Kinematic simulation of turbulent dispersion of triangles

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.

Scale-dependent statistical geometry in two-dimensional flow

By studying the shape dynamics of three-particle clusters, we investigate the statistical geometry of a spatiotemporally chaotic experimental quasi-two-dimensional flow. We show that when shape and size are appropriately decoupled, these Lagrangian triangles assume statistically stationary shape distributions that depend on the flow scale, with smaller scales favoring more distorted triangles. These preferred shapes are not due to trapping by Eulerian flow structures. Since our flow does not have developed turbulent cascades, our results suggest that more careful work is required to understand the specific effects of turbulence on the advection of Lagrangian clusters.

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.

Intermittent particle distribution in synthetic free-surface turbulent flows

Tracer particles on the surface of a turbulent flow have a very intermittent distribution. This preferential concentration effect is studied in a two-dimensional synthetic compressible flow, both in the inertial (self-similar) and in the dissipative (smooth) range of scales, as a function of the compressibility C . The second moment of the concentration coarse grained over a scale r , n_{r};{2} , behaves as a power law in both the inertial and the dissipative ranges of scale, with two different exponents. The shapes of the probability distribution functions of the coarse-grained density n_{r} vary as a function of scale r and of compressibility C through the combination C/r;{kappa} (kappa approximately 0.5) , corresponding to the compressibility, coarse grained over a domain of scale r , averaged over Lagrangian trajectories.

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.

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

We study the evolution of three- and four-particle diffusion at large Reynolds numbers using kinematic simulation (KS) in isotropic turbulent flows. We vary the Reynolds number and find that the geometrical characteristics of triangles and tetrahedrons as functions of time do not depend on the Reynolds number but only on the ratio Delta0/L1 that is on the portion of the inertial range that was contained within the triangle or tetrahedron at the initial time. We also study the effect of the modeling of the unsteadiness term in the KS.

Investigation of the dispersion of heavy-particle pairs and Richardson's law using kinematic simulation

In this paper we investigate the dispersion of heavy-particle pairs (particles with inertia in a gravity field). We vary the particles' inertia when there is no gravity, and the particles' drift at constant inertia. We use kinematic simulation (KS) for which large values of the Reynolds number can be achieved. We investigate the pair diffusivity to discuss Richardson's law, and the locality-in-scale hypothesis that underlies that law, for different particle drifts and Stokes numbers. The effect of inertia and gravity on Richardson's law and the autocorrelation in time of the pair's separation are studied for an inertial scale ratio of 1000 and different initial separations delta0 . We extend results from F. Nicolleau and J. C. Vassilicos, Phys. Rev. Lett. 90, 024503 (2003) to three-dimensional (3D) KS and the diffusivity-based analysis of F. Nicolleau and G. Yu, Phys. Fluids 16, 2309 (2004) to particles with inertia and gravity. We find that inertia impedes the locality-in-scale hypothesis whereas gravity improves it. However, the overall effect of gravity and inertia is to decrease the pair's diffusivity in the inertial range.