Symmetry breaking Paradigm In Typical Laminar-Turbulence Transition System

TL;DR

This paper investigates the symmetry-breaking process during laminar-turbulence transition in a liquid system with a rotating vessel, using equilibrium statistical mechanics and comparing theoretical predictions with experimental data.

Contribution

It introduces a symmetry-breaking framework based on Landau's phase transition theory to model the laminar-turbulence transition in a polygon vortex system.

Findings

High agreement between theory and experiment

Identification of limits of equilibrium mechanics in complex transitions

Proposal of a linear approximation for the transition process

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.