×

The language of pattern and form. (English) Zbl 1169.76347

Balmforth, Neil J. (ed.) et al., Geomorphological fluid mechanics. Lecture notes from the Gran Combin summer school, Saint Oyen, Aosta, Italy, June 19–30, 2000. Berlin: Springer (ISBN 3-540-42968-9/hbk). Lect. Notes Phys. 582, 3-33 (2001).
From the text: Geology and geomorphology deal with some of the most striking patterns of Nature. From mountain ranges and mid-ocean ridges, to river networks and sand dunes, there is a whole family of forms, structures, and shapes that demand rationalization as well as mathematical description. In the various chapters of this volume, many of these patterns will be explored and discussed, and attempts will be made to both unravel the mathematical reasons for their very existence and to describe their dynamics in quantitative terms. In this introductory chapter, we discuss some of the methods that can be adopted in the study of patterns, and use the specific examples of convection – an evergreen classic in nonlinear fluid dynamics – and of the formation of aeolian ripples– another phenomenon that strikes the imagination of anybody who has been travelling in a sand desert.…
In this Introduction, we have rushed through a variety of mathematical methods that can be used to build models of geological and geomorphological patterns. Some of these methods are rigorous, such as the derivation of amplitude equations in proximity of a supercritical bifurcations, but have correspondingly a limited range of applicability. Other methods are heuristic, and are based on a mixture of phenomenological intuition and uncontrolled mathematical approximations.
Most of the methods mentioned in this chapter have a long history of successes and failures, and provide a starting point for the description of complex geological and geomorphological systems. In the chapters to come, we shall see many of these methods in action. Sometimes they will lead to great success, sometimes not. In any event, it is worth trying to use them, especially because there is not much else that can be done to obtain a theoretical understanding of the systems we are dealing with. Bon voyage.
For the entire collection see [Zbl 1030.00040].

MSC:

76E06 Convection in hydrodynamic stability
86A05 Hydrology, hydrography, oceanography
PDFBibTeX XMLCite
Full Text: DOI