Generative Probability Density Function for Atmospheric Turbulence Flows

Atmospheric turbulence is a paradigm of multiscale complexity, where physical processes interact at different scales. Traditional statistical descriptions, such as Kolmogorov's theory of 1941, only supplant isotropic flow and predict the energy spectrum in the inertial subrange. In contrast, Charles Meneveau's work extends this framework to multifractal models that capture the intermittent and scale-dependent nature of turbulence energy dissipation. Although these models successfully describe the scale-wise distribution of dissipation, they are fundamentally descriptive. In this research, we propose an alternative probabilistic framework for characterizing turbulence by applying probability generating functions (PGFs) and universal generating functions (UGFs). This framework discretizes key aspects of turbulence behavior, enabling a compact representation and systematic combination of probabilistic information across different scales and conditions. Our approach aims to enhance the description of intermittency and variability in atmospheric turbulence and may provide a complementary perspective to traditional distribution-fitting techniques.