弱Soret效应混合流体对流系统的分岔与非线性演化  

Bifurcation and nonlinear evolution of convection in binary fluid mixtures with weak Soret effect

作　　者：郑来运[1] 赵秉新 杨建青 Zheng Lai-Yun;Zhao Bing-Xin;Yang Jian-Qing(School of Mechanical Engineering,Ningxia University,Yinchuan 750021,China;School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China;Ningxia Key Laboratory of Scientific/Engineering Computing and Data analysis,Yinchuan 750021,China)

机构地区：[1]宁夏大学机械工程学院,银川750021 [2]宁夏大学数学统计学院,银川750021 [3]宁夏科学工程计算与数据分析重点实验室,银川750021

出　　处：《物理学报》2020年第7期132-143,共12页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11662016);宁夏自然科学基金(批准号:NZ16005);宁夏高等学校科学研究(批准号:NGY2016061)资助的课题.

摘　　要：混合流体Rayleigh-Bénard(RB)对流是研究非平衡耗散系统的自组织斑图及非线性动力学特性的典型模型.本文利用高精度数值方法模拟了底部均匀加热的矩形腔体中混合流体RB对流,研究了具有极微弱Soret效应(分离比ψ=-0.02)的混合流体对流的分岔特性及斑图的形成和演化,给出了分岔曲线图.获得了行波交替闪动的Blinking状态、局部行波对流和定常对流(SOC)三种稳定状态,讨论了状态之间的过渡.研究发现从Blinking状态到局部行波对流状态的过渡存在迟滞现象,过渡时行波频率、对流振幅和对流传热Nusselt数等均有明显的跳跃.在Blinking状态存在的Rayleigh数区间下界附近,外部施加的不对称初始扰动是形成该状态的诱因.随着Rayleigh数增大,临界SOC状态经过多次分岔并形成多个具有不同波数的SOC状态后过渡为混沌状态.Rayleigh-Benard(RB)convection in binary fluid mixtures,which shows rich and interesting pattern formation behavior,is a paradigm for understanding instabilities,bifurcations,self-organization with complex spatiotemporal behavior and turbulence,with many applications in atmospheric and environmental physics,astrophysics,and process technology.In this paper,by using a high-order compact finite difference method to solve the full hydrodynamic field equations,we study numerically the RB convection in binary fluid mixtures such as ethanol-water with a very weak Soret effect(separation ratioφ=-0.02)in a rectangular container heated uniformly from below.The direct numerical simulations are conducted in the rectangular container with aspect ratio ofΓ=12 and with four no-slip and impermeable boundaries,isothermal horizontal and perfectly insulated vertical boundaries.The bifurcation and the origin and evolution of pattern in RB convection for the considered physical parameters are studied,and the bifurcation diagram is presented.By performing twodimensional simulations,we observe three stable states of Blinking state,localized traveling wave and stationary overturning convection(SOC)state,and discuss the transitions between them.The results show that there is a hysteresis in the transition from the Blinking state to the localized traveling wave state for the considered separation ratio,and the evolution of the oscillation frequency,convection amplitude and Nusselt number are discontinuous.Near the lower bound of the Rayleigh number range where the Blinking state exists,a asymmetric initial disturbance is the inducement for the formation of the Blinking state.Inside the range,its inducing effect is weakened,and the oscillatory instability becomes the main reason.It is further confirmed that reflections of lateral walls are responsible for the survival of the stable Blinking state.With the increase of the Rayleigh number,the critical SOC state undergoes multiple bifurcations and forms multiple SOC states with different wa

关 键 词：对流 分岔 混合流体 行波 

分 类 号：O415.5[理学—理论物理]