Busse F H, Petry M
Physikalisches Institut, Universität Bayreuth, Bayreuth, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046316. doi: 10.1103/PhysRevE.80.046316. Epub 2009 Oct 23.
The onset of convection in two superimposed fluid layers of the same height is considered. It is found that the neutral curve for R(a) for the onset Rayleigh number R in dependence on the wave number a is an invariant of a multidimensional parameter space of property ratios of the system even though the corresponding convection solutions may vary strongly with these property ratios. For each neutral curve R(a) two manifolds of solutions are found one of which can be understood on the basis of symmetry properties of the system, while the other does not exhibit simple symmetry features. In particular the neutral curves R(a) for various single Rayleigh-Bénard convection layers are shown to correspond to two two-dimensional manifolds of solutions. Analytical expressions for the latter are derived in the case of outer stress-free boundary conditions.
考虑了两个高度相同的叠加流体层中对流的起始情况。研究发现，起始瑞利数(R)关于波数(a)的(R(a))中性曲线是系统物性比多维参数空间的一个不变量，尽管相应的对流解可能随这些物性比有很大变化。对于每条中性曲线(R(a))，发现了两个解流形，其中一个可以基于系统的对称性来理解，而另一个不具有简单的对称特征。特别地，各种单个瑞利 - 贝纳德对流层的中性曲线(R(a))对应于两个二维解流形。在外部无应力边界条件的情况下，推导出了后者的解析表达式。
