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Solenoidal advection in d dimensions may induce inertial-range behavior 〈 (x, t) -T (x+r, t) ^n〉r^ (T) of a passive scalar field T (x, t). If the velocity field changes very rapidly in time, the ₍ (T) are determined by the two-particle eddy-diffusion coefficient (r) r^ (). An approximation to the molecular-diffusion terms yields ₍ (T) =1/2 2nd2- () +^2 -1/2 where =d+ () -2. As n, ₍ (T).
Robert H. Kraichnan (Mon,) studied this question.