Asymptotic Modelling of Fluid Flow Phenomena

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This work delves into the stochastic modeling of fluctuations in incompressible systems, inspired by discussions with J. P. Guiraud. It explores the relationship between large eddy behavior and probability space, deriving Reynolds stresses through a Monte-Carlo process applied to fluctuation equations. By employing a random set of equations that replicate large eddy fluctuations, the authors utilize stochastic averaging to analyze solutions. The underlying asymptotic principles are subtly connected to homogenization and localization processes, offering a novel perspective on fluid dynamics.