Concentration fluctuations of large Stokes number particles in a one-dimensional random velocity field

We analyze the behavior of an ensemble of inertial particles in a one-dimensional smooth Gaussian velocity field, in the limit of large inertia, but considering a finite correlation time for the random field. We derive in this limit a perturbative scheme for the calculation of the concentration correlation and of the particle relative velocity distribution, providing analytical expressions for the concentration fluctuation amplitude, its correlation length, and the modification in the particle pair relative velocity variance. The amplitude of the concentration fluctuations is characterized by slow decay at large inertia and a much larger correlation length than that of the random field. The fluctuation structure in velocity space is very different from predictions from short-time correlated random velocity fields, with only few particle pairs crossing at sufficiently small relative velocity to produce correlations. Concentration fluctuations are associated with depletion of the relative velocity variance of colliding particles.Comment: 8 pages, 1 figure, revtex

Chaotic diffusion of particles with finite mass in oscillating convection flows

Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor. The diffusion constants are numerically calculated for convection models with free and rigid boundary conditions.Comment: 5 figure

Continuum description of finite-size particles advected by external flows. The effect of collisions

The equation of the density field of an assembly of macroscopic particles advected by a hydrodynamic flow is derived from the microscopic description of the system. This equation allows to recognize the role and the relative importance of the different microscopic processes implicit in the model: the driving of the external flow, the inertia of the particles, and the collisions among them. The validity of the density description is confirmed by comparisons of numerical studies of the continuum equation with Direct Simulation Monte Carlo (DSMC) simulations of hard disks advected by a chaotic flow. We show that the collisions have two competing roles: a dispersing-like effect and a clustering effect (even for elastic collisions). An unexpected feature is also observed in the system: the presence of collisions can reverse the effect of inertia, so that grains with lower inertia are more clusterized.Comment: Final (strongly modified) version accepted in PRE; 6 pages, 3 figure

Clustering in mixing flows

We calculate the Lyapunov exponents for particles suspended in a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time. In this limit Lyapunov exponents are obtained as a power series in epsilon, a dimensionless measure of the particle inertia. Although the perturbation generates an asymptotic series, we obtain accurate results from a Pade-Borel summation. Our results prove that particles suspended in an incompressible random mixing flow can show pronounced clustering when the Stokes number is large and we characterise two distinct clustering effects which occur in that limit.Comment: 5 pages, 1 figur

Turbulent thermal diffusion in a multi-fan turbulence generator with the imposed mean temperature gradient

We studied experimentally the effect of turbulent thermal diffusion in a multi-fan turbulence generator which produces a nearly homogeneous and isotropic flow with a small mean velocity. Using Particle Image Velocimetry and Image Processing techniques we showed that in a turbulent flow with an imposed mean vertical temperature gradient (stably stratified flow) particles accumulate in the regions with the mean temperature minimum. These experiments detected the effect of turbulent thermal diffusion in a multi-fan turbulence generator for relatively high Reynolds numbers. The experimental results are in compliance with the results of the previous experimental studies of turbulent thermal diffusion in oscillating grids turbulence (Buchholz et al. 2004; Eidelman et al. 2004). We demonstrated that turbulent thermal diffusion is an universal phenomenon. It occurs independently of the method of turbulence generation, and the qualitative behavior of particle spatial distribution in these very different turbulent flows is similar. Competition between turbulent fluxes caused by turbulent thermal diffusion and turbulent diffusion determines the formation of particle inhomogeneities.Comment: 9 pages, 9 figure, REVTEX4, Experiments in Fluids, in pres

Dissipative chaotic scattering

We show that weak dissipation, typical in realistic situations, can have a metamorphic consequence on nonhyperbolic chaotic scattering in the sense that the physically important particle-decay law is altered, no matter how small the amount of dissipation. As a result, the previous conclusion about the unity of the fractal dimension of the set of singularities in scattering functions, a major claim about nonhyperbolic chaotic scattering, may not be observable.Comment: 4 pages, 2 figures, revte

Singular Scaling Functions in Clustering Phenomena

We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size.This scaling function is singular for small argument -- it exhibits a cusp singularity for particles with mutual exclusion, and a divergence for noninteracting particles. The steady state is characterized by giant fluctuations which do not damp down in the thermodynamic limit. The autocorrelation function is a singular scaling function of time and system size. The scaling properties are surprisingly similar to those for particles moving in a quenched disordered environment that results if the surface is frozen.Comment: 8 pages, 3 figures, Invited talk delivered at Statphys 23, Genova, July 200

Size-selective concentration of chondrules and other small particles in protoplanetary nebula turbulence

Size-selective concentration of particles in a weakly turbulent protoplanetary nebula may be responsible for the initial collection of chondrules and other constituents into primitive body precursors. This paper presents the main elements of this process of turbulent concentration. In the terrestrial planet region, both the characteristic size and size distribution of chondrules are explained. "Fluffier" particles would be concentrated in nebula regions which were at a lower gas density and/or more intensely turbulent. The spatial distribution of concentrated particle density obeys multifractal scaling}, suggesting a close tie to the turbulent cascade process. This scaling behavior allows predictions of the probability distributions for concentration in the protoplanetary nebula to be made. Large concentration factors (>10^5) are readily obtained, implying that numerous zones of particle density significantly exceeding the gas density could exist. If most of the available solids were actually in chondrule sized particles, the ensuing particle mass density would become so large that the feedback effects on gas turbulence due to mass loading could no longer be neglected. This paper describes the process, presenting its basic elements and some implications, without including the effects of mass loading.Comment: 34 pages, 7 figures; in press for Astrophys. J; expected Jan 01 2001 issu

Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems

We show that, even in the most favorable case, the motion of a small spherical tracer suspended in a fluid of the same density may differ from the corresponding motion of an ideal passive particle. We demonstrate furthermore how its dynamics may be applied to target trajectories in Hamiltonian systems.Comment: See home page http://lec.ugr.es/~julya