Turbulent pair dispersion of inertial particles

Abstract

The relative dispersion of pairs of inertial particles in incompressible, homogeneous, and isotropic turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Reλ∼200 and 400. The evolution of both heavy and light particle pairs is analysed at varying the particle Stokes number and the fluid-to-particle density ratio. For heavy particles, it is found that turbulent dispersion is schematically governed by two temporal regimes. The first is dominated by the presence, at large Stokes numbers, of small-scale caustics in the particle velocity statistics, and it lasts until heavy particle velocities have relaxed towards the underlying flow velocities. At such large scales, a second regime starts where heavy particles separate as tracers particles would do. As a consequence, at increasing inertia, a larger transient stage is observed, and the Richardson diffusion of simple tracers is recovered only at large times and large scales. These features also arise from a statistical closure of the equation of motion for heavy particle separation that is proposed, and which is supported by the numerical results. In the case of light particles with high density ratios, strong small-scale clustering leads to a considerable fraction of pairs that do not separate at all, although the mean separation increases with time. This effect strongly alters the shape of the probability density function of light particle separations

Anisotropy in pair dispersion of inertial particles in turbulent channel flow

“…The departure of inertial particles from tracers behavior is remarkable, covers roughly the first three crossing times and is made clearly evident by virtue of the small initial distance imposed to paired tracers/particles (note that d 0 is always smaller than the local Kolmogorov length scale). Similar findings have been reported in previous studies 32, 51 yet for homogeneous isotropic turbulent flow. For this flow instance, the observed differences from the tracer behavior were attributed to the occurrence of caustics 31,52 which give singular contributions to the particle velocity increments inside the viscous range thus making the particle velocity difference with respect to the underlying fluid large.…”

“…For this flow instance, the observed differences from the tracer behavior were attributed to the occurrence of caustics 31,52 which give singular contributions to the particle velocity increments inside the viscous range thus making the particle velocity difference with respect to the underlying fluid large. 32 More specifically, it was found that turbulent dispersion of heavy particles is governed by two temporal regimes: the first is dominated by small-scale caustics in the particle velocity statistics, the second starts once particle velocity has relaxed towards fluid velocity and the usual Richardson dispersion is observed for both particles and tracers. 32 Counter to intuition, present results seem to indicate that the behavior just mentioned is macroscopically recovered when pairs are released in the near-wall region, where anisotropy and flow inhomogeneities dominate, rather than in the channel centerline, where turbulence becomes more homogeneous and isotropic.…”

“…17,[29][30][31] From a modelling standpoint, reproducing accurately pair relative velocity and dispersion statistics is crucial to predict the effect of particle clustering on turbulent collisions and sedimentation. 17 In a series of recent papers, 32,33 Bec and co-workers characterized the relative dispersion of heavy point particles in homogeneous isotropic turbulence, focusing specifically on the scaling of particle velocity distribution at changing the degree of inertia in the different dispersive regimes (dissipative, inertial, and diffusive). A further complication is the presence of shear, which stretches the distance between particles and is expected to induce strong deviations from the usual diffusion laws.…”

Pair separation of magnetic elements in the quiet Sun

“…This is for instance the case of the celebrated Richardson diffusion (Richardson 1926) for homogeneous and isotropic turbulent flows in the range of spatial scales where the velocity obeys a Kolmogorov 1941 turbulent cascade (Frisch 1995). In this case it is predicted and observed the presence of a super-diffusion with γ = 3 and self-similar Richardson-like PDF (Jullien et al 1999;Falkovich 2001;Yeung & Borgas 2004;Monin & Yaglom 2007;Salazar & Collins 2009;Bec et al 2010). Similarly, it is known that in the presence of a spatially smooth velocity field with very long temporal correlation, there might be an anomalous (super-or sub-) diffusion (see, e.g., the pioneering works of Geisel et al 1985;Avellaneda & Majda 1992;Zaslavsky et al 1993).…”

Detection of turbulent thermal diffusion of particles in numerical simulations

“…Numerous laboratory [4,[13][14][15][16][17] and numerical [18][19][20][21][22][23][24] experiments as well as observations in atmospheric [6,8,25,26] and astrophysical [9-12, 27, 28] turbulent flows have shown different kinds of large-scale and smallscale long-living inhomogeneities (clusters) in the spatial distribution of particles. It is well known that turbulent diffusion causes destruction of large-scale inhomogeneities in the spatial distributions of particles.…”