A numerical study of the effects of cloud droplets on the diffusional growth of snow crystals

We studied the effect of supercooled cloud droplets on the diffusional growth rate of isolated ice plates and ice columns by approximating the shape of a plate as an oblate spheroid and a column as a prolate spheroid. This work is an extension of the pioneering work of Marshall and Palmer [Marshall, J.S. and Langleben, M.P., A theory of snow-crystal habit and growth, J. Met., 11, 104–120, 1954] who studied the influence of cloud droplets on the growth rate of spherical ice crystals. The vapour density field for oblate and prolate spheroids was obtained by solving Helmholtz's equation with the assumption that the vapour at the ice surface had the equilibrium value. As result, it was possible to calculate separately the temporal evolution of the axis length and the mass of the snow crystals.The results indicate that the presence of cloud droplets around the snow crystal can increase by around 10% of the ice growth rate relative to an environment free of cloud droplets. The magnitude of the growth enhancement is proportional to the liquid water content. The results also corroborate the importance of the shape and aspect ratio on the crystal growth. A general mass growth rate equation for diffusional growth was found, which incorporates effects of cloud droplets and crystal shape through the size and aspect ratio of the snow crystal.