Related papers: Hydrodynamic Turbulence Has Infinitely Many Anomal…
Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. One of the significant advances in this respect has been the numerical discovery of simple…
Energy dissipation rate is an important parameter for nearly every experiment on turbulent flow. Mathematically precise relationships between energy dissipation rate and other measurable statistics for the case of anisotropic turbulence are…
The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. The velocity field is Gaussian,…
The scale factors of an arbitrary orthogonal space are a measure of its content of homogeneous orthogonal space. In the present study, it is shown, that their spatial and temporal rates of variation do not contribute to the differential…
Anomalous scaling in the statistics of an active scalar in homogeneous turbulent convection is studied using a dynamical shell model. We extend refined similarity ideas for homogeneous and isotropic turbulence to homogeneous turbulent…
Relativistic fluids are Lorentz invariant, and a non-relativistic limit of such fluids leads to the well-known Navier-Stokes equation. However, for fluids moving with respect to a reference system, or in critical systems with generic…
In this paper we derive here, on the basis of the NS eqs. a set of fusion rules for correlations of velocity differences when all the separation are in the inertial interval. Using this we consider the standard hierarchy of equations…
Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow…
The random forced Navier-Stokes equation can be obtained as a variational problem of a proper action. By virtue of incompressibility, the integration over transverse components of the fields allows to cast the action in the form of a large…
The weak version of universality in turbulence refers to the independence of the scaling exponents of the $n$th order strcuture functions from the statistics of the forcing. The strong version includes universality of the coefficients of…
In this work, we investigate the Navier-Stokes equation in the presence of thermal noise, both at finite viscosity (revisiting the seminal work by Forster-Nelson-Stephen) and in the inviscid limit, which has not yet been explored. We…
In Navier-Stokes turbulence, energy and helicity injected at large scales are subject to a joint direct cascade, with both quantities exhibiting a spectral scaling $\propto k^{-5/3}$. We demonstrate via direct numerical simulations that the…
The present work proposes a theory of isotropic and homogeneous turbulence for incompressible fluids, which assumes that the turbulence is due to the bifurcations associated to the velocity field. The theory is formulated using a…
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…
The anomalous scaling of correlation functions in the turbulent statistics of active scalars (like temperature in turbulent convection) is understood in terms of an auxiliary passive scalar which is advected by the same turbulent velocity…
A fundamental aspect of turbulence theory is related to the identification of realizable phase-space statistical descriptions able to reproduce in some suitable sense the stochastic fluid equations of a turbulent fluid. In particular, a…
Local analysis of the two dimensional Navier-Stokes equations is used to obtain estimates on the energy and enstrophy fluxes involving Taylor and Kraichnan length scales and the size of the domain. In the framework of zero driving force and…
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…
Equal-time scaling exponents in fully developed turbulence typically exhibit non anomalous scaling in the inverse cascade of two-dimensional (2D) turbulence and anomalous scaling in three dimensions. We demonstrate that multiscaling is not…
We inquire about the properties of 2d Navier-Stokes turbulence simultaneously forced at small and large scales. The background motivation comes by observational results on atmospheric turbulence. We show that the velocity field is amenable…