# Lyapunov exponents of heavy particles in turbulence

@article{Bec2006LyapunovEO,
title={Lyapunov exponents of heavy particles in turbulence},
author={J{\'e}r{\'e}mie Bec and Luca Biferale and Guido Boffetta and Massimo Cencini and Stefano Musacchio and Federico Toschi},
journal={Physics of Fluids},
year={2006},
volume={18},
pages={091702}
}
• Published 8 June 2006
• Physics
• Physics of Fluids
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 counterintuitive 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…
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## References

SHOWING 1-10 OF 28 REFERENCES
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
Intermittent distribution of inertial particles in turbulent flows.
• Physics, Environmental Science
Physical review letters
• 2001
It is shown that the statistics of these fluctuations is independent of details of the velocity statistics, which allows us to predict that the particles cluster on the viscous scale of turbulence and describe the probability distribution of concentration fluctuations.
Intermittent distribution of heavy particles in a turbulent flow
• Physics
• 2004
The retardation of weakly inertial particles depends on the acceleration of the ambient fluid, so the particle concentration n is determined by the divergence of Lagrangian acceleration which we
Intermittency and predictability in turbulence.
• Physics
Physical review letters
• 1993
It is found that the maximum Lyapunov exponent λ and the variance of the effective Lyap unov exponent diverge as a power of the Reynolds number with scaling exponents which can be calculated from the eddy turnover time at the Kolmogorov length using the multifractal approach.
Self-Excitation of Fluctuations of Inertial Particle Concentration in Turbulent Fluid Flow.
• Physics, Environmental Science
Physical review letters
• 1996
It is shown that the growth rates of the higher moments of particle concentration are higher than those of the lower moments, i.e., particle spatial distribution is intermittent and similar phenomena occur for noninertial admixtures advected by divergent turbulent velocity field.
Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence
• Physics, Environmental Science
Journal of Fluid Mechanics
• 1993
The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, has been shown to differ from that in still fluid owing to a bias from the
Clustering instability of the spatial distribution of inertial particles in turbulent flows.
• Physics, Environmental Science
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2002
A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested and a mechanism of saturation of the clustering instability associated with the particles collisions in the clusters is suggested.
Preferential concentration of heavy particles in a turbulent channel flow
• Engineering
• 1994
An investigation of the instantaneous particle concentration at the centerline of a turbulent channel flow has been conducted. The concentration field was obtained by digitizing photographs of
Caustics in turbulent aerosols
• Physics
• 2004
Networks of caustics can occur in the distribution of particles suspended in a randomly moving gas. These can facilitate coagulation of particles by bringing them into close proximity, even in cases
Acceleration statistics of heavy particles in turbulence
• Physics
Journal of Fluid Mechanics
• 2006
We present the results of direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, up to resolution $512^3$ ($R_\lambda\approx 185$). Following