具有水平流动的对流斑图成长和动力学特性  

Growth and Dynamics of Convection Patterns With Horizontal Flow

作　　者：宁利中[1] 宁碧波[2] 胡彪 田伟利[4] NING Lizhong;NING Bibo;HU Biao;TIAN Weili(State Key Laboratory of Eco-Hydraulics in Northwest Arid Region of China,Xi’an University of Technology,Xi’an 710048,P.R.China;College of Civil Engineering and Architecture,Jiaxing University,Jiaxing,Zhejiang 314001,P.R.China;Jiangxi Provincial Water Conservancy Planning,Design&Research Institute,Nanchang 330029,P.R.China;Department of Architecture,Shanghai University,Shanghai 200444,P.R.China)

机构地区：[1]西安理工大学省部共建西北旱区生态水利国家重点实验室,西安710048 [2]嘉兴学院建筑工程学院,浙江嘉兴314001 [3]江西省水利规划设计研究院,南昌330029 [4]上海大学建筑系,上海200444

出　　处：《应用数学和力学》2020年第10期1146-1156,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(10872164)。

摘　　要：采用二维流体力学基本方程组对Prandtl数Pr=0.72具有水平流动的对流斑图成长和动力学特性进行了数值模拟.结果说明,对于给定的相对Rayleigh数Rar=5(Rayleigh数Ra=8540)和Reynolds数Re=22.5,行波对流斑图的成长分为三个阶段,即对流发展阶段、指数成长阶段、周期变化阶段(过渡调整区、稳定周期变化区).行波对流的平均波数随着时间的发展或者对流斑图的成长而减小.随着相对Rayleigh数的增加,行波对流的指数成长阶段的时间变短,对流最大垂直流速的成长率变大.对于水平流动Re=5时,对流最大垂直流速的成长率γm与Rar的关系为γm=0.0048Ra6.0653 r.在周期变化阶段,经过行波对流斑图和对流参数的过渡调整区后,对流进入斑图和对流参数的稳定周期变化区.对于给定的Rar=5时,行波对流的无量纲周期Tt随着Re变化的关系式为Tt=0.0014Re2.3635.The growth and dynamic characteristics of convection patterns with horizontal flow for Prandtl number Pr=0.72 were numerically simulated with 2D basic equations of fluid me⁃chanics.The results show that,for given relative Rayleigh number Rar=5(Rayleigh number Ra=8540)and Reynolds number Re=22.5,the growth of the traveling wave convection pat⁃tern can be divided into 3 stages:the convection development stage,the exponential growth stage and the periodic variation stage(including the transition adaptation region and the stable periodic variation region).The average wave number in the traveling wave convection decreases with time or with the growth of the convection pattern.The exponential growth stage length in traveling wave convection becomes shorter and the growth rate of the maximum vertical veloci⁃ty of convection increases with relative Rayleigh number Rar.For Reynolds number Re=5,the growth rate of the maximum vertical velocity of convection relates with the variation of relative Rayleigh number Rar in the form ofγm=0.0048Ra6.0653 r.In the periodic variation stage,after the transition adaptation region of the convection pattern and parameters in traveling wave convec⁃tion,the convection enters the stable periodic variation region of the convection pattern and pa⁃rameters.For given relative Rayleigh number Rar=5,dimensionless period Tt of traveling wave convection varying with Re can be expressed as Tt=0.0014Re2.3635.

关 键 词：水平流动 平均波数 指数成长阶段 周期变化阶段 成长率 

分 类 号：O357[理学—流体力学]