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arXiv · 2108.09486

Symmetry breaking Paradigm In Typical Laminar-Turbulence Transition System

Chun Huang·Yuchen Jiang
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Abstract

A stationary cylindrical vessel containing a rotating plate near the bottle surface is partially filled with liquid. With the bottom rotating, the shape of the liquid surface would become polygon-like. This polygon vortex phenomenon is an ideal system to demonstrate the Laminar-Turbulent transition process. Within the framework of equilibrium statistical mechanics, a profound comparison with Landau's phase transition theory was applied in the symmetry-breaking aspect to derive the evolution equation of this system phenomenologically. A comparison between theoretical prediction and experimental data is carried out. We concluded a considerably highly matched result, while some exceptions are viewed as the natural result that the experiment breaks through the up-limit of using equilibrium mechanics as an effective theory, namely breaking through the Arnold Tongue. Some extremely complex Non-equilibrium approaches were desired to solve this problem thoroughly in the future. So our method could be viewed as a linear approximation of this theoretical framework.

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Chun Huang, Yuchen Jiang. 2022-09-30. Symmetry breaking Paradigm In Typical Laminar-Turbulence Transition System. https://arxiv.org/abs/2108.09486

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