Staircase solutions and stability in vertically confined salt-finger convection
Staircase solutions and stability in vertically confined salt-finger convection
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DOI：
10.1017/jfm.2022.865
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发表时间：
2022-07
影响因子：
3.7
通讯作者：
Chan Liu;K. Julien;E. Knobloch
中科院分区：
文献类型：
--
作者：
Chan Liu;K. Julien;E. Knobloch
摘要本文利用水平方向上严重截断的傅立叶展开式得到的单模方程组对盐指对流进行了分岔分析。强非线性阶梯状的解决方案，分别有一个（S1），两个（S2）和三个（S3）区域的混合盐度在垂直方向上计算使用数值延拓，并确定其稳定性。近发病，一层S1解决方案是稳定的，并对应于最大的盐度传输之间的三个解决方案。S2和S3的解决方案是不稳定的，但施加的直接数值模拟（DNS）中观察到的统计在较大的二维（2-D）域的影响。二次分叉S1导致倾斜指（TF 1）或行波（TW 1）的解决方案，都伴随着自发产生的大规模剪切，有利于较低的密度比和普朗特数（$Pr$）的过程。低$Pr$的这些状态分别与平均两层和三层阶梯状盐度剖面相关。还计算了中平面反射对称性破缺的态。在两个维度和低$Pr$，DNS结果有利于方向反转倾斜的手指类似于在其他系统中观察到的脉动波状态。两层和三层的平均盐度剖面对应于反向倾斜的手指和TW 1观察在2-D DNS随时间平均。接近高波数起始的单模解与2-D DNS在小的水平域中非常一致，并且与3-D DNS比较好。
Abstract Bifurcation analysis of confined salt-finger convection using single-mode equations obtained from a severely truncated Fourier expansion in the horizontal is performed. Strongly nonlinear staircase-like solutions having, respectively, one (S1), two (S2) and three (S3) regions of mixed salinity in the vertical direction are computed using numerical continuation, and their stability properties are determined. Near onset, the one-layer S1 solution is stable and corresponds to maximum salinity transport among the three solutions. The S2 and S3 solutions are unstable but exert an influence on the statistics observed in direct numerical simulations (DNS) in larger two-dimensional (2-D) domains. Secondary bifurcations of S1 lead either to tilted-finger (TF1) or to travelling wave (TW1) solutions, both accompanied by the spontaneous generation of large-scale shear, a process favoured for lower density ratios and Prandtl numbers ($Pr$). These states at low $Pr$ are associated, respectively, with two-layer and three-layer staircase-like salinity profiles in the mean. States breaking reflection symmetry in the midplane are also computed. In two dimensions and for low $Pr$, the DNS results favour direction-reversing tilted fingers resembling the pulsating wave state observed in other systems. Two-layer and three-layer mean salinity profiles corresponding to reversing tilted fingers and TW1 are observed in 2-D DNS averaged over time. The single-mode solutions close to the high wavenumber onset are in an excellent agreement with 2-D DNS in small horizontal domains and compare well with 3-D DNS.