Related papers: Turbulence Dynamics based on Lagrange Mechanics an…
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,…
The fate of small particles in turbulent flows depends strongly on the surrounding fluid's velocity gradient properties such as rotation and strain-rates. For non-inertial (fluid) particles, the Restricted Euler model provides a simple,…
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…
The Euler-Poincar\'e approach to complex fluids is used to derive multiscale equations for computationally modelling Euler flows as a basis for modelling turbulence. The model is based on a \emph{kinematic sweeping ansatz} (KSA) which…
In recent works, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential, and examined the proposed mechanics of turbulence formation in a simple model of two particles for a variety…
Using the Lagrangian transport of momentum, the Reynolds shear stress can be expressed in terms of basic turbulence parameters. In this view, the Reynolds stress gradient represents the lateral transport of streamwise momentum, balanced by…
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…
Tools of quantum and statistical field theories have been successfully ported to turbulence. Here, we review the key results of turbulence field theory. \textit{Equilibrium field theory} describes thermalized spectrally-truncated Euler…
We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with a single free relaxation time that depends on space and time. A proper kinetic equation is constructed from averaging the…
The internal interactions of fluids occur at all scales therefore the resulting force fields have no reason to be smooth and differentiable. The release of the differentiability hypothesis has important mathematical consequences, like scale…
A new phenomenological model of turbulent fluctuations is constructed by considering the Lagrangian dynamics of 4 points (the tetrad). The closure of the equations of motion is achieved by postulating an anisotropic, i.e. tetrad shape…
The dynamics of the Reynolds stress tensor for turbulent flows is described with an evolution equation coupling both geometric effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are…
Through Ginzburg-Landau and Navier-Stokes equations, we study turbulence phenomena for viscous incompresible and compressible fluids by a second order phase transition. For this model, the velocity is defined by the sum of classical 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…
The modeling of turbulence, whether it be numerical or analytical, is a difficult challenge. Turbulence is amenable to analysis with linear theory if it is subject to rapid distortions, i.e., motions occurring on a time scale that is short…
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…
A rational theory is proposed to describe the large-scale motion in turbulence. The fluid element with inner orientational structures is proposed to be the building block of fluid dynamics. The variance of the orientational structures then…
A stochastic Euler equation is proposed, describing the motion of a particle density, forced by the random action of virtual photons in vacuum. After time averaging, the Euler equation is reduced to the Reynolds equation, well studied in…
Turbulence in fluids is an ubiquitous phenomenon, characterized by spontaneous transition of a smooth, laminar flow to rapidly changing, chaotic dynamics. In 1883, Reynolds experimentally demonstrated that, in an initially laminar flow of…
Turbulence remains one of the central open problems in classical physics, largely due to the absence of a closed dynamical description of the Reynolds stress. Existing approaches typically rely either on local constitutive assumptions or on…