Behavoir of a Very Large Number of Constant-Volume Trajectories

A numerical experiment is performed with the purpose of investigating the behavior of the trajectories of a very large number of constant-volume particles. Practical significance is given to this problem by the possibility of using superpressured, constant-volume balloons for routine upper air observations. The computational scheme of the experiment is described with emphasis on some aspects of trajectory computations. Thirty-day diagnostic trajectories are computed for two levels using the total velocity components, and for one level using only the nondivergent ones, and the resulting spacing of the trajectory points is discussed. Theory of the distances to the nearest among a large number of points is developed and applied for the statistical description of the results. Histograms of distances from the constant-volume particles as well as from random points in space to the nearest neighboring constant-volume particle are computed, and compared with the frequency function of those distances for ...