arXiv subjects

Piero Olla

Publications and source records attributed to Piero Olla.

At least 37 records · Page 2Linked to original sources

arXiv2010

Preferential concentration vs. clustering in inertial particle transport by random velocity fields

The concept of preferential concentration in the transport of inertial particles by random velocity fields is extended to account for the possibility of zero correlation time and compressibility of the velocity field. It is shown that, in the case of an uncorrelated in time random velocity field, preferential concentration takes the form of a condition on the field history leading to the current particle positions. This generalized form of preferential concentration appears to be a necessary condition for clustering in the uncorrelated in time case. The standard interpretation of preferential concentration is recovered considering local time averages of the velocity field. In the compressible case, preferential concentration occurs in regions of negative divergence of the field. In the incompressible case, it occurs in regions of simultaneously high strain and negative field skewness.

cond-mat.stat-mech↗

arXiv2008

Renormalized transport of inertial particles in surface flows

Surface transport of inertial particles is investigated by means of the perturbative approach, introduced by Maxey (J. Fluid Mech. 174, 441 (1987)), which is valid in the case the deflections induced on the particle trajectories by the fluid flow can be considered small. We consider a class of compressible random velocity fields, in which the effect of recirculations is modelled by an oscillatory component in the Eulerian time correlation profile. The main issue we address here is whether fluid velocity fluctuations, in particular the effect of recirculation, may produce nontrivial corrections to the streaming particle velocity. Our result is that a small (large) degree of recirculation is associated with a decrease (increase) of streaming with respect to a quiescent fluid. The presence of this effect is confirmed numerically, away from the perturbative limit. Our approach also allows us to calculate the explicit expression for the eddy diffusivity, and to compare the efficiency of diffusive and ballistic transport.

nlin.CD↗

arXiv2008

Clustering and collision of inertial particles in random velocity fields

The influence of clustering on the collision rate of inertial particles in a smooth random velocity field, mimicking the smaller scales of a turbulent flow, is analyzed. For small values of the the ratio between the relaxation time of the particle velocity and the characteristic time of the field, the effect of clusters is to make more energetic collisions less likely. The result is independent of the flow dimensionality and is due only to the origin of collisions in the process of caustic formation.

cond-mat.stat-mech↗

arXiv2008

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.

cond-mat.stat-mech↗

arXiv2008

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.

cond-mat.stat-mech↗

arXiv2007

Return times for Stochastic processes with power-law scaling

An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried on. The calculation is based on an epsilon-expansion in the correlation exponent: C(t)=|t|^{-1+epsilon}. The fixed point of the theory is associated with stretched exponential scaling of the distribution; analytical expressions, valid in the pre-asymptotic regime, have been provided. Also the permanence time distribution appears to be characterized by stretched exponential scaling. The conditions for application of the theory to non-Gaussian processes have been analyzed and the relations with the issue of return times in the case of multifractal measures have been discussed.

cond-mat.stat-mech↗

arXiv2006

Orientation dynamics of weakly Brownian particles in periodic viscous flows

Evolution equations for the orientation distribution of axisymmetric particles in periodic flows are derived in the regime of small but non-zero Brownian rotations. The equations are based on a multiple time scale approach that allows fast computation of the relaxation processes leading to statistical equilibrium. The approach has been applied to the calculation of the effective viscosity of a thin disk suspension in gravity waves.

physics.flu-dyn↗

arXiv2006

Local evolution equations for non-Markovian processes

A Fokker-Planck equation approach for the treatment of non-Markovian stochastic processes is proposed. The approach is based on the introduction of fictitious trajectories sharing with the real ones their local structure and initial conditions. Different statistical quantities are generated by different construction rules for the trajectories, which coincide only in the Markovian case. The merits and limitations of the approach are discussed and applications to transport in ratchets and to anomalous diffusion are illustated.

