42 research outputs found
The clustering instability of inertial particles spatial distribution in turbulent flows
A theory of clustering of inertial particles advected by a turbulent velocity
field caused by an instability of their spatial distribution is suggested. The
reason for the clustering instability is a combined effect of the particles
inertia and a finite correlation time of the velocity field. The crucial
parameter for the clustering instability is a size of the particles. The
critical size is estimated for a strong clustering (with a finite fraction of
particles in clusters) associated with the growth of the mean absolute value of
the particles number density and for a weak clustering associated with the
growth of the second and higher moments. A new concept of compressibility of
the turbulent diffusion tensor caused by a finite correlation time of an
incompressible velocity field is introduced. In this model of the velocity
field, the field of Lagrangian trajectories is not divergence-free. A mechanism
of saturation of the clustering instability associated with the particles
collisions in the clusters is suggested. Applications of the analyzed effects
to the dynamics of droplets in the turbulent atmosphere are discussed. An
estimated nonlinear level of the saturation of the droplets number density in
clouds exceeds by the orders of magnitude their mean number density. The
critical size of cloud droplets required for clusters formation is more than
m.Comment: REVTeX 4, 15 pages, 2 figures(included), PRE submitte
Reactive dynamics of inertial particles in nonhyperbolic chaotic flows
Anomalous kinetics of infective (e.g., autocatalytic) reactions in open,
nonhyperbolic chaotic flows are important for many applications in biological,
chemical, and environmental sciences. We present a scaling theory for the
singular enhancement of the production caused by the universal, underlying
fractal patterns. The key dynamical invariant quantities are the effective
fractal dimension and effective escape rate, which are primarily determined by
the hyperbolic components of the underlying dynamical invariant sets. The
theory is general as it includes all previously studied hyperbolic reactive
dynamics as a special case. We introduce a class of dissipative embedding maps
for numerical verification.Comment: Revtex, 5 pages, 2 gif figure
Ergodic properties of a model for turbulent dispersion of inertial particles
We study a simple stochastic differential equation that models the dispersion
of close heavy particles moving in a turbulent flow. In one and two dimensions,
the model is closely related to the one-dimensional stationary Schroedinger
equation in a random delta-correlated potential. The ergodic properties of the
dispersion process are investigated by proving that its generator is
hypoelliptic and using control theory
Perturbation theory for large Stokes number particles in random velocity fields
We derive a perturbative approach to study, in the large inertia limit, the
dynamics of solid particles in a smooth, incompressible and finite-time
correlated random velocity field. We carry on an expansion in powers of the
inverse square root of the Stokes number, defined as the ratio of the
relaxation time for the particle velocities and the correlation time of the
velocity field. We describe in this limit the residual concentration
fluctuations of the particle suspension, and determine the contribution to the
collision statistics produced by clustering. For both concentration
fluctuations and collision velocities, we analyze the differences with the
compressible one-dimensional case.Comment: Latex, 12 pages, 2 eps figures include
Particles-vortex interactions and flow visualization in He4
Recent experiments have demonstrated a remarkable progress in implementing
and use of the Particle Image Velocimetry (PIV) and particle tracking
techniques for the study of turbulence in He4. However, an interpretation of
the experimental data in the superfluid phase requires understanding how the
motion of tracer particles is affected by the two components, the viscous
normal fluid and the inviscid superfluid. Of a particular importance is the
problem of particle interactions with quantized vortex lines which may not only
strongly affect the particle motion, but, under certain conditions, may even
trap particles on quantized vortex cores. The article reviews recent
theoretical, numerical, and experimental results in this rapidly developing
area of research, putting critically together recent results, and solving
apparent inconsistencies. Also discussed is a closely related technique of
detection of quantized vortices negative ion bubbles in He4.Comment: To appear in the J Low Temperature Physic