具有水平流动的对流斑图成长和动力学特性

宁利中; 宁碧波; 胡彪; 田伟利

doi:10.21656/1000-0887.410104

具有水平流动的对流斑图成长和动力学特性

doi: 10.21656/1000-0887.410104

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

基金项目: 国家自然科学基金(10872164)

详细信息

作者简介:
宁利中（1961—），男，教授，博士（通讯作者. E-mail: ninglz@xaut.edu.cn）.

中图分类号: O357
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出版历程
- 收稿日期: 2020-04-10
- 修回日期: 2020-05-25
- 刊出日期: 2020-10-01

Growth and Dynamics of Convection Patterns With Horizontal Flow

¹State Key Laboratory of EcoHydraulics in Northwest Arid Region of China,Xi’an University of Technology, Xi’an 710048, P.R.China;²College of Civil Engineering and Architecture, Jiaxing University, Jiaxing, Zhejiang 314001, P.R.China;³Jiangxi Provincial Water Conservancy Planning, Design & Research Institute,Nanchang 330029, P.R.China;⁴Department of Architecture, Shanghai University, Shanghai 200444, P.R.China

Funds: The National Natural Science Foundation of China(10872164)

摘要

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Ra_r=5(Rayleigh数Ra=8 540)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γ_m与Ra_r的关系为γ_m=0.004 8Ra^{6.065 3_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Ra_r=5时，行波对流的无量纲周期T_{t_{随着Re变化的关系式为T_t=0.001 4Re^{2.363 5}.}}}
- 水平流动 /
- 平均波数 /
- 指数成长阶段 /
- 周期变化阶段 /
- 成长率
Abstract: 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 mechanics. The results show that, for given relative Rayleigh number Ra_r=5(Rayleigh number Ra=8 540) and Reynolds number Re=22.5, the growth of the traveling wave convection pattern 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 velocity of convection increases with relative Rayleigh number Ra_r.For Reynolds number Re=5,the growth rate of the maximum vertical velocity of convection relates with the variation of relative Rayleigh number Ra_r in the form of γ_m=0.004 8Ra^{6.065 3}_r.In the periodic variation stage, after the transition adaptation region of the convection pattern and parameters in traveling wave convection, the convection enters the stable periodic variation region of the convection pattern and parameters. For given relative Rayleigh number Ra_r=5,dimensionless period T_t of traveling wave convection varying with Re can be expressed as T_t=0.001 4Re^{2.363 5}.
- horizontal flow /
- average wave number /
- exponential growth stage /
- periodic variation stage /
- growth rate

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