Extended Self-Similarity in Geophysical and Geological Applications

In this paper we demonstrate application of the Extended Self-Similarity (ESS) concept, recently developed in turbulence physics, for geological and geophysical phenomena. The theoretical background is discussed first and then the ESS properties in fluvial turbulence, sand wave dynamics, Martian topography, river morphometry, gravel-bed mobility, and atmospheric barometric pressure are explored. The main attention is paid to fluvial turbulence and sand waves, while other examples are presented to support the generality of the ESS concept in earth sciences. The results show that the ESS properties of the considered phenomena are remarkably similar to those reported for turbulence, in spite of different underlying mechanisms. This suggests that a general rule should exist which governs a wide class of complex natural phenomena.