Clustering in mixing flows

TL;DR

This paper calculates Lyapunov exponents for particles in a 3D random flow, revealing clustering behavior at high Stokes numbers through perturbation series and summation techniques.

Contribution

It provides a novel calculation of Lyapunov exponents for inertial particles in mixing flows, highlighting clustering effects at large Stokes numbers.

Findings

Particles exhibit pronounced clustering at large Stokes numbers.

Accurate Lyapunov exponents obtained via Pade-Borel summation.

Identification of two distinct clustering mechanisms.

Abstract

We calculate the Lyapunov exponents for particles suspended in a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time. In this limit Lyapunov exponents are obtained as a power series in epsilon, a dimensionless measure of the particle inertia. Although the perturbation generates an asymptotic series, we obtain accurate results from a Pade-Borel summation. Our results prove that particles suspended in an incompressible random mixing flow can show pronounced clustering when the Stokes number is large and we characterise two distinct clustering effects which occur in that limit.