High-order structure functions for planet surfaces: a turbulence metaphor

A theoretical framework for interpreting high-order structure functions of scale-invariant planet surfaces in a fashion similar to that for the high-Reynolds number turbulence is proposed. Following this approach, a relationship showing that the structure function scaling depends on the governing physical processes and the generalized fractal dimensions is derived. This relationship may be superimposed with the effects of discrete morphological structures (e.g., impact craters). Such a superposition may in principle significantly modify scaling exponents as sometimes can be seen in turbulence due to the effects of coherent structures. The proposed framework may help in identifying appropriate physical factors controlling surface formation at difference ranges of spatial scales as well as in testing various scaling models of the planet topography.