By Renata Dmowska, Barry Saltzman

The whole sequence might be within the library of each crew operating in geophysics

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W, v) of the flow velocity vector V can be derived from i/r. On the other hand, using the original momentum equation formulation would require solving for two dependent variables. Unfortunately, the attractiveness of the streamfunction formulation disappears for three-dimensional flows. While it is still possible to define a streamfunction, this function will be a vector instead of a scalar (see, for example, Anderson et ah, 1984). This means that three separate component equations of the streamfunction need to be solved instead of one.

Some investigators have carried out a few such cases. 3. HYDRODYNAMICS OF SMALL ICE PARTICLES 45 Again, more realistic solutions were obtained by numerical methods. , Thom, 1933; Dennis and Chang, 1969, 1970; Hamielec and Raal, 1969; Takami and Keller, 1969; Schlamp et al, 1975). The numerical flow fields around thin oblate spheroids, used to approximate hexagonal ice plates, were obtained by Rimon and Lugt (1969), Masliyah and Epstein (1971), and Fitter et al (1974). All the studies mentioned above have two things in common.

A simulated sample of 15 ice crystals generated by Eq. 4. 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.

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Advances in Geophysics, Vol. 45 by Renata Dmowska, Barry Saltzman
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