发表机构
Iowa State University; Virginia Tech（爱荷华州立大学; 弗吉尼亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过数值模拟，探究了瑞利-贝纳德对流中对流卷前沿的速度与波数随约化瑞利数ε的标度规律，对比了振幅方程、Swift-Hohenberg方程的预测及实验结果，明确了波数标度的独立性与临界波数的依赖性。
AI 中文摘要
我们研究了超临界条件下静止流体层中局部触发的瑞利-贝纳德对流内反向旋转对流卷的传播，探讨了分隔静止流体与正在形成的对流卷的前沿速度，以及前沿后方形成的对流卷的波数。我们在二维和三维域中，针对五个数量级的约化瑞利数ε，在广泛的边界条件和不同的前沿触发方式下，对正在形成的对流卷的前沿进行了数值研究。在所有情况下，当ε≲1时，前沿速度随ε的1/2次方增长，这与振幅方程的预测一致；当ε≲10时，振幅方程对前沿速度的描述仍然准确，除非普朗特数很大，此时流体层远离阈值，前沿速度会比预测值更快。对流卷的波数随ε线性增长，这与线性区中使扰动增长率最大化的波数一致；远离 onset 时，波数增长转变为ε的1/4次方的缩减标度，这与大ε极限下Swift-Hohenberg方程的预测一致。描述波数随ε变化的标度与域几何、边界条件及前沿触发方式无关，但临界态下前沿选定的波数通常不等于体不稳定性的临界波数，且显著依赖于这些细节；我们尽可能将结果与实验测量值进行了对比。
英文摘要
We investigate the propagation of counter-rotating convection rolls in Rayleigh-Bénard convection initiated locally in a quiescent fluid layer under supercritical conditions. The velocity of the front separating quiescent fluid from the forming convection rolls, and the wavenumber of the convection rolls remaining behind the front, are explored. We numerically investigate fronts of forming convection rolls over five orders of magnitude of the reduced Rayleigh number, $ε$, in 2D and 3D domains, for a broad range of boundary conditions, and for different front initiation approaches. In all cases, the front velocity increases as $ε^{1/2}$ with increasing $ε$ for $ε\lesssim 1$ in agreement with predictions using the amplitude equation. The amplitude equation description of the front velocity remains accurate for $ε\lesssim 10$ except when the Prandtl number is large which yields a velocity that is faster than predicted for a fluid layer far from threshold. The wavenumber of the convection rolls increases linearly with $ε$ in agreement with the wavenumber that maximizes the growth rate of perturbations in the linear regime. Farther from onset, the wavenumber growth transitions to a reduced scaling of $ε^{1/4}$ in agreement with predictions using the Swift-Hohenberg equation in the large $ε$ limit. The scalings describing the wavenumber variation with $ε$ are independent of the domain geometry, boundary conditions, and front initiation method. However, the front-selected wavenumber at criticality does not equal the critical wavenumber of the bulk instability, in general, and depends significantly upon these details. We compare our results with experimental measurements where possible.
CommentsAuthor-accepted manuscript; accepted for publication in the Journal of Fluid Mechanics and currently in production. 22 pages, 12 figures
Journal refJournal of Fluid Mechanics. 2026;1043:A44
