Longitudinal impact of cylindrical shells with discontinuous cross-sectional area.
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The relation between glory undulations and the detailed nature of the potential energy of interaction of two molecules having a minimum containing one or more bound states is clarified, i.e., a physical interpretation is given to the undulations. Although the number, amplitude, and spacing of the oscillations all give information about the potential, the spacing is most often used because it can be most accurately measured. Results are given which show fairly explicitly just what information on the interaction potential is contained in the spacing of the glory oscillations. Glory oscillations put strong known constraints on any potential model.
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The behavior of vortex flow at high swirls is investigated. The problem was first formulated in the method of weighted residuals, using Bessel functions as approximating functions. Convergent solutions require a large number of steps in the axial direction and do not seem to offer an advantage over traditional methods. As the results do not differ substantially from those of the zeroth approximation (the solution for 'cylindrical' flow), this approximation is then explored and discussed in more detail. It is used to derive a relationship predicting a critical radius for which stagnation on the axis (vortex breakdown) can be expected for a given swirl. Flow patterns with open and closed vortex bubbles are explored. At high swirls, even minute variations in outer streamtube radius have profound effects on the flow. Vortex breakdown bubbles in divergences, tubes, and free flows can be explained.
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