Concentration fluctuations of large Stokes number particles in a one-dimensional random velocity field

TL;DR

This paper develops an analytical framework to understand how inertial particles with large Stokes numbers behave in a one-dimensional Gaussian velocity field, revealing significant concentration fluctuations and altered collision dynamics.

Contribution

It introduces a perturbative scheme for calculating concentration correlations and relative velocities of inertial particles in finite correlation time fields, extending previous models.

Findings

Concentration fluctuations decay slowly at large inertia.

Correlation length of fluctuations exceeds that of the velocity field.

Velocity space structure differs from short-time correlated models.

Abstract

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.