Symmetry breaking Paradigm In Typical Laminar-Turbulence Transition System
| Autor: | Huang, Chun, Jiang, Yuchen |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 7 pages, 2 figures. This is the first work of our academic career, and we dedicate it to our parents and all our loved ones |
| Databáze: | arXiv |
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