Alignment of ice crystals settling in turbulent clouds

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 non-zero, but 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 [Gustavsson et al, New Journal of Physics 21 (2019) 083008] 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, and in this work, we consider how this effect affects the orientation of small crystals settling in turbulent air. With the help of analytic as well as numerical methods, we find that particle inertia 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. Parameter values for ice crystals in turbulent clouds lie near the boundaries between these regions; ice crystal-alignment in such clouds is unlikely to follow a simple power law. The theory predicts how the degree of alignment depends on particle size, shape, and turbulence intensity. We compare our results with those of an alternative theory [Klett, JAS 52 (1995) 2276].