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FORMAION OF PATTERN,TRANSITION,CHAOS AND TURBULENCE IN RAYLEIGH-BENARD CONVECTION

瑞利-伯纳德对流中的模式、转变、混沌和湍流的形成

基本信息

批准号：
06640535
负责人：
MIZUSHIMA Jiro
金额：
$ 1.41万
依托单位：
DOSHISHA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06640535/
关键词：
Rayleigh-Benard Convection Thermal Convection Stability of Flow Bifurcation Transition to Turbulence Appearance of Pattern Chaos

项目摘要

The mechanism of the pattern formation, transition, chaos and properties of turbulence in Rayleigh-Benard convection was investigated by numerical calculation of the nonlinear equilibrium solution and by the stability analysis. The present project consists of the following four researches.1. The mechanism of the pattern formation in the thermal convection between two hoizontal planes with infinite extent is investigated. An amplitude equation is derived by the weakly nonlinear stability theory and its coefficients are evaluated numerically. The conditions for the onset of hexagonal or roll-like patterns are determined.2. The onset and stability of the convection in a vessel of finite volume is investigated. It is shown that the number of vortices varies depending on the lateral extent of the vessel.3. The stability and the transition of the thermal convection is investigated by numerical simulation. It is found that a large scale circular motion appears as a result of the thermal instability first, but thermal convection with two circular vorties take the place of the large scale circular motion when the temperature of the bottom is raised.4. When the vessel is placed at an angle from the horizontal plan, the thermal convection always appears even if the difference of the temperatures at the top and bottom is very small. The occurrence of the convection is found due to the imperfect pitchfork bifurcation. The equilibrium solution for the thermal convection was obtained numerically and its stability was clarified.

通过对非线性平衡解的数值计算和稳定性分析，研究了Rayleigh-Benard对流中斑图的形成、转捩、混沌和湍流特性的机理。本课题主要包括以下四个方面的研究.本文研究了两无限大平面间热对流斑图的形成机理。利用弱非线性稳定性理论导出了振幅方程，并对方程系数进行了数值计算。确定了六角或卷状斑图出现的条件.本文研究了有限体积容器中对流的开始和稳定性。结果表明，涡的数量随船舶的横向范围而变化。通过数值模拟研究了热对流的稳定性和转捩。研究发现，热不稳定性首先导致大尺度的圆周运动，但当底部温度升高时，大尺度的圆周运动被双圆涡热对流所取代.当容器与水平面成一定角度放置时，即使容器顶部和底部的温差很小，也会出现热对流。对流的发生是由于不完美的干草叉分叉。通过数值计算得到了热对流的平衡解，并阐明了其稳定性。