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Published October 1981 | Published
Journal Article Open

A differentiable trajectory approximation to turbulent diffusion


The problem of turbulent diffusion is posed as determining the time evolution of the probability density of the concentration given those for the fluid velocity components, sources, and the initial concentration. At each time, all variables are elements of the Hilbert space L^2_R(R^3), and a finite-dimensional approximation based on expansions in orthonormal basis functions is developed. An expression for the joint probability density of all the Fourier coefficients is derived, the evaluation of which is shown to be particularly straightforward. Diffusion of material from a single source in an unbounded mildly turbulent fluid is considered as an application.

Additional Information

© 1981 American Institute of Physics. Received 17 February 1981; accepted 20 July 1981.

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October 18, 2023