Behavior of large waterdrops in shear flow

Abstract

Nondimensionalized equations of motion for waterdrops, not necessarily obeying Stokes's law, are derived and used to calculate the response of various size drops to changes in horizontal wind speed. We find that (1) cloud drops respond almost instantaneously to changes in wind speed, whereas raindrops require considerable time to adjust, (2) one can ignore the dependence of drag coefficient on Reynolds number in small shear, and (3) the probability of collision between raindrops and cloud drops is likely to be increased very slightly by the presence of wind shear. Waterdrops of different sizes falling through a fluid will respond differently to vertical shears in the horizontal mean flow, and their subsequent trajectories will differ from those in a uniform flow. The_ problem of determining the responses is fairly simple if the drop size is in the Stokes law region but bec. omes more complicated for larger drops. Fuchs [1964] presented some equations for aerosol motion at high Reynolds number in still air that require graphical solution. We have reformulated the problem and solved the nonlinear equations numerically. The equations show that vertical and horizontal motions are coupled unless the drag is a linear function of air speed, as it is in the Stokes law regime. The shear flow problems examined in this report are confined to linear wind speed gradients. The special case of raindrops falling through a logarithmic wind profile near the ground was examined in another paper [Caldwell and Elliott, 1971]. In the present study we include drops ranging in size from the Stokes law region (maximum radius of ~0.004 cm) through large raindrops, and we consider specifically the Reynolds number dependence of the drag coefficient. All the pertinent physical data are from List [1966], and thus it is assumed that the drag coefficients are not affected by accelerations. Ogden and Jayaweera [1971] have found experimentally that for very large accelerations the drag coefficient of a waterdrop appears to be about 20% less than the unaccelerated value. This decrease in drag would affect Copyright () 1973 by the American Geophysical Union. these calculations only quantitatively and would be significant only for shears much larger than those likely to be found in natural atmospheric ./