On the hydrodynamic behavior of supercooled water drops interacting with columnar ice crystals

A numerical evaluation of the complete Navier-Stokes equations of motion for steady-state, incompressible flow past an infinite circular cylinder is given in terms of the stream function, vorticity, and pressure distribution past such bodies. A method is described which allows use of these flow characteristics: (1) to approximate the characteristics of air flow past hexagonal columnar ice crystals falling under gravity at terminal velocity in air, (2) to compute the trajectory of supercooled cloud drops relative to such ice crystals, and (3) to determine the efficiency with which short columnar ice crystals and needle shaped ice crystals collide with supercooled cloud drops. It is found that for all columnar type ice crystals riming is negligible if the cloud drop size is less than 5 m, and that for riming to commence short columnar crystals must have diameters larger than 50 m, while needle crystals must have diameters larger than 40 m. It is further shown that the collision efficiency cut-offs at the small drop radius and at the large drop radius end of the collision efficiency diagram can be explained on the basis of the cloud drop trajectories for these drop size ranges.