728 research outputs found
Fractal clustering of inertial particles in random flows
It is shown that preferential concentrations of inertial (finite-size)
particle suspensions in turbulent flows follow from the dissipative nature of
their dynamics. In phase space, particle trajectories converge toward a
dynamical fractal attractor. Below a critical Stokes number (non-dimensional
viscous friction time), the projection on position space is a dynamical fractal
cluster; above this number, particles are space filling. Numerical simulations
and semi-heuristic theory illustrating such effects are presented for a simple
model of inertial particle dynamics.Comment: 4 pages, 4 figures, Physics of Fluids, in pres
Timescales of Turbulent Relative Dispersion
Tracers in a turbulent flow separate according to the celebrated
Richardson--Obukhov law, which is usually explained by a scale-dependent
effective diffusivity. Here, supported by state-of-the-art numerics, we revisit
this argument. The Lagrangian correlation time of velocity differences is found
to increase too quickly for validating this approach, but acceleration
differences decorrelate on dissipative timescales. This results in an
asymptotic diffusion of velocity differences, so that the
long-time behavior of distances is that of the integral of Brownian motion. The
time of convergence to this regime is shown to be that of deviations from
Batchelor's initial ballistic regime, given by a scale-dependent energy
dissipation time rather than the usual turnover time. It is finally argued that
the fluid flow intermittency should not affect this long-time behavior of
relativeComment: 4 pages, 3 figure
Universality of Velocity Gradients in Forced Burgers Turbulence
It is demonstrated that Burgers turbulence subject to large-scale
white-noise-in-time random forcing has a universal power-law tail with exponent
-7/2 in the probability density function of negative velocity gradients, as
predicted by E, Khanin, Mazel and Sinai (1997, Phys. Rev. Lett. 78, 1904). A
particle and shock tracking numerical method gives about five decades of
scaling. Using a Lagrangian approach, the -7/2 law is related to the shape of
the unstable manifold associated to the global minimizer.Comment: 4 pages, 2 figures, RevTex4, published versio
Clustering and collisions of heavy particles in random smooth flows
Finite-size impurities suspended in incompressible flows distribute
inhomogeneously, leading to a drastic enhancement of collisions. A description
of the dynamics in the full position-velocity phase space is essential to
understand the underlying mechanisms, especially for polydisperse suspensions.
These issues are here studied for particles much heavier than the fluid by
means of a Lagrangian approach. It is shown that inertia enhances collision
rates through two effects: correlation among particle positions induced by the
carrier flow and uncorrelation between velocities due to their finite size. A
phenomenological model yields an estimate of collision rates for particle pairs
with different sizes. This approach is supported by numerical simulations in
random flows.Comment: 12 pages, 9 Figures (revTeX 4) final published versio
Acceleration statistics of heavy particles in turbulence
We present the results of direct numerical simulations of heavy particle
transport in homogeneous, isotropic, fully developed turbulence, up to
resolution (). Following the trajectories of up
to 120 million particles with Stokes numbers, , in the range from 0.16 to
3.5 we are able to characterize in full detail the statistics of particle
acceleration. We show that: ({\it i}) The root-mean-squared acceleration
sharply falls off from the fluid tracer value already at quite
small Stokes numbers; ({\it ii}) At a given the normalised acceleration
increases with consistently
with the trend observed for fluid tracers; ({\it iii}) The tails of the
probability density function of the normalised acceleration
decrease with . Two concurrent mechanisms lead to the above results:
preferential concentration of particles, very effective at small , and
filtering induced by the particle response time, that takes over at larger
.Comment: 10 pages, 3 figs, 2 tables. A section with new results has been
added. Revised version accepted for pubblication on Journal of Fluid
Mechanic
Dynamics and statistics of heavy particles in turbulent flows
We present the results of Direct Numerical Simulations (DNS) of turbulent
flows seeded with millions of passive inertial particles. The maximum Taylor's
Reynolds number is around 200. We consider particles much heavier than the
carrier flow in the limit when the Stokes drag force dominates their dynamical
evolution. We discuss both the transient and the stationary regimes. In the
transient regime, we study the growt of inhomogeneities in the particle spatial
distribution driven by the preferential concentration out of intense vortex
filaments. In the stationary regime, we study the acceleration fluctuations as
a function of the Stokes number in the range [0.16:3.3]. We also compare our
results with those of pure fluid tracers (St=0) and we find a critical behavior
of inertia for small Stokes values. Starting from the pure monodisperse
statistics we also characterize polydisperse suspensions with a given mean
Stokes.Comment: 13 pages, 10 figures, 2 table
Lyapunov exponents of heavy particles in turbulence
Lyapunov exponents of heavy particles and tracers advected by homogeneous and
isotropic turbulent flows are investigated by means of direct numerical
simulations. For large values of the Stokes number, the main effect of inertia
is to reduce the chaoticity with respect to fluid tracers. Conversely, for
small inertia, a counter-intuitive increase of the first Lyapunov exponent is
observed. The flow intermittency is found to induce a Reynolds number
dependency for the statistics of the finite time Lyapunov exponents of tracers.
