The Effect of Turbulence on the Collision Rates of Small Cloud Drops.
Abstract
The role of turbulence in the process of collision and coalescence of small cloud droplets is still an outstanding problem in the area of cloud physics. In particular, the growth of droplets in the radius range for 10 to 15 μm is not well understood. The present research has been motivated by the curiosity whether or not turbulence affects the growth rate of such small drops. We developed a method to calculate collision rates of small hydrodynamically interacting drops embedded in an external flow field; we call it the flux method. Then, the method was tested for simple cases of laminar flows such as linear shear and a twodimensional deformation field. The tests were designed not only to validate the method but also to examine the mechanisms associated with the simplified types of external flows which may be equally important for real turbulent flows. In order to obtain estimates of collision rates for turbulent flows, the flux method was used in conjunction with a probabilistic approach. Numerous simulations of trajectories of two hydrodynamically interacting droplets in a turbulent field were carried out. The ratio of the number of collisions to the total number of simulations gave the probability of collision for different relative positions of the drops. Because the Reynolds number of the flow around droplets (based on the drop radius and terminal velocity) is small, the trajectories were calculated with the help of a model based on the linear Stokes hydrodynamics. Turbulence was modelled in the form of random Fourier modes with both the space and the time spectrum prescribed. Both spectra were characterized by Kolmogorov scaling. The space spectrum was modelled in the inertial and dissipation subranges. On the basis of scale analysis, only small scale time variations were allowed, and, the so called EulerianLagrangrian time spectrum was applied. The results show that most collision rates increase moderately in a turbulent flow characterized by a rate of energy dissipation of the order of 1, 10, and 100 cm ^2 sec^{3}. The estimated increase in collision efficiencies, however, is not uniform, and a rather complicated relation between the increase in the collision efficiency and the parametersthe drop radii, and the rate of energy dissipation can be observed.
 Publication:

Ph.D. Thesis
 Pub Date:
 1995
 Bibcode:
 1995PhDT.......172K
 Keywords:

 Physics: Atmospheric Science