Café Latte：侧向冷却双扩散对流中的自发层结形成
Café Latte: Spontaneous layer formation in laterally cooled double diffusive convection
AI总结：
本研究针对拿铁咖啡制作中的层结现象，通过二维直接数值模拟探究侧向冷却双扩散对流系统，揭示了稳定力强度影响下的层结形成与合并机制。
摘要：
在制作拿铁咖啡（Café Latte）的过程中，注入玻璃杯牛奶中的浓缩咖啡液与牛奶之间会形成引人注目的层状结构。Xue等人（2017年发表于《自然·通讯》第8卷，第1-6页）的研究表明，浓缩咖啡的注入速度决定了咖啡-牛奶混合液的深度。一段时间后，当混合液中形成稳定分层时，该层结过程可被建模为一个侧向冷却的双扩散对流系统，系统内为稳定分层的咖啡-牛奶混合液。更具体地说，我们针对广泛的参数范围开展了（二维）侧向冷却双扩散对流的直接数值模拟，其中对流流动由侧向温度梯度驱动，同时受到垂直浓度梯度的稳定作用。当热驱动力占优于稳定力时，流动表现为垂直对流，会形成大尺度环流。然而，随着稳定力强度的增加，会出现亚稳态的层结流态。初始阶段会形成若干垂直堆叠的对流涡旋，这些充分混合的层由具有大浓度梯度的陡峭界面分隔。这些新生层的初始厚度可通过平衡热驱动所做的功与将流体从稳定分层流体的平衡位置移出所需的势能来估算。在层结流态下，我们进一步观察到连续的层合并现象，最终仅剩下单个对流涡旋。我们阐明了如下合并机制：由于环流减弱导致热流体在热侧壁附近积聚，与更热流体相关的更大浮力最终会破坏层界面。随后两层合并为一个更大的层，环流在合并后的结构内重新建立。
英文摘要：
In the preparation of Café Latte, spectacular layer formation can occur between the expresso shot in a glass of milk and the milk itself. Xue et al. (Nat. Commun., vol. 8, 2017, pp. 1-6) showed that the injection velocity of expresso determines the depth of coffee-milk mixture. After a while when a stable stratification forms in the mixture, the layering process can be modelled as a double diffusive convection system with a stably-stratified coffee-milk mixture cooled from the side. More specifically, we perform (two-dimensional) direct numerical simulations of laterally cooled double diffusive convection for a wide parameter range, where the convective flow is driven by a lateral temperature gradient while stabilized by a vertical concentration gradient. When the thermal driving force dominates over the stabilizing force, the flow behaves like vertical convection in which a large-scale circulation develops. However, with increasing strength of the stabilizing force, a meta-stable layered regime emerges. Initially, several vertically-stacked convection rolls develop, and these well-mixed layers are separated by sharp interfaces with large concentration gradients. The initial thickness of these emerging layers can be estimated by balancing the work exerted by thermal driving and the required potential energy to bring fluid out of its equilibrium position in the stably stratified fluid. In the layered regime, we further observe successive layer merging, and eventually only a single convection roll remains. We elucidate the following merging mechanism: As weakened circulation leads to accumulation of hot fluid adjacent to the hot sidewall, larger buoyancy forces associated with hotter fluid eventually break the layer interface. Then two layers merge into a larger layer, and circulation establishes again within the merged structure.
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