# Laboratoire de Mécanique des Fluides et d’Acoustique - UMR 5509

LMFA - UMR 5509
Laboratoire de Mécanique des Fluides et d’Acoustique
Lyon
France

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Article dans J. Atmos. Sci. (2021)

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

K. Gustavsson, M. Z. Sheikh, A. Naso, A. Pumir & B. Mehlig

Small nonspherical 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 randomizes the orientations to some extent, and this affects the reflection patterns of polarized 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 randomizes 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, on the order of $1\; \mathrm{cm}^2\, \mathrm{s}^{−3}$ or less.

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