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2. 5 FIG. 2. U . A 2-D columnar crystal (in reality, a rectangle) generated by Eq. 14) with a = 2 and c = 1. We note that the cross section of a finite circular cylinder through its axis is a rectangle. If we can find an equation closely approximating the rectangle, then rotating the resulting curve along its long axis will yield a close approximation of a finite circular column. 14) where x and z are the common Cartesian coordinates; a and c are the half-lengths in the x and z direction, respectively; and s is an adjustable positive parameter that can be set as small as we wish (but never equal to zero)^ to closely fit the sharp comers of a rectangle.

For example, Braza et al. (1986) achieved this on a two-dimensional cylinder by performing a rotation of the cylinder along its axis. 3. The directions of the perturbation are opposite each other in the regions A and B so as to form a shear along the central plane of the flow. As we shall see, at high enough Reynolds numbers, this perturbation will generate a periodic eddy shedding pattern in the simulated flow. On the other hand, the perturbation will be damped out in a short time if the Reynolds number is low.

33) z=zm where Zm is the z-coordinate of the maximum point. 34 PAO K. 37) may be subject to errors and deviations and may be smaller than 1 occasionally. In this case we have to set k = 1. 4. Sometimes it is desirable to calculate x^ and Zm from a given combination of a, C, and k. 4. 3. Examples and Discussion Using the above steps, I have tried to fit many conical graupel and hailstones documented in the literature. 20 shows two examples taken from Mason (1971) and one from Iribame and Cho (1979).