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Stochastic models for turbulent diffusion and large-eddy simulations of turbulent fluids flows


The mathematical modelling of turbulent quantities in terms of stochastic differential equations is of increasing importance for efficient flow computations in geophysical and industrial applications Using the Mori-Zwanzig projector formalism from Brownian motion theory, we formally derive exact non-Markovian Langevin models for turbulent diffusion from the Navier-Stokes equations. The first aim, the rigorous formulation of stochastic models for the atmospheric dispersion of contaminants, has almost been completed and emphasizes the fundamental Markofi approximation. Constructing a stochastic process for the Lagrangian velocities consistent with an analytic mean-field theory, unified approach will be developed to stochastic diffusion models, second-order Reynolds stress closures, and subgrid models for large-eddy simulations. Expected novel results are a theoretical derivation of the stochastic backscatter in large-eddy simulations and the explicit Reynolds-number dependence of the model coefficients. All models will be tested numerically against data from direct numerical simulations. Applications to the dispersion of hazardous contaminants, turbulent boundary layers, and combustion problems will be considered

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University of Cambridge
Silver street
CB3 9EW Cambridge
United Kingdom

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