Effect of the Reynolds number on three- and four-particle diffusion in three-dimensional turbulence using kinematic simulation

Wavelet synthetic method for turbulent flow

Based on the idea of random cascades on wavelet dyadic trees and the energy cascade model known as the wavelet p model, a series of velocity increments in two-dimensional space are constructed in different levels of scale. The dynamics is imposed on the generated scales by solving the Euler equation in the Lagrangian framework. A dissipation model is used in order to cover the shortage of the p model, which only predicts in inertial range. Wavelet reconstruction as well as the multiresolution analysis are then performed on each scales. As a result, a type of isotropic velocity field is created. The statistical properties show that the constructed velocity fields share many important features with real turbulence. The pertinence of this approach in the prediction of flow intermittency is also discussed.

Effect of gravity on clustering patterns and inertial particle attractors in kinematic simulations

In this paper, we study the clustering of inertial particles using a periodic kinematic simulation. The systematic Lagrangian tracking of particles makes it possible to identify the particles' clustering patterns for different values of particle inertia and drift velocity. The different cases are characterized by different pairs of Stokes number (St) and Froude number (Fr). For the present study, 0≤St≤1 and 0.4≤Fr≤1.4. The main focus is to identify and then quantify the clustering attractor-when it exists-that is the set of points in the physical space where the particles settle when time goes to infinity. Depending on the gravity effect and inertia values, the Lagrangian attractor can have different dimensions, varying from the initial three-dimensional space to two-dimensional layers and one-dimensional attractors that can be shifted from a horizontal to a vertical position.

Geometrical properties of turbulent dispersion

It is shown that the shape statistics of four correlated particles, known as a tetrad, in a direct numerical simulation of three-dimensional homogeneous isotropic turbulence agree very well with a simple diffusion equation with a separation-dependent eddy diffusivity. The latter is essentially an extension of Richardson's model for particle-pair dispersion to tetrads. It is also shown that the degree of elongation of the tetrad in the inertial subrange of a turbulentlike flow is controlled by the exponent, m, in an eddy diffusivity of the form K(r)[proportionality]r(m) where r is the interparticle separation, becoming more elongated as m increases in the range 0≤m<2.

Presence of a Richardson's regime in kinematic simulations

In this paper we investigate kinematic simulation (KS) consistency with the theory of Richardson [Proc. Roy. Soc. A 110, 24 (1926)] for two-particle diffusivity. In particular we revisit the sweeping problem. It has been argued by Thomson and Devenish [J. Fluid Mech. 526, 277 (2005).] that due to the lack of sweeping of small scales by large scales in kinematic simulation, the validity of Richardson's power law might be affected. Here, we argue that the discrepancies between authors on the ability of kinematic simulation to predict Richardson power law may be linked to the inertial subrange they have used. For small inertial subranges, KS is efficient and the significance of the sweeping can be ignored, as a result we limit the KS agreement with the Richardson scaling law t(3) for inertial subranges k(N0/k(1)≤10000. For larger inertial range KS does not fully follow the t(3) law. Unfortunately, there is no experimental data to compare KS with and draw conclusions for such large inertial subranges. It cannot be concluded either that the discrepancy between KS and Richardson's theory for larger inertial subranges is exactly taken into account by the theory developed in Thomson and Devenish [J. Fluid Mech. 526, 277 (2005).].

Dispersion of heavy particle sets in isotropic turbulence using kinematic simulation

We study the dispersion of heavy particle sets, triangle and tetrahedron, in an isotropic and incompressible three-dimensional turbulent flow. The turbulent velocity field is generated using kinematic simulation, which allows us to vary the inertial range and to reach large values of the Reynolds numbers. We study the time evolution of the parameters characterizing the geometry, the size and shape of the triangle and tetrahedron. The Lagrangian correlations of the sets' size, area or volume, are also studied. Different initial separations between particles, inertial ranges, Stokes numbers, and particle drift velocities are considered. We found that the Reynolds number has no effect on the shape evolution of the triangle and tetrahedron provided that the initial distance between the particles is larger than the Kolmogorov length scale.

Turbulence with combined stratification and rotation: Limitations of Corrsin's hypothesis

The properties of one-particle and particle-pair diffusion in rotating and stratified turbulence are studied by applying the rapid distortion theory to a kinematic simulation of the Boussinesq equation with a Coriolis term. We discuss the simplified Corrsin hypothesis and restrict the validity of its predictions to pure rotation. We emphasize the existence of two tau regimes driven by very different physics when rotation is present. Particular attention is given to the locality-in-scale hypothesis for two-particle diffusion in both the horizontal and the vertical directions.