Multipoint statistical structure of the ideal spray .1. Fundamental concepts and the realization density

In this study we develop the theoretical framework required for analysis of the time-based multipoint statistics of sprays. This is accomplished in the context of the ideal spray-a random assemblage of droplets modeled as noninteracting point particles. It is shown that such a spray may be decomposed into a series of independent single-class sprays, each of which is driven by an inhomogeneous temporal Poisson process. Complete spray behavior is found by superposition of these processes. A function is derived that contains all possible information about one of these single-class sprays, the realization density. All of the customary multipoint statistics-the autocorrelation, power spectral density, fluctuation moments, etc.-may be developed from the realization density by suitable integrations over its probability space. Derivations of these quantities from the realization density are reported in a series of companion articles.