Random Processes with Stationary Increments and Composite Spectra

A technique for deriving and interpreting fractal geophysical processes with power-law spectra of a different nature is described. Examples include the energy spectra of atmospheric processes and their role in the mixing of impurities, the frequency spectra of sea wind waves, and the spatial spectra of the surface relief of celestial bodies in the solar system. A.N. Kolmogorov's works in the early 1930s, which were subsequently developed by his followers A.M. Obukhov, A.S. Monin, A.M. Yaglom, and others, are the most important for this. Kolmogorov's probabilistic laws serve as a model for the analysis of the processes under consideration by methods of the similarity and dimensionality theory.