二维固定通量瑞利-贝纳德对流中的全域填充卷
Domain-filling rolls in two-dimensional fixed-flux Rayleigh-Bénard convection
AI总结：
本文研究二维固定通量、无滑移边界的瑞利-贝纳德对流，发现存在全域填充卷的(R,Pr)区域，其边界处卷会分裂，有助于厘清维度与边界条件的竞争效应并验证尺度选择解释。
AI中文摘要：
大水平范围的瑞利-贝纳德对流有时会自组织形成全域填充结构。在二维情况下，当速度边界条件为无应力时，全域填充卷会从部分而非全部初始条件中持续存在；当速度边界条件为无滑移时，采用固定温度热边界条件未发现全域填充卷，而采用固定通量热边界条件的情况尚未被研究。本文探讨这一缺失的情况，由于无滑移边界不利于形成全域填充卷，而固定通量边界在三维中无论速度边界条件如何都会形成全域填充结构，因此该情况难以预测。我们在水平周期为高度20倍的二维区域中，模拟固定通量、无滑移边界下的对流，研究固定通量瑞利数R和普朗特数Pr的各种组合。全域填充卷在小R时为弱非线性，易于发现，通过随时间缓慢改变参数，可将其延续至其他(R,Pr)组合。我们发现全域填充卷的(R,Pr)区域范围较大，但存在边界；当R过大或Pr过小时，一对全域填充卷会分裂为两对。这些发现与其他维度和边界条件组合形成对比，后者的尺度选择未被发现强烈依赖参数值。本研究有助于厘清维度与边界条件的竞争效应，为已提出的尺度选择解释提供更严格的测试。
英文摘要：
Rayleigh-Bénard convection of large horizontal extent sometimes self-organizes into domain-filling structures. In two dimensions, domain-filling rolls persist - from some but not all initial conditions - when velocity boundary conditions are stress-free. When velocity boundary conditions are no-slip, domain-filling rolls are not found with fixed-temperature thermal boundary conditions, but they have not been sought with fixed-flux thermal boundary conditions. Here we explore the latter missing case, which is hard to predict because no-slip boundaries do not encourage domain-filling rolls, but fixed-flux boundaries give domain-filling structures in three dimensions for either boundary condition on velocity. We simulate convection with fixed-flux, no-slip boundaries in two-dimensional domains with horizontal period 20 times their height and at various combinations of the fixed-flux Rayleigh number R and Prandtl number Pr. Domain-filling rolls, which are easily found when they are weakly nonlinear at small R, are continued to other (R,Pr) by changing these parameters slowly in time. The (R,Pr) regime where we find domain-filling rolls is substantial but has a boundary. When R is too large or Pr too small, relative to each other, a domain-filling roll pair breaks up into two pairs. These findings contrast with other combinations of dimension and boundary conditions, where scale selection has not been seen to depend strongly on parameter values. The present case helps disentangle competing effects of dimension and boundary conditions, and it offers a more stringent test for explanations of scale selection that have been proposed.
