INTRODUCTION

As a basic study for the growth process of snowflakes, it is important to analyze the structure and falling motion of early snowflakes, ie those composed of a few crystals. Magono and Oguchi (1955) observed the combined state of crystals in snowflakes and found that branches of dendritic crystals play a leading role in their aggregation. Higuchi (1955, 1960) observed initial growth stages of snowflakes and calculated the probability of aggregation between two crystals of the plane type. Recently, Kajikawa (1982) observed free-fall pattern of early snowflakes by a stereophotogrammetric method. He found that about 80% ?G snowflakes fall with spiral or rotational motion.

The purpose of this study is to analyze relations between the structure and the falling motion of early snowflakes based on previous observation (Kajikawa 1982). The data used in this analysis were obtained at Mt Teine observatory (1024 m a.s.l.) of Hokkaido University, during periods of continuous snowfall. Large snowflakes were not involved.

SNOWFLAKES CONSISTING OF TWO CRYSTALS

To analyze snowflakes consisting of two crystals of the plane type, crystals were divided into seven groups as shown in Table 1. For each group, an experimental ormula of falling velocity vs size of crystals is available (Kajikawa 1975).

Relationship between the sizes of two component crystals of the dendritic type is shown in Figure 1 It seems likely that two crystals of the same shape are similar to each other in size because of the aggregation of two crystals in their initial stage (Nakaya 1954 Higuchi 1955). In the case of different shapes of the dendntic type, the two crystals in each pair are different in size. The characteristics mentioned above also appeared in other groups.

The combined state of component crystals is an important factor affecting falling motion, and hence the aggregation of other snowflakes or crystals. A measure (b) of the combined state of two crystals has been introduced by Higuchi (1960) (Figure 2), where d₁. and d₂ are the sizes of two crystals, and 1 is the distance between their centers.

Table 1. Seven Groups Of The Plane Snow Crystals Classified After The Manner Ofmagono And Lee (1966). N Is The Observed Number Of Snowflakes, Which Were Composed Of Two Crystals Of The Sane Shape.

Figure 3 shows the frequency distribution of S in snowflakes consisting of plane-type crystals The distribution of S for the different shapes is similar to that of Higuchi’s result, although its peak (about 0.65 in S) is larger than his. This means that a smaller crystal attaches near the tips of other crystal because of the large difference in their falling velocities (Kajikawa 1975). On the other hand, in crystals of the same shape, S has a primary peak at about 0.2, with a secondary peak at about 0.65. This suggests that one crvstal attaches near the center of another crystal because of the small difference in their falling velocities.

Kajikawa (1982) found that 70% snowflakes consisting of two crystals show spiral or rotational falling. The relationship between the nondimensional amplitude (a' = a/d) of the spiral motion and S is shown in Figure 4, where a is the amplitude of the spiral path, d the size of the snowflakes. It can be seen that a' for differently shaped crystals is slightly larger than that for similar crystals. Moreover, a' of the same shape is smaller than 2, and hence the period of spiral motion is shorter than 1 second (Kajikawa 1982). These facts suggest that snowflakes consisting of different shapes are more likely to aggregate than other snowflakes or crystals, because of the increased chance of collision due to the larger amplitude of spiral or horizontal motion.

Fig. 1. Relationship between the sizes (d₁>d₂) of two component crystals.

Fig. 2. An example of snowflakes consisting of two dendritic crystals.

Fig. 3. Frequency distribution of S in the snowflakes consisting of plane crystals.

Fig. 4. Relationship between the nondimensional amplitude (a¹) of the spiral motion and S.

SNOWFLAKES CONSISTING OF THREE CRYSTALS

To analyze the combined state of three component crystals, a parameter (A/A_max) was defined as shown in Figures 5 and 6. Here, A is the area of a triangle surrounded by three centers (C₁, C₂ and C₃) of crysuls, and A/A_max is the maximum value of A. From the frequency distribution of A/A _max, it is clear that most of A/A_max is very small, This means that there is a tendency for the centers of three crystals to be arranged in a straight line.

The relationship between the nondimensional amplitude (a'=a/d) of the spiral falling motion and A/A_max is shown in Figure 7. Although the data are scattered, it can be seen that a1 increases with a shift from the straight-line arrangement of the three crystals. Most of a' is smaller than about 2 and not related to the shapes of component crystals.

Fig. 5. An example of snowflakes consisting of three crystals.

Fig. 6. Frequency distribution of A/A_max

Fig. 7. Relationship between the nondimensional amplitude (a¹) of the spiral motion and A/A_max

CONCLUSIONS

Frequency distribution of S (see Figure 2) in snowflakes of the same shape shows a peak at about 0.2. This means that one crystal becomes attached near the center of another crystal because of small difference in their falling velocities. On the other hand, S of a different shape shows a peak at about 0.65, which implies that a smaller crystal becomes attached near the tips of other crystal because of the large difference in their falling velocities.

The nondimensional amplitude of the spiral falling motion in snowflakes consisting of two crystals of different shape is slightly larger than those having crystals of the same shape, This fact suggests that snowflakes consisting of different shapes have an advantage for aggregation over other snowflakes or crystals of the same shape.

In the snowflakes consisting of three crystals, it is probable their centers will be arranged in a straight line. Nondimensional amplitude of the spiral falling motion increases with a shift from the straight-line arrangement of their centers.