Related papers: Analytic solution for a class of turbulence proble…
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for…
The Eulerian variational formulation of the gyrokinetic system with electrostatic turbulence is presented in general spatial coordinates by extending our previous work [H. Sugama, {\it et al}., Phys.\ Plasmas {\bf 25}, 102506 (2018)]. The…
We study the transport of a passive tracer particle in a steady strongly mixing flow with a nonzero mean velocity. We show that there exists a probability measure under which the particle Lagrangian velocity process is stationary. This…
In this paper we present a new model for modeling the diffusion and relative dispersion of particles in homogeneous isotropic turbulence. We use an Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid particles,…
The angle between subsequent particle displacement increments is evaluated as a function of the timelag in isotropic turbulence. It is shown that the evolution of this angle contains two well-defined power-laws, reflecting the multi-scale…
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,…
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is…
Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic…
We derive the (d-dimensional) periodic incompressible and viscous Camassa-Holm equation as well as the Leray-alpha equations via a stochastic variational principle. We discuss the existence of solution for this equation in the space H1…
A Bayesian approach is developed for the inference of an eddy-diffusivity field from Lagrangian trajectory data. The motion of Lagrangian particles is modelled by a stochastic differential equation associated with the advection-diffusion…
Lagrangians linear in velocities were analyzed using the fractional calculus and the Euler-Lagrange equations were derived. Two examples were investigated in details, the explicit solutions of Euler-Lagrange equations were obtained and the…
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…
Through laboratory measurements, we compare the rotation of spherical and ellipsoidal particles in homogeneous, isotropic turbulence. We find that the particles' angular velocity statistics are well described by an Ornstein-Uhlenbeck (OU)…
The aim of the present paper is to introduce and to discuss inconsistencies errors that may arise when Eulerian and Lagrangian models are coupled for the simulations of turbulent poly-dispersed two-phase flows. In these hydrid models, two…
A virtual element discretisation of an Arbitrary Lagrangian-Eulerian method for two-dimensional convection-diffusion equations is proposed employing an isoparametric Virtual Element Method to achieve higher-order convergence rates on curved…
The Lagrangian statistics of relative dispersion in fully developed turbulence is numerically investigated. A scaling range spanning many decades is achieved by generating a synthetic velocity field with prescribed Eulerian statistical…
By tracking tracer particles at high speeds and for long times, we study the geometric statistics of Lagrangian trajectories in an intensely turbulent laboratory flow. In particular, we consider the distinction between the displacement of…
A new single-time two-point closure is proposed, in which the equation for the two-point correlation between the displacement of a fluid particle and the velocity allows one to estimate a Lagrangian timescale. This timescale is used to…
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…
We study the Lagrangian flow associated to velocity fields arising from various models of fluid mechanics subject to white-in-time, $H^s$-in-space stochastic forcing in a periodic box. We prove that in many circumstances, these flows are…