312j

The classical composition probability density function (PDF) for scalars in a turbulent flow field is usually evolved using a Monte Carlo procedure. Notional particles represent the fine-grained PDF and the compositions for each particle satisfy a Langevin equation. In our formulation, the scalar concentrations are further subdivided among different wavenumbers, representing a decomposition into different length scales. Exchanges of scalar from low to high wavenumbers corresponds roughly to transfer and mixing is represented explicitly in this description. The extension of the method to inhomogeneous scalar fields requires each particle move with a velocity that corresponds to the mean velocity plus a fluctuation velocity that is chosen randomly. A consistency condition further requires the particle motion in the direction of the mean scalar gradient be carefully connected to the generation term for the scalar fluctuation. The appropriate constraint has been derived and is enforced in the numerical algorithm. One-dimensional mixing of a scalar slab of varying widths by homogeneous turbulence has been computed and compared to direct numerical simulations. The results highlight advantages the spectral model has over conventional single-point closures of the PDF equations.

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