Such intermittency effects are found to persist at increasing inertia.Comment: 4 pages, 4 figure
"Locally homogeneous turbulence" Is it an inconsistent framework?
In his first 1941 paper Kolmogorov assumed that the velocity has increments
which are homogeneous and independent of the velocity at a suitable reference
point. This assumption of local homogeneity is consistent with the nonlinear
dynamics only in an asymptotic sense when the reference point is far away. The
inconsistency is illustrated numerically using the Burgers equation.
Kolmogorov's derivation of the four-fifths law for the third-order structure
function and its anisotropic generalization are actually valid only for
homogeneous turbulence, but a local version due to Duchon and Robert still
holds. A Kolomogorov--Landau approach is proposed to handle the effect of
fluctuations in the large-scale velocity on small-scale statistical properties;
it is is only a mild extension of the 1941 theory and does not incorporate
intermittency effects.Comment: 4 pages, 2 figure
Geometry and violent events in turbulent pair dispersion
The statistics of Lagrangian pair dispersion in a homogeneous isotropic flow
is investigated by means of direct numerical simulations. The focus is on
deviations from Richardson eddy-diffusivity model and in particular on the
strong fluctuations experienced by tracers. Evidence is obtained that the
distribution of distances attains an almost self-similar regime characterized
by a very weak intermittency. The timescale of convergence to this behavior is
found to be given by the kinetic energy dissipation time measured at the scale
of the initial separation. Conversely the velocity differences between tracers
are displaying a strongly anomalous behavior whose scaling properties are very
close to that of Lagrangian structure functions. These violent fluctuations are
interpreted geometrically and are shown to be responsible for a long-term
memory of the initial separation. Despite this strong intermittency, it is
found that the mixed moment defined by the ratio between the cube of the
longitudinal velocity difference and the distance attains a statistically
stationary regime on very short timescales. These results are brought together
to address the question of violent events in the distribution of distances. It
is found that distances much larger than the average are reached by pairs that
have always separated faster since the initial time. They contribute a
stretched exponential behavior in the tail of the inter-tracer distance
probability distribution. The tail approaches a pure exponential at large
times, contradicting Richardson diffusive approach. At the same time, the
distance distribution displays a time-dependent power-law behavior at very
small values, which is interpreted in terms of fractal geometry. It is argued
and demonstrated numerically that the exponent converges to one at large time,
again in conflict with Richardson's distribution.Comment: 21 page
Population dynamics at high Reynolds number
We study the statistical properties of population dynamics evolving in a
realistic two-dimensional compressible turbulent velocity field. We show that
the interplay between turbulent dynamics and population growth and saturation
leads to quasi-localization and a remarkable reduction in the carrying
capacity. The statistical properties of the population density are investigated
and quantified via multifractal scaling analysis. We also investigate
numerically the singular limit of negligibly small growth rates and
delocalization of population ridges triggered by uniform advection.Comment: 5 pages, 5 figure
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