Classical Physics


Turbulence, a Controlled Route of Energy from Order Into Chaos

Authors: Udo E. Steinemann

One of the earliest attemps to understand turbulence dated back to a theory of L.F. RICHARDSON, later enhanced by A.N. KOLMOGOROV. By this theory turbulence is considered as energy-transfer taking place in cascade-form between eddies of various orders of magnitude. The transfer gets stated by disturbance acting on fibre-eddies and is evaluated by stretching of the fibres. This can explain many topics, but it is impossible this way to determine the cascade-structure and its development more detailed. In order to step forward, one will have to provide e.g. numbers of eddies for every cascade-generation, eddies sizes and their appropriate life-times and a characterization of the disturbance as well. For this reason the eddy- model will be replaced by a spinning sphere with surface-tension and a specified disturbance acting on it. Due to this, decay of an eddy can be explained as a partitioning of a sphere into equal parts in a self-organizing balance between disturbance and a reaction forced by surface-tension. Eeddies life-times as well as increases in phase-speed can then be determined. The disturbance-signal is specified as a sum of resonance-terms, each prepared for acting on a sphere of a proper size. On account of these model-extensions, turbulence comes out as a controlled route of energy from order into chaos, similar to many other dynamical Systems too.

Comments: 10 Pages.

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Submission history

[v1] 2018-01-03 13:17:01

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