A recent experiment indicates that clouds in the atmosphere have fractal surfaces which are characterized by a fractal dimension $D\sim 2.35$. Here we present a theory of the fractal dimension of clouds. We show that the fractal dimension of clouds is calculable from the theory of relative turbulent diffusion. We claim that previous approaches to the theory of relative diffusion are in contradiction with this experiment and that a newly developed theory gives $D\sim 2.35$ as a natural consequence. The new theory of relative diffusion is simultaneously in agreement with the intermittency-modified "$\frac{4}{3}$ (power) law" [i.e., the $\frac{(4+2\mathrm{}\mu )}{3}$ (power) law, where $\mu$ is the intermittency exponent].

• Received 5 May 1983

DOI:https://doi.org/10.1103/PhysRevA.29.1461