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Statistical orientation and distribution of columnar ice crystals in turbulent flows

Alain Pumir1,2,3,*, Muhammad Zubair Sheikh4, Kristian Gustavsson5, Emmanuel Lévêque6, Bernhard Mehlig5, and Aurore Naso6,†

  • *Contact author: alain.pumir@ens-lyon.fr
  • †Contact author: aurore.naso@cnrs.fr
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Phys. Rev. Fluids 11, 064608 – Published 10 June, 2026

DOI: https://doi.org/10.1103/dqkh-1xtd

Abstract

We study the motion of columnar ice crystals that form in clouds over a range of low temperature. Our focus here is on elongated ice crystals, which are smaller than the size of the smallest eddies in the flow, with a moderate aspect ratio comprised between 3 and 5. We determine turbulent solutions of the Navier-Stokes equations over a range of turbulent kinetic energy dissipation characteristic of clouds (4.41cm2/s3≤ɛ≤1120cm2/s3) by using direct numerical simulations, and we follow the motion of crystals using simplified but realistic models for the motion of nonspherical, elongated particles. The influence of the fluid inertia leads to a preferential alignment of the crystals perpendicular to the direction of gravity, the alignment effect being opposed by the turbulent fluctuations. Along with the strong alignment of the crystal axis perpendicular to gravity, we observe only a weak alignment with the vorticity, much weaker than in the absence of gravity. The settling velocity depends only weakly on the orientation of the crystals, but is strongly enhanced when ɛ increases, an effect that we attribute to preferential concentration in the flow. As the inertia of the columnar ice crystals considered here is significant, we observe a strong spatial clustering. Finally, we discuss the relevance of the effects identified here on the collision frequency between ice crystals in cloud conditions.

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Phys. Rev. Fluids 11, 064608– Published 10 June, 2026
  • Received 3 December 2025
  • Accepted 14 May 2026
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