nlin.CD↗

arXiv2005

Effective viscosity of grease ice in linearized gravity waves

Grease ice is an agglomeration of disc-shaped ice crystals, named frazil ice, which forms in turbulent waters of the Polar Oceans and in rivers as well. It has been recognized that the properties of grease ice to damp surface gravity waves could be explained in terms of the effective viscosity of the ice slurry. This paper is devoted to the study of the dynamics of a suspension of disc-shaped particles in a gravity wave field. For dilute suspensions, depending on the strength and frequency of the external wave flow, two orientation regimes of the particles are predicted: a preferential orientation regime with the particles rotating in coherent fashion with the wave field, and a random orientation regime in which the particles oscillate around their initial orientation while diffusing under the effect of Brownian motion. For both motion regimes, the effective viscosity has been derived as a function of the wave frequency, wave amplitude and aspect ratio of the particles. Model predictions have been compared with wave attenuation data in frazil ice layers grown in wave tanks.

physics.flu-dyn↗

arXiv2004

Some relations between Lagrangian models and synthetic random velocity fields

We propose an alternative interpretation of Markovian transport models based on the well-mixedness condition, in terms of the properties of a random velocity field with second order structure functions scaling linearly in the space time increments. This interpretation allows direct association of the drift and noise terms entering the model, with the geometry of the turbulent fluctuations. In particular, the well known non-uniqueness problem in the well-mixedness approach is solved in terms of the antisymmetric part of the velocity correlations; its relation with the presence of non-zero mean helicity and other geometrical properties of the flow is elucidated. The well-mixedness condition appears to be a special case of the relation between conditional velocity increments of the random field and the one-point Eulerian velocity distribution, allowing generalization of the approach to the transport of non-tracer quantities. Application to solid particle transport leads to a model satisfying, in the homogeneous isotropic turbulence case, all the conditions on the behaviour of the correlation times for the fluid velocity sampled by the particles. In particular, correlation times in the gravity and in the inertia dominated case, respectively, longer and shorter than in the passive tracer case; in the gravity dominated case, correlation times longer for velocity components along gravity, than for the perpendicular ones. The model produces, in channel flow geometry, particle deposition rates in agreement with experiments.

nlin.CD↗

arXiv2002

Particle transport in a random velocity field with Lagrangian statistics

The transport properties of a random velocity field with Kolmogorov spectrum and time correlations defined along Lagrangian trajectories are analyzed. The analysis is carried on in the limit of short correlation times, as a perturbation theory in the ratio, scale by scale, of the eddy decay and turn-over time. Various quantities such as the Batchelor constant and the dimensionless constants entering the expression for particle relative and self-diffusion are given in terms of this ratio and of the Kolmogorov constant. Particular attention is paid to particles with finite inertia. The self-diffusion properties of a particle with Stokes time longer than the Kolmogorov time are determined, verifying on an analytical example the dimensional results of [nlin.CD/0103018]. Expressions for the fluid velocity Lagrangian correlations and correlation times along a solid particle trajectory, are provided in several parameter regimes, including the infinite Stokes time limit corresponding to Eulerian correlations. The concentration fluctuation spectrum and the non-ergodic properties of a suspension of heavy particles in a turbulent flow, in the same regime, are analyzed. The concentration spectrum is predicted to obey, above the scale of eddies with lifetime equal to the Stokes time, a power law with universal -4/3 exponent, and to be otherwise independent of the nature of the turbulent flow. A preference of the solid particle to lie in less energetic regions of the flow is observed.

nlin.CD↗

arXiv2002

Transport properties of heavy particles in high Reynolds number turbulence

The statistical properties of heavy particle trajectories in high Reynolds numbers turbulent flows are analyzed. Dimensional analysis assuming Kolmogorov scaling is compared with the result of numerical simulation using a synthetic turbulence advecting field. The non-Markovian nature of the fluid velocity statistics along the solid particle trajectories is put into evidence, and its relevance in the derivation of Lagrangian transport models is discussed.

