Stochastic Lagrangian Models of Relative Dispersion of a Pair of Fluid Particles in Turbulent Flows

Abstract

Stochastic Lagrangian Models of relative motion of two fluid particles in one-and three dimensions for locally isotropic incompressible turbulent flow are presented. A principle of consistency of statistics between the Eulerian and Lagrangian velocity fields for general random forcing models of a diffusion type is proposed. This enables us to analyze and improve some well known models. An analog of the well-mixed condition for the relative dispersion is proposed. An explicit form of an co-order consistency model is given. While there is a series of applications (both in theory and applied turbulence) of the relative motion of two particles, a relation to the problem of concentration fluctuations reflect our motivation by the problem of pollutant scattering in the turbulent atmosphere.

A 3D Stochastic Model of Relative Dispersion of Particle Pairs in Local-Isotropic Turbulence

“…ae\\(ô) is a universal stochastic process). A detailed mathematical analysis of the system (3) was undertaken in [3]. Some results of this analysis will be used in section.…”

“…(52)Integrating (32) with respect to î± and taking into account (42), the last relation as well as the equation (50a) was obtained in[3] on the basis of quasi-one-dimensional model (3), (48a).Multiplying (50) by ÄÏ and then integrating it with respect to ÄÏ and taking into account (53) we get the following relation Brought to you by |…”

“…A complete survey of literature on the given subject can be found in [1][2][3]. The major problem in constructing such models is that existing approaches do not yield a unique result, i.e.…”

“…First, on the basis of Kolmogorov's similarity hypothesis, dimensional considerations and some additional assumptions a 3D model of two-particle relative dispersion in inertial subrange of high-Reynolds-number turbulence is presented. Then using a principle of consistency of statistics between the Eulerian and Lagrangian relative velocity fields (see [1][2][3]5]) some methods providing a choice of random parameters in this model are proposed.…”

Monte Carlo Simulation of Particle's Dispersion in Convective Boundary Layer of the Atmosphere

“…However, difficult problems arise then since there is a lack of information, both theoretical and experimental (due mainly to the difficulty in measuring instantaneous Lagrangian velocities) about the Lagrangian statistics of the flow. Therefore, Lagrangian stochastic: models are constructed so that the velocities along the trajectories are consistent in some sense with the Eulerian velocity field (see [5][6][7][8][9][10][11]). …”