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 inter- pretations 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 dierent 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.
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