Effect of particle inertia on the alignment of small ice crystals in turbulent clouds

TL;DR

This paper investigates how particle inertia influences the orientation of small ice crystals in turbulent clouds, revealing that inertia can significantly increase orientation variability and affect alignment depending on turbulence and particle properties.

Contribution

It extends existing overdamped models by incorporating particle inertia effects, providing a more comprehensive understanding of ice crystal orientation in turbulence.

Findings

Particle inertia increases orientation variance of ice crystals.

Strong horizontal alignment occurs only under weak turbulence.

Different asymptotic regimes describe tilt-angle variance dependence.

Abstract

Small non-spherical particles settling in a quiescent fluid tend to orient so that their broad side faces down, because this is a stable fixed point of their angular dynamics at small particle Reynolds number. Turbulence randomises the orientations to some extent, and this affects the reflection patterns of polarised light from turbulent clouds containing ice crystals. An overdamped theory predicts that turbulence-induced fluctuations of the orientation are very small when the settling number Sv (a dimensionless measure of the settling speed) is large. At small Sv, by contrast, the overdamped theory predicts that turbulence randomises the orientations. This overdamped theory neglects the effect of particle inertia. Therefore we consider here how particle inertia affects the orientation of small crystals settling in turbulent air. We find that it can significantly increase the orientation variance, even when the Stokes number St (a dimensionless measure of particle inertia) is quite small. We identify different asymptotic parameter regimes where the tilt-angle variance is proportional to different inverse powers of Sv. We estimate parameter values for ice crystals in turbulent clouds and show that they cover several of the identified regimes. The theory predicts how the degree of alignment depends on particle size, shape and turbulence intensity, and that the strong horizontal alignment of small crystals is only possible when the turbulent energy dissipation is weak, of the order of $1\,$cm$^2$/s$^3$ or less.