Collision rate of small graupel and water drops

An approach permitting one to calculate the collision efficiency and the co llision kernel of spherical particles of different densities for Reynolds n umbers up to 100 (300-mum-radius drops, or 700-mum-radius graupel) is prese nted. It is used for the calculation of graupel-drop collision efficiencies and collision kernels in calm air for low-, medium-, and high-density grau pel at 750- and 500-mb pressure levels. Low-density graupel interacts with water droplets in a way similar to ice c rystals: there exists a cutoff size, below which graupel cannot collect wat er droplets. The authors have shown that the cutoff size decreases with the growth of graupel density, so that medium- and high-density graupel is abl e to collect droplets with the radii exceeding a certain minimum size. The graupel-drop collision efficiency increases with the drop size up to a maxi mum value and then sharply decreases to zero, when the drops' terminal velo city approaches the terminal velocity of graupel. As soon as the terminal v elocity of drops exceeds that of graupel (so that graupel is captured by dr ops), the collision efficiency experiences a jump to values significantly e xceeding 1, and then decreases rapidly to about 1 with the increase of the drop size. It is shown by means of detailed hydrodynamic calculations that low- and me dium- density graupel particles have significantly lower collision efficien cies with cloud droplets as compared to those of drop collectors of both th e same size or mass as graupel. This result contradicts the widely used int uitive assumption that graupel-drop collision efficiencies are equal to the drop-drop collision efficiencies. Calculations show that the graupel-drop collision kernel increases with hei ght, especially when droplets with the radii under 10 mum are collected. Th e graupel-drop collision efficiencies and kernels for low-, medium-, and hi gh-density graupel are presented in tables.