Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/de-gruyter/turbulence-of-real-functions-79JbtcHY30
References
References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.
- Publisher
- de Gruyter
- Copyright
- © Heldermann Verlag
- ISSN
- 1072-947X
- eISSN
- 1072-9176
- DOI
- 10.1515/GMJ.2008.225
- Publisher site
- See Article on Publisher Site
Abstract
The concept of 𝐴-level sets of real functions 𝑢(𝑥, 𝑦) (i.e., the solutions of 𝑢(𝑥, 𝑦) = 𝐴 = const ) in a given domain admits numerous interpretations in applied sciences: level sets are potential lines, streamlines in hydrodynamics, meteorology and electromagnetics, isobars in gas-dynamics, isotherms in thermodynamics, etc. In fact, the level sets of 𝑢 considered for all values 𝐴 make the “map” of this function and their interpretations in different sciences make the “maps” of the corresponding processes. In this paper we study the geometry of these maps for broad classes of functions and arbitrary values 𝐴. In particular, we study how much twisted or, speaking in general, how turbulent these maps are. The concepts and results admit some immediate interpretations and can be stated in terms of flow rotation and turbulence. The study gives a new, in fact a geometric description of these applied phenomena.
Journal
Georgian Mathematical Journal – de Gruyter
Published: Jun 1, 2008
Keywords: Real functions of several variables; turbulence; Gamma-lines