Related papers: Dynamical Origins for Non-Gaussian Vorticity Distr…
The purpose of the present paper is to derive a partial differential equation (PDE) for the single-time single-point probability density function (PDF) of the velocity field of a turbulent flow. The PDF PDE is a highly non-linear…
We develop the kinetic theory of point vortices in two-dimensional hydrodynamics and illustrate the main results of the theory with numerical simulations. We first consider the evolution of the system "as a whole" and show that the…
We probe the diffusive motion of particles in slowly sheared three dimensional granular suspensions. For sufficiently large strains, the particle dynamics exhibits diffusive Gaussian statistics, with the diffusivity proportional to the…
The statistical properties of fully developed hydrodynamic turbulence can be successfully described using methods from nonextensive statistical mechanics. The predicted probability densities and scaling exponents precisely coincide with…
We study the dynamics of inertial particles in turbulence using datasets obtained from both direct numerical simulations and laboratory experiments of turbulent swirling flows. By analyzing time series of particle velocity increments at…
Vortex crystals, ordered structures observed in superconductors and rotating superfluids, have also been hypothesized to form in classical fluids, based on numerical simulations and observations of the Jovian polar atmospheres. We perform…
We present new simulation results on a hard sphere system at high densities. Using three-time correlations, we can account for the anomalous diffusion, which results from a homogeneous back-dragging effect. Furthermore, we calculate the…
We propose a unified framework to study the turbulent transport problem from the perspective of nonequilibrium statistical mechanics. By combining Krarichnan's turbulence thermalization assumption and Ruelle's recent work on nonequilibrium…
We prove a bifurcation result of uniformly-rotating/stationary non-trivial vortex sheets near the circular distribution for a model of two irrotational fluids with same density taking into account surface tension effects. As bifurcation…
Vorticity is locally created on a boundary at the rate measured by the boundary vorticity flux, which can be further decomposed as the sum of the orbital rotation and the (generalized) spin. For incompressible viscous flow interacting with…
Drag for wall-bounded flows is directly related to flux of spanwise vorticity outward from the wall. In turbulent flows a key contribution arises from cross-stream "vorticity cascade" by nonlinear advection and stretching of vorticity. We…
Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…
The ultimate goal of a sound theory of turbulence in fluids is to close in a rational way the Reynolds equations, namely to express the tensor of turbulent stress as a function of the time average of the velocity field. Based on the idea…
Through a discussion of some typical unsteady hydrodynamic flows, we argue that the time averaged hydrodynamic functions at each point give a rather sparse filling of the local jet space. This situation then suggests a set of time dependent…
The aim of this paper is to understand the tendency to organization of the turbulence in two-dimensional ideal fluids. We show that nonlinear processes as inverse cascade of the energy and vorticity concentration are essentially determined…
In inviscid, incompressible flows, the evolution of vorticity is exactly equivalent to that of an infinitesimal material line-element, and hence vorticity can be traced forward or backward in time in a Lagrangian fashion. This elegant and…
We investigate the velocity statistics by calculating the Biot--Savart velocity induced by vortex filaments in steady counterflow turbulence investigated in a previous study [Phys. Rev. B {\bf 81}, 104511 (2010)]. The probability density…
In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an…
A statistical mechanics theory for a fluid stratified in density is presented. The predicted statistical equilibrium state is the most probable outcome of turbulent stirring. The slow temporal evolution of the vertical density profile is…
A theoretical framework is developed for the phenomenon of non-Gaussian normal diffusion that has experimentally been observed in several heterogeneous systems. From the Fokker-Planck equation with the dynamical structure with largely…