Classical Physics


Turbulence as Structured Route of Energy from Order Into Chaos

Authors: Udo E. Steinemann

A contemptuous attempt to understand the phenomenon of turbulence dated back to a theory of L. F. RICHARDSON which later became enhanced by A. N. KOLMOGOROV. By the contents of this theory turbulence is considered as a transfer of energy taking place in forms of cascades between eddies of various orders of magnitude. The transfer becomes started by unspecified disturbance acting on eddies in forms of fibres and is further evaluated on account of their stretching. This principally can explain for eddies of various sizes being created in generations while energy is distributed along these generations from the largest eddies down to the smallest. But it is impossible to determine a specific structure of the cascade and its development in details. In order to step forward this way, this paper will show, when spinning spheres with surface-tension are models for the eddies and a specifically designed disturbance act on them, eddies of large size will decay in a cascade of hierarchically structured generations into smaller ones. The dynamics of this development is due to the balance between the acting force of the disturbance and the reaction due to sphere-tension on each eddy in a self-organisation mode. All eddies within one step of the hierarchy will obtain same size, life-time and rotation-phase, for follower-generations these quantities will be different in a definite way. Each predecessor-generation will double its number of eddies relative to its follower-generation, while each eddy partitions its rotation-energy for its followers and those will get increased their surface-energy by disturbance. Finally the whole cascade will form a structured route of energy from order into chaos similar to many other dynamical systems. By ⟨, "Final-State-Diagram of quadratic Iterator topologically equivalent with an Eddy's Decay-Cascade in turbulent Fluids" publisher Udo E. Steinemann ( category: Physics, Classical Physics, 1809[23])⟩ an addendum has been provided for this text. It was intended to put out the decay-cascade of an eddy as a further example for routes from order into chaos observed together with dynamical systems.

Comments: 12 Pages.

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Submission history

[v1] 2018-01-03 13:17:01
[v2] 2018-02-26 20:02:58
[v3] 2018-09-13 19:24:12

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