis of [Zhou and Sornette, Physica D 165, 94-125, 2002] showing statistically significant log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number ($\approx…
We study the statistics of turbulent velocity fluctuations in the neighbourhood of a strong large scale vortex at very large Reynolds number. At each distance from the vortex core, we observe that the velocity spectrum has a power law…
The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a…
We study the sub-grid scale characteristics of a vorticity-transport-based approach for large-eddy simulations. In particular, we consider a multi-dimensional upwind scheme for the vorticity transport equations and establish its properties…
We review the Parisi-Frisch MultiFractal formalism for Navier--Stokes turbulence with particular emphasis on the issue of statistical fluctuations of the dissipative scale. We do it for both Eulerian and Lagrangian Turbulence. We also show…
Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds ($\mbox{Re}$) numbers. Our direct numerical simulations show that elastic…
Energy cascades lie at the heart of the dynamics of turbulent flows. In a recent study of turbulence in fluids with odd-viscosity [de Wit \textit{et al.}, Nature \textbf{627}, 515 (2024)], the two-dimensionalization of the flow at small…
Turbulent shear flows, such as those occurring in the wall region of turbulent boundary layers, manifest a substantial increase of intermittency with respect to isotropic conditions. This suggests a close link between anisotropy and…
Turbulence problem is often considered as "the last unsolved problem of classical physics". It is due to strong interaction between velocity and/or velocity gradient fluctuations, a high Reynolds number flow is a fascinating mixture of…
This is a paper about multi-fractal scaling and dissipation in a shell model of turbulence, called the GOY model. This set of equations describes a one dimensional cascade of energy towards higher wave vectors. When the model is chaotic,…
In this paper we revisit an idea originally proposed by Mandelbrot about the possibility to observe ``negative dimensions'' in random multifractals. For that purpose, we define a new way to study scaling where the observation scale $\tau$…
Intermittency, measured as log(F(r)/3), where F(r) is the flatness of velocity increments at scale r, is found to rapidly increase as viscous effects intensify, and eventually saturate at very small scales. This feature defines a finite…
In previous papers I have argued that the \emph{fusion rules hypothesis}, which was originally introduced by L'vov and Procaccia in the context of the problem of three-dimensional turbulence, can be used to gain a deeper insight in…