Through theoretical analysis, Chen and Lamb [1994] showed that the shape of an ice crystal due to depositional growth is controlled by two main factors: 1) the differe nce in the condensation coefficients of the prism and basal faces of the ice crystal, which is primarily a function of temperature, and 2) the difference in fluxes of water vapor to the prism and basal faces of 795 796 RASMUSSEN: A REVIEW OF THEORETICAL AND OBSERVATIONAL STUDIES the crystal. The vapor density gradients around a non-spherical particle and ventilation effects were also considered. Based on this theoretical analysis, a simple parameterization of the shape of an ice crystal grown by vapor deposition was developed that agreed well with previous empirical relations derived from observational data, providing a physical explanation for the observed form of the power law. The exponent of the power law turns out to be identical to the inherent growth rate (the ratio of the basal-face and prism-face condensation coefficients). This scheme was used to simulate the growth of ice crystals under both fixed and time varying conditions, with good agreement with previous results. This parameterization scheme developed on theoretical grounds provides a self-consistent way for understanding the evolution of ice crystal sizes and shapes, and may lead to improved microphysical parameterizations of ice crystal growth and shape in cloud and mesoscale models.
Shapes and Fall Characteristics of HydrometeorsFeng and Beard [1991] developed a perturbation model of raindrop oscillation which includes aerodynamic effects using the method of multiple moments. They show that the characteristic frequencies for the axisymmetric oscillation (oblate-prolate type oscillation) modes increase with increasing flow past the drop, while the sectoral modes (oscillation between ellipsoids with alternating major axis 90° apart in the horizontal plane) decrease. They also suggest that the fine structure in the frequency spectrum of falling drops may play a role in determining which of the two modes mentioned above are dominant for a given raindrop.A general theory for the drag and fall speed of hydrometeors has been developed by Bohm [1992a] which includes the effects of hydrometeor growth and melting on terminal velocity. This theory takes into account continuously varying particle shape and mass, including columnar and branched planar ice crystals, rimed and unrimed aggregates, lump, conical, and hexagonal graupel, hail, and raindrops.
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