Distribution of velocity gradients and rate of caustic formation in turbulent aerosols at finite Kubo numbers

TL;DR

This paper analyzes the distribution of velocity gradients and caustic formation rates in turbulent aerosols using a one-dimensional model, highlighting effects of finite Kubo numbers and non-ergodic dynamics.

Contribution

It extends previous models by computing distributions at finite Kubo numbers for arbitrary Stokes numbers, incorporating finite-time correlations and non-ergodic effects.

Findings

Distributions are consistent with earlier limits for small Ku and large St.

Finite-time correlations significantly influence particle dynamics.

Non-ergodic effects alter the rate of caustic formation.

Abstract

In a one-dimensional model for a turbulent aerosol (inertial particles suspended in a random flow) we compute the distributions of particle-velocity gradients and the rate of caustic formation at finite but small Kubo numbers Ku, for arbitrary Stokes numbers St. Our results are consistent with those obtained earlier in the limit of small Ku and and large St, such that Ku^2 St remains constant. We show how finite-time correlations and non-ergodic effects influence the inertial-particle dynamics at finite but small Kubo numbers.