A Lagrangian model for turbulent dispersion with turbulent-like flow structure: Comparison with direct numerical simulation for two-particle statistics

Abstract

A wide range of relative two-particle dispersion statistics from the Lagrangian Kinematic Simulation ͑KS͒ model, which contains turbulent-like flow structures, compares well with Yeung's ͓Phys. Fluids 6, 3416 ͑1994͔͒ DNS results. In particular, the Lagrangian flatness factor 4 (t) compares excellently ͑better than Heppe's ͓J. Fluid Mech. 357, 167 ͑1998͔͒ nonlinear stochastic model͒. For higher Reynolds numbers the results from KS show that 4 (t) is significantly greater than 3 over a wide range of times within the inertial range of time scales.

Richardson’s Pair Diffusion and the Stagnation Point Structure of Turbulence

“…KS, however, offers the flexibility to chose the energy spectrum at will and thereby modify, as we show below, the fractal structure of the set of straining stagnation points. An additional advantage of KS is that the Lagrangian pair diffusion statistics it produces compare well with DNS results when the energy spectrum chosen is that of the DNS turbulence [8]. KS also succesfully generates [12] all the pair diffusion results of the laboratory experiment of [13].…”

“…These are models of turbulent diffusion based on kinematically simulated turbulent velocity fields which are non-Markovian (not delta-correlated in time), incompressible and consistent with up to second order statistics of the turbulence such as energy spectra. Kinematic Simulations are interesting in particular because they do reproduce the very high flatness factors of Lagrangian relative velocities [8]. The mechanism by which fluid element pairs separate in Kinematic Simulations (KS) might therefore be comparable to the one in turbulent flows and is clearly different from the Wiener process which causes fluid element pairs to separate in Lagrangian models of relative diffusion based on Langevin type equations.…”

“…Attempts have been made to model the relative diffusion of fluid element pairs in terms of Langevin type equations based on the assumption that relative Lagrangian accelerations are Markovian in time [5,6]. These models can reproduce the right algebraic time growth of separation statistics of fluid elements in turbulent flows; but they fail to explain the very large values taken by the flatness factor of Lagrangian relative velocities in Direct Numerical Simulations of isotropic turbulence [6,7,8]. In fact these models based on Markovian acceleration statistics underestimate this flatness factor by as much as one order of magnitude.…”

Self-similar two-particle separation model

“…This situation calls for alternative tools to study the influence of such limitations. We mention the eddy-damped quasi-normal Markovian model ͑EDQNM͒, 22,23 the Lagrangian-history direct-interaction ͑LHDI͒ theory, 18 kinematic simulations ͑KS͒, [7][8][9]24 and the concept of persistent critical point flow patterns referred to as the statistical persistence hypothesis ͑SPH͒. 25,26 Yet another approach is the class of Lagrangian stochastic models ͑LSMs͒.…”

“…Despite its importance, even relative dispersion of passive fluid particles is still relatively poorly understood. Kinematic simulations ͑KS͒ of turbulent-like flows [7][8][9] offers the possibility to study a number of dispersion aspects, also at high Reynolds numbers. Only recently [10][11][12][13][14][15] has it become possible to study the second moment of the probability density function ͑PDF͒ of the separation r͑t͒ between two particles also in real turbulence via direct numerical simulation ͑DNS͒ or experiment, with the notable exception of Bourgoin et al 15 at typically low to intermediate Reynolds numbers.…”