Abstract
A hyperbolic equation, analogous to the telegrapher's equation in onedimension, is introduced to describe turbulent diffusion of a passiveadditive in a turbulent flow. The predictions of this equation, and those ofthe usual advection-diffusion equation, are compared with data on smokeplumes in the atmosphere and on heat flow in a wind tunnel. Thepredictions of the hyperbolic equation fit the data at all distances fromthe source, whereas those of the advection-diffusion equation fit only atlarge distances. The hyperbolic equation is derived from anintegrodifferential equation for the mean concentration which allows it tovary rapidly. If the mean concentration varies sufficiently slowlycompared with the correlation time of the turbulence, the hyperbolicequation reduces to the advection-diffusion equation. However, if themean concentration varies very rapidly, the hyperbolic equation should bereplaced by the integrodifferential equation.
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