驱动模式对具有库源平衡的黏性流体中空间反射时间反演联合对称性的影响

摘要

In the past few years, the balanced sink and source macroscopic open system, which satisfies the parity and time-reversal symmetry, has become a research hot point. We introduce parity and time-reversal (PT) symmetry into fluid system by setting up balanced inflow and outflow in a two-dimensional channel. The flow is governed by Navier-Stokes equation and we use lattice Boltzmann method to solve them. Defining configuration-dependent asymmetric functions in velocity, kinetic energy density, and vorticity fields, we find that the PT function of the flow increases with the increase of the 2th power of Reynolds number i.e.,ρn∼Ren. In this work, we use three different velocity profiles to drive the flow. It is demonstrated that in the three driven modes, the power-law schedule holds true. It is concluded that PT asymmetry of the viscous flow is determined by the flow dynamics not by the driven modes, thereby verifies the universality of the power-law scaling in viscous flow with balanced inflow and outflow.%满足空间反射时间反演parity and time-reversal (PT)联合对称性的库源平衡宏观开放系统近几年成为一个研究热点。本文将PT对称性引入到动力学系统，用格子玻尔兹曼方法求解Navier-Stokes方程，发现在二维黏性流体中，如果进口和出口的条件完全等同，在低雷诺数流动中，流场的PT对称函数(ρ)随雷诺数(Re)的增高以ρn ∼Ren 指数增长。用三种不同的速度剖面来驱动流体，计算流场达到稳定状态时的PT对称性。结果发现，进出口平衡的黏性管流中，ρn ∼Ren 的规律在三种驱动模式中出现，表明流场的PT 对称性是由流体本身决定的，与驱动模式没有关系，从此论证所得到的指数率的谱适性。