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
