Related papers: Fusion Rules in Navier-Stokes Turbulence: First Ex…
We study steady vortex sheet solutions of the Navier-Stokes in the limit of vanishing viscosity at fixed energy flow. We refer to this as the turbulent limit. These steady flows correspond to a minimum of the Euler Hamiltonian as a…
Starting from the fluctuating Boltzmann equation for smooth inelastic hard spheres or disks, closed equations for the fluctuating hydrodynamic fields to Navier-Stokes order are derived. This requires to derive constitutive relations for…
On the basis of the Navier-Stokes equations we develop the statistical theory of many space-time correlation functions of velocity differences. Their time dependence is {\em not} scale invariant: $n$-order correlations functions exhibit…
We use recent developments in the theory of finite-time dynamical systems to objectively locate the material boundaries of coherent vortices in two-dimensional Navier--Stokes turbulence. We show that these boundaries are optimal in the…
The majority of practical flows, particularly those flows in applications of importance to transport, distribution and climate, are turbulent and as a result experience complex three-dimensional motion with increased drag compared with the…
We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This solution family is equivalent to a fractal curve in complex…
A new exact solution of the Navier-Stokes equation is derived for the compressible flows which are far from equilibrium in the limit of extremely low shear viscosity and relatively large volume viscosity. The closed description of the…
In this article we consider a damped version of the incompressible Navier-Stokes equations in the whole three-dimensional space with a divergence-free and time-independent external force. Within the framework of a well-prepared force and…
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…
The Navier--Stokes (NS) equations describe fluid dynamics through a high-dimensional, nonlinear system of partial differential equations (PDEs). Despite their fundamental importance, their behavior in turbulent regimes remains incompletely…
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…
In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear…
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…
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,…
Singularity of Navier-Stokes equations is uncovered for the first time which explains the mechanism of transition of a smooth laminar flow to turbulence. It is found that when an inflection point is formed on the velocity profile in…
A new formulation of the Navier-Stokes equation, in terms of the gradient of the total mechanical energy, is derived for the time-averaged flows, and the singular point possibly existing in the Navier-Stokes equation is exactly found.…
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…
A chaotic system is called ultra-chaos when its statistics have sensitivity dependence on initial condition and/or other small disturbances. In this paper, using two-dimensional turbulent Kolmogorov flow as an example, we illustrate that…
It has been recently demonstrated, [3], that according to the principle of release of constraints, absence of shear stresses in the Euler equations must be compensated by additional degrees of freedom, and that led to a Reynolds-type…
The instant Lagranian coordinator system is used to describe the fluid material motion. By this way, the instant deformation gradient (expressed by spatial velocity gradient) concept is established. Based on this geometrical understanding,…