MULTIPOINT STATISTICAL STRUCTURE OF THE IDEAL SPRAY .1. FUNDAMENTAL-CONCEPTS AND THE REALIZATION DENSITY

In this study we develop the theoretical framework required for analys is of the time-based multipoint statistics of sprays. This is accompli shed in the context of the ideal spray-a random assemblage of droplets modeled as noninteracting point particles. It is shown that such a sp ray 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 o ne of these single-class sprays, the realization density. All of the c ustomary multipoint statistics-the autocorrelation, power spectral den sity, fluctuation moments, etc.-may be developed from the realization density by suitable integrations over its probability space. Derivatio ns of these quantities from the realization density are reported in a series of companion articles.