Symmetry breaking Paradigm In Typical Laminar-Turbulence Transition System

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 a 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 symmetry breaking aspect to derive the evolution equation of this system phenomenologically. Comparison between theroietical prediction and experimental data is carried out. We conclued a considerably highly matched result, while some exceptions are viewed as the nautral result that the experiment break through the up-limit of using equilibrium mechanics as a effective theory, namely breaking through the Arnold Tongue. Some extremely complex Non-equilibrium approaches was desired to solve this problem thoroughly in the furture. So our method could be viewed as a linear approximation of this theoretical framework.