A hyperbolic equation for turbulent diffusion

A hyperbolic equation, analogous to the telegrapher's equation in one dimen sion, is introduced to describe turbulent diffusion of a passive additive i n a turbulent flow. The predictions of this equation, and those of the usua l advection-diffusion equation, are compared with data on smoke plumes in t he atmosphere and on heat flow in a wind tunnel. The predictions of the hyp erbolic equation fit the data at all distances from the source, whereas tho se of the advection-diffusion equation fit only at large distances. The hyp erbolic equation is derived from an integrodifferential equation for the me an concentration which allows it to vary rapidly. Lf the mean concentration varies sufficiently slowly compared with the correlation time of the turbu lence, the hyperbolic equation reduces to the advection-diffusion equation. However, if the mean concentration varies very rapidly, the hyperbolic equ ation should be replaced by the integrodifferential equation. AMS classific ation scheme number: 76.