Description of clustering of inertial particles in turbulent flows via finite-time Lyapunov exponents

Abstract

An asymptotic solution is derived for the motion of inertial particles exposed to Stokes drag in an unsteady random flow. This solution provides the finite-time Lyapunov exponents as a function of Stokes number and Lagrangian strain- and rotation-rates autocovariances. The sum of these exponents, which corresponds to a concentration-weighted divergence of particle velocity field, is considered as a measure of clustering. For inertial particles dispersed in an isotropic turbulent flow our analysis predicts maximum clustering at an intermediate Stokes number and minimal clustering at small and large Stokes numbers. Direct numerical simulations are performed for quantitative validation of our analysis, showing a reasonable agreement between the two.

11 pages and 4 figures

References in corpus (4)

• Heavy particle concentration in turbulence at dissipative and inertial scales
• Multifractal concentrations of inertial particles in smooth random flows
• Lyapunov exponents of heavy particles in turbulence
• Quantifying turbulence induced segregation of inertial particles

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• Restricted Euler dynamics along trajectories of small inertial particles in turbulence
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• Investigating the magnitude and temporal localization of inertial particle mixing in turbulent channel flows