Random advection of chemically reacting species

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Abstract
In the absence of molecular diffusion there exists a space-independent transformation which transforms the probability density of dynamically passive scalars undergoing chemical reaction and advection into the probability density of scalar fields undergoing advection alone. In two well-known limits the equation for the probability density of non-reacting scalars is linear and parabolic in physical space. In such cases it is shown that the equation for the probability density of reacting scalars is likewise linear and parabolic in physical space, although hyperbolic in concentration space. The general solution of such an equation is obtained and the particular case of a second-order, decaying, single-species reaction is displayed.