nlin.CD↗

arXiv1999

Forces and torques on non-spherical particles in viscous shear flows

The behavior of a non-spherical particle in a viscous, plane channel flow is studied by means of a combination of analytical technique and geometrical reasoning. An efficient implementation of Lamb's general solution is adopted, allowing rapid calculation, in the perturbative quasi-spherical regime, of forces and torques coming from the particle interaction with the flow gradients and from the presence of the walls. Particular attention is given to the role of symmetries in the problem. A classification of the effects of departures from spherical shape on the motion of a particle in various kinds of shear flow is provided. Additional applications to problems involving particles with streaming boundaries are presented.

chao-dyn↗

arXiv1999

The behavior of closed inextensible membranes in linear and quadratic shear flows

The dynamics of a spheroidal vesicle, bounded by an inextensible membrane, is analyzed in function of the enclosed fluid viscosity, and of the membrane mechanical properties. The two situations in which a bending rigidity and a shear elasticity are the potential energy source in the membrane have been compared, and the stability properties of quasi-spherical vesicle shapes discussed. The transition from tank-treading to flipping motion in an external shear flow, has been studied in function of the vesicle internal viscosity and of the strength of the shear quadratic component. The transverse lift strength has been calculated in both cases of a tank-treading and of a flipping motion regime.

chao-dyn↗

arXiv1998

A simplified model for red cell dynamics in small blood vessels

A simple mechanism for the confinement of red cells in the middle of narrow blood vessels is proposed. In the presence of a quadratic shear, red cells deform in such a way to loose fore-aft symmetry and to achieve a fixed orientation with respect to the flow. This leads to a drift away from the vessel walls, when the vessel diameter goes below a critical value depending on the viscoelastic properties and the dimensions of the cell.

chao-dyn↗

arXiv1998

Coherence, space non-locality and lacunarity in a cascade model of turbulence

We use multiscale-multispace correlations and Fourier transform techniques, to study some intermittent random field properties, which escape analysis by structure function scaling. These properties are parametrized in terms of a set of scale ratios, giving the typical interaction distances in space and scale of the random field fluctuations, and the characteristic lengths over which these fluctuations act coherently to generate intermittency. The relevance of these techniques in turbulence theory is discussed.

chao-dyn↗

arXiv1998

Intermittency, synthetic turbulence and wavelet structure functions

Some techniques for the study of intermittency by means of wavelet transforms, are presented on an example of synthetic turbulent signal. Several features of the turbulent field, that cannot be probed looking at standard structure function scaling, become accessible in this way. The concept of a directly measurable intermittency scale, distinct from the scale of the fluctuations, is introduced. A method for optimizing the analyzing wavelets, which exploits this concept, and allows to minimize non-local contributions in scale to wavelet correlations, is described. The transition from a wavelet to a Fourier transform based description of an intermittent random field, and the possibility of using Fourier correlations to measure intermittency are discussed. Important limitations in the ability of structure functions to give a local in scale description of intermittent random fields, are observed.

chao-dyn↗

arXiv1998

Three applications of scaling to inhomogeneous, anisotropic turbulence

The energy spectrum in three examples of inhomogeneous, anisotropic turbulence, namely, purely mechanical wall turbulence, the Bolgiano-Obukhov cascade and helical turbulence, is analyzed. As one could expect, simple dimensional reasoning leads to incorrect results and must be supplemented by informations on the dynamics. In the case of wall turbulence, an hypothesis of Kolmogorov cascade, starting locally from the gradients in the mean flow, produces an energy spectrum which obeys the standard $k^{-{5\over 3}}$ law only for $kx_3>1$, with $x_3$ the distance from the wall, and an inverse power law for $kx_3<1$. An analysis of the energy budget for turbulence in stratified flows, shows the unrealizability of an asymptotic Bolgiano scaling. Simulation with a GOY model, leads instead to a $k^{-α}$ spectrum for both temperature and velocity, with $α\simeq 2$, and a cross-correlation between the two vanishing at large scales. In the case of not reflection invariant turbulence, closure analysis suggests that a purely helical cascade, associated with a $k^{-{7\over 3}}$ energy spectrum cannot take place, unless external forcing terms are present at all scales in the Navier-Stokes equation.

chao-dyn↗