论文标题
不稳定分层的剪切流与相边界之间的非线性相互作用
Nonlinear interactions between an unstably stratified shear flow and a phase boundary
论文作者
论文摘要
分辨出良好的数值模拟用于研究中等值的雷利 - 贝纳德 - 伪式流动流，用于中等值（$ pe \ in \ weft [0，50，50 \右] $）和rayleigh（$ ra \ in \ in \ weft [2.15 \ times times times 10^3，10^3，10^6 \ right] $）编号。平均剪切和浮力的相对效果使用批量Richardson编号进行量化：$ ri_b = ra \ cdot pr/pe^2 \ in [8.6 \ times 10^{ - 1}，10^4] $，其中$ pr $是prandtl编号。对于$ ri_b = \ Mathcal {O}（1）$，我们发现Poiseuille流动抑制了对流运动，导致热传输仅是由于传导而引起的；并且，对于$ ri_b \ gg 1 $，流属性和热传输与纯对流案例密切相对应。我们还发现，对于某些$ ra $和$ pe $，因此$ ri_b \ in \ weft [15,95 \右] $，有一个模式竞争，用于具有首选长宽比的对流单元。此外，在$ pe \ neq 0 $时，我们在定性的固定界面上发现了与其他剪切的对流流相一致的行驶波，在Gilpin \ Emph {et al。}的实验中（\ emph {j。.emph { toppaladoddi和wettlaufer（\ emph {j。FluidMech。} {\ bf 868}，第648-665页，2019年）。
Well-resolved numerical simulations are used to study Rayleigh-Bénard-Poiseuille flow over an evolving phase boundary for moderate values of Péclet ($Pe \in \left[0, 50\right]$) and Rayleigh ($Ra \in \left[2.15 \times 10^3, 10^6\right]$) numbers. The relative effects of mean shear and buoyancy are quantified using a bulk Richardson number: $Ri_b = Ra \cdot Pr/Pe^2 \in [8.6 \times 10^{-1}, 10^4]$, where $Pr$ is the Prandtl number. For $Ri_b = \mathcal{O}(1)$, we find that the Poiseuille flow inhibits convective motions, resulting in the heat transport being only due to conduction; and, for $Ri_b \gg 1$ the flow properties and heat transport closely correspond to the purely convective case. We also find that for certain $Ra$ and $Pe$, such that $Ri_b \in \left[15,95\right]$, there is a pattern competition for convection cells with a preferred aspect ratio. Furthermore, we find travelling waves at the solid-liquid interface when $Pe \neq 0$, in qualitative agreement with other sheared convective flows in the experiments of Gilpin \emph{et al.} (\emph{J. Fluid Mech} {\bf 99}(3), pp. 619-640, 1980) and the linear stability analysis of Toppaladoddi and Wettlaufer (\emph{J. Fluid Mech.} {\bf 868}, pp. 648-665, 2019).
