TURBULENT RELATIVE DISPERSION

Abstract

▪ Abstract This review begins with the classical foundations of relative dispersion in Kolmogorov's similarity scaling. Analysis of the special cases of isotropic and homogeneous scalar fields is then used to establish most simply the connection with turbulent mixing. The importance of the two-particle acceleration covariance in relative dispersion is demonstrated from the kinematics of the motion of particle-pairs. A summary of the development of two-particle Lagrangian stochastic models is given, with emphasis on the assumptions and constraints involved, and on predictions of the scalar variance field for inhomogeneous sources. Two-point closures and kinematic simulation are also reviewed in the context of their prediction of the Richardson constant and other fundamental constants. In the absence of reliable field data, direct numerical simulations and laboratory measurements seem most likely to provide suitable data with which to test the assumptions and predictions of these theories.

An Investigation of Scalar Dispersion in Grid Turbulence

“…Such scalar-dispersion structure away from the release point is typically modeled assuming a Gaussian profile. This provides a good description for the mean scalar profile as a function of the transverse distance from a line parallel with the flow and downstream of the release point, as also confirmed by experiment (Yamamoto & Sato 1979, Gad-el-Hak & Morton 1979, Nakamura et al 1987, Sawford 2001. The instantaneous three-dimensional structure, however, reveals a rich topology of scalar structures that was found to persist in the volume interrogated, spanning a distance from the grid and release point between 22 and 30 grid mesh lengths, which is in the self-similar grid-turbulence regime where the present three-dimensional scalar-field measuremehts were conducted.…”

Relative dispersion from a high-resolution coastal model of the Adriatic Sea

“…The reader is referred to Bennett (1987) and Sawford (2001) for a comprehensive review of the subject matter. Here, a short summary of this material is provided followed by how the present study is motivated and why it is original in the context of oceanic flows.…”

“…While it is possible to parse further the spatial and temporal scales into other regimes of dispersion on a theoretical basis (Sawford, 2001;Piterbarg, 2005), there appears to be a high degree of uncertainty about which regimes are actually attained in practice, namely in the laboratory, atmospheric and oceanic observations, and numerical simulations. Each one of these methods introduces various factors that can cause deviations from theory.…”

Richardson's Law in Large-Eddy Simulations of Boundary-Layer Flows

“…One of the most powerful concepts which highlighted the dynamical role of the active scales in the atmosphere was due to Richardson (1926). He introduced in his pioneering work the concept of turbulent relative dispersion (see Sawford, 2001 for a recent review) with the aim of investigating the large variations of atmospheric turbulent diffusion when observed at different spatial scales. In his work, Richardson proposed a diffusion equation for the probability density function, p(r, t), of pair separation.…”