By Renata Dmowska, Barry Saltzman
The complete sequence may be within the library of each team operating in geophysics
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Additional info for Advances in Geophysics, Vol. 45
A radiating dendrite generated by Eq. 001. 30 PAO K. WANG Fitting observed 3-D crystals by the above expressions is analogous to the procedure for 2-D crystals, except the measurements may be difficult to perform as mentioned previously. The easiest way to do this is probably by measuring the 2-D projection of the crystals and then performing the fitting process for the 2-D crystals as described in Wang and Denzer (1983) and Wang (1987). Since the expressions given here generate polygonally symmetric shapes, it should be easy to obtain a 2-D projection.
19), while a, C, and X are parameters to be determined. The parameters a and C have dimensions of length whereas A is a dimensionless number; C is one-half the length from the apex to the bottom along the z-axis, the center point being defined as the origin O, and a is defined in the following paragraph. 26) is the equation of an ellipse whose semi-axes in the x and z directions are a and C, respectively. Therefore, Eq. 25) can be thought of as an ellipse modulated FIG. 19. Definitions of the coordinate system and various quantities appearing in Eq.
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.