Stochastic Lagrangian Models for Two-Particle Motion in Turbulent Flows. Numerical Results

Abstract

Abstracts -It is shown that the relative diffusion in a stationary incompressible Gaussian isotropic random field does not exhibit the Richardson cubic law. A two particle combined Eulerian-Lagrangian stochastic model which correctly reflects the behaviour in the inertial subrange is developed. In addition, in this model, the "two-to-one" reduction due to Thomson is satisfied with high accuracy except for a small initial time interval where the error is slightly higher.

Stochastic Flow Simulation and Particle Transport in a 2D Layer of Random Porous Medium

“…In more complicated cases the correlation functions may have heavy tails, for instance decreasing according to the power law (as in the fractal media with multiscale heterogeneities, e.g., see [9]). In this cases, a detailed representation of all the scales is a difficult problem, and a modification of the Randomization spectral models called Stratified Randomization spectral models can be successfully applied (e.g., see [12] and [11]). …”

Comparative analysis of multiscale Gaussian random field simulation algorithms

“…One example is in turbulent transport [30,11,45,46,21,17,12,42,27], where the velocity field representing the turbulent flow is modeled as a random field v( x, t) with statistics encoding important empirical features, and the temporal dynamics of the position X(t) and velocity V (t) = d X dt of immersed particles is then governed by equations involving this random field such as…”

“…In the studies [41,27], a logarithmically stratified subdivision of wavenumber space was found to be significantly more efficient in representing self-similar power-law spectra such as those corresponding to Kolmogorov turbulence. This implementation of the Randomization method [27], a similar implementation of the standard Fourier method with wavenumber discretized uniformly and deterministically in logarithmic space [46], and a multiscale wavelet method [11] have all been employed to simulate disper-sion of pair particles in isotropic Gaussian frozen pseudoturbulence with a Kolmogorov spectrum extending over several decades, in some cases with a constant mean sweep.…”

“…This implementation of the Randomization method [27], a similar implementation of the standard Fourier method with wavenumber discretized uniformly and deterministically in logarithmic space [46], and a multiscale wavelet method [11] have all been employed to simulate disper-sion of pair particles in isotropic Gaussian frozen pseudoturbulence with a Kolmogorov spectrum extending over several decades, in some cases with a constant mean sweep. Of particular interest in these works is whether the classical Richardson's cubic law can be observed in numerically generated pseudoturbulence [27,46,11].…”

Stochastic Spectral and Fourier-Wavelet Methods for Vector Gaussian Random Fields

“…The main conclusion is that to construct the samples of a multiscale random field with a fixed desired accuracy, the cost of RSM is considerably lower than that of FWM if lg(l max /l min ) ≤ 4 where l min and l max are the minimal and maximal spatial scales of the random field, respectively. In [23] we have shown that a logarithmically uniform subdivision of the spectral space (we have introduced such a subdivision in [26]) when calculating two-and a few-point statistical characteristics of the fractal random field, the RSM is more efficient than FWM for all values of l max /l min . In particular, when calculating the structure function of a multiscale random field with α = −5/3, l max /l min = 10 12 it was found that the cost of FWM was 12 times larger than that of RSM; results were obtained for 9 decades, with a fixed accuracy.…”