Collision Efficiency of Drops in a Wide Range of Reynolds Numbers: Effects of Pressure on Spectrum Evolution

Abstract

An approach is developed enabling one to calculate the collision efficiency and the collision kernel within a wide range of the Reynolds numbers (from 0 to 100) corresponding to drops up to 300-?m radii. The flow velocity field induced by falling drops is obtained by interpolation of two analytical solutions: the Stokes solution suitable for description of cloud droplets with radii below 30 ?m (Re < 0.4) and the solution given by Hamielec and Johnson suitable for drops with radii ranging from 40 to 300 ?m. The collision efficiency and the collision kernel are calculated at different heights of 1000, 750, and 500 mb. It is shown that both the collision efficiencies and the collision kernel significantly increase with height. This increase of the collision kernel is by 90% caused by the increase in the collision efficiency, and only by 10% is related to the increase of the swept volume. This is because of the high sensitivity of the collision efficiency to the relative drop?drop velocity. The increase of the collision kernel with height is different for different drop pairs. It is maximal for droplets of 5?10 ?m colliding with comparably small drop collectors of 15?25-?m radii. For these drop pairs the collision kernel at the 500-mb level is twice as large as (and even more than) that at the 1000-mb level. The collision efficiencies are calculated and presented in tables, with the high resolution required to describe sharp gradients for small droplets. The drop spectrum broadening and the rate of precipitation formation are found to be sensitive with respect to the variations of the collision rate with height. This is illustrated by solving the stochastic equation of collisions. The increase of the drop?drop collision rate with height turned out to be significant and thus should be incorporated in numerical cloud models. The increase of the collision kernels with height for certain drop sizes can be of much importance in the context of the problem of the effect of ?coalescence nuclei? arising on ultragiant cloud condensation nuclei, on the rain formation. This effect can also be important in rain enhancement by means of hygroscopic seeding. Possible effects of the density of colliding particles and the air density on the rate of riming are discussed.